PTIM A

Mathematical Programming Society NeiV'ttewrL

JANUARY2000

miic/rhmopenef

'Set'less

Collections of

SET Cards

I

We invite OPTIMA readers t

to the problems to Robert Bo

lin.edu). The most attractive

presented in a forthcoming is

JANUARY 2000 PAGE 2

o submit solutions 'Set'less Collections of SET Cards

isch (bobb@cs.ober-

Robert A. Bosch

solutions will be August 29, 1999

sue.

TS is a card game played with a special 81-card

deck. Each SET card has four attributes (num-

SSETber, color, shading, and shape), and on each card,

each attribute assumes one of three possible values. More precisely, a SET

card displays a drawing of one, two, or three symbols. The symbols are all

red, green, or purple; filled-in, outlined, or striped; oval-shaped, squiggle-

shaped, or diamond-shaped. The SET deck contains 34=81 cards, one for

each possible combination of attribute values.

The basic object in SET is the 'Set,' a collection of three cards that

has, with respect to every attribute, either all or none of its cards in agree-

ment. At the beginning of the game, the deck is shuffled and twelve cards

are laid out on the table, face up. The first player to spot a 'Set' removes

S it, placing it in his or her pile. Then three more cards are placed on the

table, and play continues. Note that the cards displayed in Figure 1 form

a 'Set': all of them agree with respect to color, and none of them agree

with respect to number, shading, or shape.

r -

C I

Purple plwqpf purple

Figure 1. Three set cards that form a 'Set'

The rulebook states "If all players agree that there is no 'Set' in the

twelve cards showing, three more cards (making a total of fifteen) are laid

face up. These cards are not replaced when the next 'Set' is picked up,

reducing the number to twelve again." The implication is that every col-

lection of fifteen cards contains at least one 'Set.' This is not true. In fact,

it is easy to find collections of fifteen cards that are 'Set'less (i.e. contain

no 'Sets').

In December 1996, Rajmohan Rajagopolan-then an undergraduate

student at Oberlin College, and now a graduate student at Cornell

University-realized that integer programming could be used to find a

largest 'Set'less collection of SET cards. Rajagopolan treated each SET

card as a point in S where S is the set {0,1,2}. There are many ways that

this can be done; one possible 'encoding' is given in Figure 2. Note that

the cards corresponding to three distinct points x, y, z e S form a 'Set' if

and only if (x + y, + z) mod 3 0 for i 1,2,3,4.

1 SET is a registered trademark of Set Enterprises Inc.

(http://www.setganm.com/).

JANUARY 2000

c number one 0 c color red 0

two 1 green 1

three 2 purple 2

c3 shading filled-in 0 c4 shape oval 0

outlined 1 squiggle 1

striped 2 diamond 2

Figure 2. Mapping a card to a point c

PAGE3

In September 1997, one of my colleagues, Oliver Schirokauer, reported

to me that he and Carl Cotner had written a clever program that used

enumeration to prove that a 'Set'less collection of SET cards can contain

no more than 20 cards. After learning from Schirokauer that I could have

fixed six (carefully chosen) variables at their upper bounds of one, I gave

CPLEX another try. This time, CPLEX was successful, solving

Rajagopolan's integer program in approximately 1,500 seconds and almost

275,000 branch-and-bound nodes.

Rajagopolan's integer program for finding a largest 'Set'less collection is

quite simple:

max Z vx

xd

s.t. vx + vy + v < 2 Vx, z e S4: x, y, z are distinct, and

(x, +y, + z) mod 3-0 for= 1,2,3,4.

v e 0,1} Vxe S4.

There are 81 binary variables, one for each SET card (each x e S'). The

variable v. is assigned the value 1 if and only if the card corresponding to

x is placed in the 'Set'less collection. There are (8)/3 =1,080 constraints,

one for each 'Set.' They ensure that no more than two of the three cards

that form a 'Set' are placed in the collection.

In June 1997, I attempted to solve Rajagopolan's integer program using

branch and bound (version 4.0.9 of CPLEX's Mixed Integer Optimizer).

After fixing four variables at their upper bounds of one, I started the opti-

mization process. Within a few seconds, CPLEX had discovered a feasible

solution with objective value 20. At this point, the upper bound on the

optimal value of the objective function was 35.0, and the branch-and-

bound tree consisted of 1,382 nodes, of which 878 were unexplored.

Approximately 0.4 MB of memory were being used to store the branch-

and-bound tree.

An hour later, branch and bound was still going. The best solution it

had found so far was the one with objective value 20. The upper bound

on the optimal value of the objective function was now 25.5. The branch-

and-bound tree had over 350,000 nodes, and over 200,000 of these nodes

were unexplored. Slightly more that 100 MB of memory were tied up in

the storage of the branch-and-bound tree! At this point, I terminated the

search.

Problems

Interested readers may enjoy trying to solve the following problems:

1. Find valid inequalities for Rajagopolan's integer program. Note:

When one additional inequality was added, CPLEX was able to solve

the resulting integer program in approximately 800 seconds, with

just over 118,000 branch-and-bound nodes. When an extra 1,170

inequalities-all of the same type-were added, CPLEX took

approximately 650 seconds, with just under 3,500 nodes! Hint: SET

can be played with certain 9-card decks (the purple squiggles, for

instance).

2. In a well-known paper on cutting planes [1], Vasec Chvital present-

ed an integer programming formulation (and a cutting-plane proof

of the solution of) Moser's Cube Problem:

Let us consider the three-dimensional tick-tack-toe cube with 27

points (0,0,0), (0,0,1), ..., (2,2,2). Our objective is to select as

many of these 27 points as possible without choosing three

collinear ones.

The problem of finding a largest 'Set'less collection of purple SET cards

(a 27-card deck) is a variant of Moser's Cube Problem. Each 'Set' can

be thought of as a line. (Just as two points determine a line, two

SET cards determine a 'Set.') Construct a cutting-plane proof that a

'Set'less collection of SET cards can contain at most nine purple

cards.

3. Suppose that each SET card has five attributes instead of four.

Determine the largest number of cards in any 'Set'less collection of

cards.

0S MA63

(c, C2, C3', C4) e S4

JANUARY 2000

Maximizing Vitality Revisited

rule set

example pattern

S 2.

0-

3. 4.

TM V

7cr #

7. 8.

PVI IlH;B

"'ANN", A!", M

10, in"Al -

1&k 4mM-,:`x A ,

M. W : twm 1 17 !17

AMMWWS, AM V ", M W,

VANE- `, V 1& 4, -M

mffmm: :'MMMMM I' 'K :M

ti''WE, :Jim

M, "MEN' "E., " 7, 'MEN'

V70: ow:Mmomw 10:

"'KA

EME-K 1. ME-M

Figure 3. The rule set and an example pattern

In the March 1999 issue of OPTIMA, we discussed a simple one-

dimensional cellular automaton that consists of n cells (numbered from

19 0 to n-1 going from left to right) arranged in a horizontal line. Each cell i

has two neighbors: a left neighbor 1(i) and a right neighbor r(i). Cell O's

left neighbor is cell n-1, and cell n-l's right neighbor is cell 0.

Recall that at each point in time, each cell is either alive or dead. To

start up the cellular automaton, we just need to decide which cells will be

alive at time t =0 and which ones will be dead then. Then to run it, we

simply apply the rule set (displayed on the left side of Figure 3) over and

over again. The first application of the rule set determines the states of the

cells at time t =1. The second application determines the states of the cells

at time t 2. And so on. In the example pattern (displayed on the right

side of Figure 3), cell 0 is alive at time 1 because of rule 3, which states

that if cell i is alive at time t and cells 1(i) and r(i) are dead at time t, then

cell i must be alive at time t +1. Cell 1 is dead at time 1 due to rule 6,

and cell 2 is alive at time 1 due to rule 7.

At the end of the March 1999 article, we challenged readers to solve

three problems. The first was to complete our integer programming for-

mulation of the maximum average vitality problem, the problem of find-

ing an initial assignment of states to cells that maximizes the average vital-

ity of the cellular automaton over a given time interval [a,b]. (The vitality

of a cell over a time interval is the fraction of the time it is alive; the aver-

age vitality of the cellular automaton over a time interval is the average of

all its cells' vitalities over that time interval.) Our integer program had a

binary variable

1 if cell is alive at time t,

X,- 0 if not

for each 0 < i < n-1 and each 0 < t b. We presented two constraints:

-11,.: -r t "j.: + 1& 0

x ~+ x, ~+ 2,i

1 "0 1 1! 2

: .1:)

The former enforces rule 1 for cell i during the transition from time t

to time t +1; the latter enforces rules 6 and 8. Each constraint works by

prohibiting the configuration that violates the rule.

Leslie Gardner submitted constraints that enforce rules 2-5 and 7 for

cell i during the time-t-to-time-t+ transition:

10PTIMA63

PAGE

JANUARY 2000

.V i > .--r

... :so, t.:- o.1: EE I 0

.:,+:.. : + t, 1 2, 0 02

.ri! qi!

1+.Z +x1t t 2 2

Gardner also solved the second and third problems. The second prob-

lem was to prove that the maximum average vitality v(a,b) of the cellular

automaton over the time interval [a,b] satisfies

3 2

v(a, ) + 2-a

5 5(a-a+

Gardner began her proof by proving the validity of the following

inequality:

xII"a,: + x,,. + .. + X" I + 1 l -1.

PAGE 5

(To prove that it holds, take the inequality -x < -1 and add to it the two

inequalities that enforce rule 5 at cell i and cell r(i) during the time-t-to-

time-t+1 transition.) She then summed up all copies of this inequality for

i between 0 and n-1 and t between a and b, obtaining

n-1 1 -1 n-1

3 + 5 Y x + 2Zx,, 3(b- a)n.

-0 i=0 -a+l i=0

From this it follows that

n-1 b

5 Z Y x,, : 3 (b a)n + 5n

and

( 1 } x 3(b- a)n+ 5n 3 2

a (b- a+1)nr0, io 5(A-a++l)n 5 5(b-a+1)

The third problem asked for a solution strategy that would exploit the

fact that once values have been assigned to the variables for time 0, the

values of the remaining nb variable are completely determined. (Once we

know the values of the time-0 variables, we can run the cellular automa-

ton to obtain the values of the remaining variables.) Gardner suggested

... a genetic algorithm approach where the chromosomes are sequences

of the n binary variables for time 0." The fitness of a chromosome would

be the resulting average vitality. Simple crossover could be used as the

genetic operator.

References

[1] V. Chvital, Edmonds polytopes and a hierarchy ofcombinatorial prob-

lems, Discrete Mathematics 4 (1973), pp. 305-337.

I I I

0S MA63

JANUARY 2000

OPTINMA wants to congratulate our distinguished colleagues on their birthdays!

GEORGE B. DANTZIG RALPH E. GOMORY

celebrated his 85th birthday. A

special "Dantzig Fest" was

organized at the INFORMS

National Meeting in

Philadelphia, Nov. 7-10, 1999,

including presentations by

Arthur E Veinott, B. Curtis

Eaves, Irv Lustig, Allan J.

Hoffman, Ellis L. Johnson, and

George B. Dantzig himself.

received as a "birthday pres-

ent," the DIMACS Workshop

on the Theory andPractice of

Integer Programming in

honor ofRalph E. Gomory on

the Occasion ofhis 70th

Birthday, organized by Bill

Cook and Bill Pulleyblank.

The workshop was organized

at IBM, Yorktown Heights, on

Aug. 2-4, 1999. Main speakers

were Vasek Chvatal, Herbert

E. Scarf, Egon Balas, George

L. Nemhauser, Gerard

Cornuejols, and Ralph E.

Gomory.

JOHN E. DENNIS, JR.-

our previous chairman, and

current vice-chairman cele-

brated his 60th birthday, and

received a dedicated issue of

SIAMJournal on OPTI-

MIZATION, a journal of

which he was the first editor.

The dedication written by

Michael L. Overton and

Robert B. Schnabel can also

be found at the following

URL: http://epubs.siam.org/

sam-bin/dbq/artice/94709

1 PTIMA63

PAGE 6

JANUARY 2000 PAGE

SOCIETY NEWS

ISMP

X V I I

The 17th International Symposium on

Mathematical Programming (ISMP 2000)

will take place in Atlanta, Georgia, USA,

on the campus of the Georgia Institute of

Technology August 7-11, 2000. For more

information, please visit the web site

(http://www.isye.gatech.edu/ismp2000/).

Nominations for 2000 Elections

The Constitution of the

Mathematical Programming

Society sets the terms of office for

all officers of the Society at three

years. Elections for all offices

(Chair, Treasurer, and four

At Large Members of Council) are

to be held four months prior to

each triennial International

Symposium. The seventeenth sym-

posium will take place in Atlanta

on August 7-11, 2000, so the next

election will be held in April 2000.

The new Members-at-Large of the

Council will take office at the time

of the symposium, the Chair-Elect

and the Treasurer-Elect will take

office one year later.

Candidates must be members of

the Society and may be proposed

either by Council or by any six

members of the Society. No proper

nomination may be refused, pro-

vided the candidate agrees to stand.

The following procedure will be

observed:

(1) Nomination to any office is to

be submitted to the Nomination

Committee, which consists of John

Dennis, Jan Karel Lenstra (chair,

jkl@win.tue.nl), and Clyde

Monma. Such nomination is to be

supported by the nominator and at

least five other members of the

Society.

(2) In keeping with tradition, the

next Chair should preferably be a

North American resident. The

membership is asked to consider no

residents from other continents as

candidates for the Chair.

(3) When the ballots are counted,

the four At-Large candidates for

Council having the highest number

of votes will be elected; however,

no more than two members having

permanent residence in the same

country may be elected.

JEAN-PHILIPPE VIAL, CHAIR

Over $35,000 Collected for Fulkerson Prize

The Fulkerson Prize for outstand-

ing papers in discrete mathemat-

ics is sponsored jointly by the

Mathematical Programming

Society and the American

Mathematical Society. Since

1979, up to three awards were

presented at each International

Symposium on Mathematical

Programming. The awards were

initially paid out of a memorial

fund that was established by

friends of the late Delbert Ray

Fulkerson to encourage mathe-

matical excellence in the fields of

research exemplified by his work.

The prize fund became depleted

several years ago. MPS and AMS

appointed a fund-raising commit-

tee, consisting of Bob Bixby, Bob

Bland, and Ron Graham. In the

past year, with the help of Steve

Wright and Jan Karel Lenstra,

they raised a total amount of

$35,697.32, which should be suf-

ficient to support the prize in per-

petuity. The new prize fund will

be administered by MPS.

Substantial corporate and institu-

tional donations were received:

Foundation 14th ISMP

(Amsterdam, 1991), $3,800; IBM,

$5,000; Lucent Technologies,

$5,000; Philips Research

Laboratories, $3,000; Telcordia

Technologies (formerly Bellcore),

$5,000. These sponsors will be

recognized on the MPS web site.

Individual contributions were

made by Bob Bixby, Ralph

Gomory, William Hogan, Clyde

Monma, George Nemhauser,

Lloyd Shapley, Irene and Richard

Van Slyke, David Weinberger,

Karen Aardal, Anant Balakrishnan,

Bill Cook, Pierre Courrieu, Curtis

Eaves, Kaoru Endo, Sharon

Filipowski, Robert Freund, David

Gay, Donald Hearn, T.C. Hu,

Paparrizos Konstantinos,

Siriphong Lawphongpanich, Jan

Karel Lenstra, Janny Leung, A.

Loshise, William Lucas, Charles

McCallum, Jr., Masataka

Nakamura, Michael Panik, Roman

Polyak, Herbert Scarf, Alexander

Schrijver, Bruce Shepherd, Richard

Soland, Jie Sun, Roman Sznajder,

Lakshman and Sarala Thakur,

Michael Todd, Jean-Philippe Vial,

Kevin Wayne, David Williamson,

and H. Yamano.

Online Algorithms: The State of the Art

Amos Fiat and Gerhard J. Woeginger (Eds.)

Lecture Notes in Computer Science, Vol. 1442, 1998

Springer Verlag

ISBN 3-540-64917-4

During the past years online computation has become an impor-

tant field in mathematics, computer science and operations

During the past years online computation has become an impor-

research. This is not only due to its intrinsic interest but also

to its many applications.

Typically when one solves problems and designs algorithms one assumes

that all the input data is known a priori. However, in many practical situa-

tions this assumption might not be true. Consider the following simple sce-

nario: during a ski season an enthusiastic skier goes skiing every weekend

that conditions permit. Since she does not own skis she asks herself whether

to rent a pair or buy one. Clearly, if our skier knew a priori how long the

season will last, then she could easily calculate her most inexpensive way

through the season. Unfortunately, she does not have this complete knowl-

edge but only discovers each weekend whether the season still continues or

has already ended. Each time she is faced anew with the decision whether

to rent or buy this time (unless she already bought some skies).

The area of online computation deals with the above outlined issue: an

online algorithm must decide how to process incoming pieces of informa-

tion without any knowledge of future ones. The online algorithm must

make its decisions before the next bit of information is revealed and it is not

allowed to revoke any of its past decisions. Competitive analysis has become

the standard yardstick of how to judge online algorithms: the quality of an

online algorithm is measured relative to the best possible performance of an

offlinee) algorithm that has complete knowledge of the future.

The book edited by Amos Fiat and Gerhard J. Woeginger addresses

many aspects of online computation and competitive analysis. The chapters

have been contributed by recognized experts in the field, and this has result-

ed in an excellent book about the current research in this area. Each chap-

ter examines a specific application area and summarizes the related results

in the literature.

The topics covered include classical online problems which initiated the

research on competitive analysis such as self-organizing data structures or

paging in virtual memory systems as well as more recent topics such as

searching and navigation of unknown environments or online financial

problems. The book also includes a good discussion on the applicability of

competitive analysis in practice and its limitations.

The first chapter, written by the editors Amos Fiat and Gerhard

J. Woeginger themselves, gives a brief introduction to competitive analysis

and its history. Chapter 2 by Susanne Albers and Jefferey Westbrook sur-

veys self-organizing data structures. Results and their proofs on organizing

linear lists are complemented by an overview of splay trees and applications.

In Chapter 3, Sandy Irani presents results about paging. This chapter also

includes information about variants of competitive analysis such as loose

competitiveness and access graphs.

Chapter 4 was written by Marek Chrobak and Lawrence L. Larmore. It

gives an overview of metrical task systems and the famous k-server problem.

This chapter contains many proofs, among them the celebrated theorem

about the competitiveness of the "work-function algorithm" for the k-serv-

er problem. In Chapter5, Yair Bartal gives a nice survey of distributed pag-

ing. This area includes file migration and file allocation problems which

have applications to distributed data bases and web-caching.

Chapter 6, written by James Aspnes, deals with the issue of combining

competitive (sub-) algorithms in distributed systems to a globally competi-

tive algorithm. Chapter 7 by Janos Csirik and Gerhard J. Woeginger covers

online packing and covering problems. The bin-packing problem was one

of the first problems to be studied from an online point of view. The

authors discuss the bin-packing problem, its extensions to higher dimen-

sions and geometric versions.

JANUARY 2000

Chapter 8 by Yossi Azar is about online load balancing. This chapter is

tightly connected to Chapter 11 on online network routing. The latter

chapter was written by Stefano Leonardi and contains an enjoyable survey

and some nice proofs. The also related area of scheduling is treated in great

detail in Chapter 9 by Jiri Sgall.

The use of competitive analysis for online searching and navigation is

discussed in Chapter 10 which was written by Piotr Berman. Chapter 12

by Bala Kalyanasundaram and Kirk Pruhs covers online network design

problems. The authors also give pointers to online versions of the traveling

salesperson problem. In Chapterl3, Hal A.Kierstead surveys online graph-

coloring problems. This chapter is an excellent source for results as well as

applications of online graph coloring.

Chapter 14 was written by Avrim Blum and provides thorough infor-

mation about online problems from Computational Learning Theory. The

chapter also contains a nice list of open problems from this area. Online

financial problems are the topic of Chapter 15 by Ran El-Yaniv. These

problems have interesting applications in portfolio selection, search and

leasing. In Chapterl6, Anna Karlin comments on the performance of com-

petitive algorithms in practice.

The last chapter is again written by the two editors, Amos Fiat and

Gerhard J. Woeginger. In this chapter they indicate the limits of competi-

tive analysis and comment on ways around some competitive odds and

ends. Often "standard" competitive analysis fails to provide a theoretical

explanation of behavior that is observed in practice. One such example is

the fact that a number of paging algorithms (First-In-First-Out, Least-

Recently-Used, etc.) all have the same competitive ratio k, where k equals

the number of page slots in memory, but their performance in practice is

quite different. Another problem with competitive analysis is that for some

problems it only allows extremely weak positive results. The best possible

competitive ratio is totally disappointing and is achieved by a trivial algo-

rithm. An example is provided again by the paging problem: the First-In-

First-Out page replacement strategy hits the "triviality barrier" of k.

In conclusion, Amos Fiat and Gerhard J. Woeginger as well as their

guests have done an excellent job in producing a comprehensive survey of

the most relevant results in online computation. There is one grain of salt

that has to be added: The reader would probably like to see more proofs in

the book (such as in Chapter 4 instance). However, due to the immense

material covered in the book it was apparently not possible to include even

more.

I strongly recommend the book edited by Amos Fiat and Gerhard

J. Woeginger as a reference for researchers in the area of online computa-

tion. For readers new to the area, the reading should be supplemented by a

study of a good textbook on online algorithms such as the recent book by

Allan Borodin and Ran El-Yaniv [BEY98].

SEVEN O. KRUMKE

Konrad-Zuse-Zentrum fur Informationstechnik Berlin

krumke@zib.de

References

[BEY98] A. Borodin and R. El-Yaniv, Online computation and competi-

tive analysis, Cambridge University Press, 1998.

[FW98] A. Fiat and G. J. Woeginger (eds.), Online algorithms: The state

of the art, Lecture Notes in Computer Science, vol. 1442,

Springer, 1998.

PAGE

Graphs, Networks andAlgorithms

by Dieter Jugnickel

Springer Verlag, 1999

ISBN 3-540-63760-5

his book is the translation of a revised version of the third edi-

tion of the German text book 'Graphen, Netzwerke und

Algorithmen' by Dieter Jungnickel. The first German edition

appeared in 1987 and it was followed by other revised editions

in 1990 and 1994. This is to say that the text has had the time to evolve and

reach maturity and this English version is a well written and balanced text-

book.

The chosen topics are in accordance with the title. As the author points

out in the preface, "the present book concerns mainly that part of

Combinatorial Optimization which can be formulated and treated by graph

theoretical methods; neither the theory of Linear Programming nor

Polyhedral Combinatorics are considered. Simultaneously, the book gives

an introduction into Graph Theory." The list of chapter titles will better

outline the scope of the book (the number of pages of each chapter is in

parentheses): 1. Basic Graph Theory (34), 2. Algorithms and Complexity

(28), 3. Shortest Paths (36), 4. Spanning Trees (30), 5. The Greedy

Algorithm (26), 6. Flows (54), 7. Applications in Combinatorics (30), 8.

Colourings (14), 9. Circulations (52), 10. Synthesis of Networks (26), 11.

Connectivity (24), 12. Matchings (34), 13. Weighted Matchings (34), 14.

A Hard Problem: the TSP (48). Then there is an appendix with the solu-

tions of the exercises and an appendix with the list of symbols. In total the

book comprises 590 pages. I would also say that sometimes the author is not

able to stay within the self-inflicted bounds, as in Chapter 5, where

matroids are presented as abstract combinatorial objects, or in Chapter 13

where he cannot refrain from introducing the matching polytope.

Given these data, it is not surprising that the topics are treated quite in

depth and extensively. Indeed there is a wealth of material which could be

suited for some advanced courses in graph or network theory. Ph.D. stu-

dents could benefit a lot from the book. However, there is probably too

much material for a typical Master's student. The book is a mathematical

one. Definitions are carefully phrased (though not explicitly stated as such)

and Theorems, Lemmas, and Corollaries go along with their proofs.

Moreover, the text is interspersed with exercises which stimulate the reader

to a more active understanding of the material. Figures are pervasive and

quite welcome.

To convey a more detailed idea on the scope and depth of the book, here

are some examples of topics which are rarely included in Graph Theory

books and can be found in Jungnickel's book: path algebras in Chapter 3;

the Matrix Tree Theorem (how to compute the number of spanning trees of

a graph) and Steiner trees in Chapter 4; greedoids in Chapter 5; preflow

ideas for maximal flows in Chapter 6; Cayley graphs in Chapter 7; edge col-

oring in Chapter 8, and so on. Clearly the basic material is always covered.

As a reference text this is a highly recommendable book to anyone work-

ing in this field. It is highly valuable and quite up-to-date. If you have to

find a result together with its proof and background, then there is a good

chance you will find it in this book. Of course this implies that it is not easy

reading for the newcomer. In the preface the author says that this book has

been used as a textbook in several universities and even at a special work-

0S MA63

JANUARY 2000

shop for high school students. Well, I am full of admiration for the German

students and their preparation if they can really go through these topics at

ease. Personally I would recommend this book as a first course textbook to

Mathematics (Master's) students (using the material to cover two semesters

or even three semesters) and as an advanced (second course) textbook to

Computer Science or Engineering students.

PAOLO SERAFINI

University di Udine

E-mail: serafini@dimi.uniud.it

Stochastic Linear Programming Algorithms:

A comparison based on a model management system

Jinos Meyer

Gordon and Breach Science Publishers, 1998

ISBN 90-5699-144-2

During the past decade there has been a lot of focus in the sto-

chastic programming community on teaching the philosophy

and tools of the field and several textbooks have appeared

recently (see, e.g., the books by Birge & Louveaux [1], Kall &

Wallace [2], and Prekopa [3]. This book by Janos Meyer focuses on a spe-

cific but important aspect of stochastic linear programming (SLP), namely

algorithms for solving two-stage and chance-constrained SLP problems.

The book consists of six chapters discussing, respectively, general mathe-

matical programming concepts, SLP models and algorithms, implementa-

tion and testing issues, and finally computational results.

The first part of the book is devoted to a survey of SLP models and algo-

rithms. Chapter 1 begins by reviewing a number of results from convex and

linear programming. Next, in Chapter 2, a number of SLP models are pre-

sented. The exposition is limited to two-stage and jointly chance-

constrained models. On the one hand, this choice may seem restrictive and

indeed rules out both interesting and relevant stochastic programming

models, but these models are on the other hand very well studied and a

number of solvers and algorithms are available for comparison. Finally,

Chapter 3 reviews a number of SLP solution approaches with emphasis on

decomposition and approximation/bounding results.

The second part of the book presents the implementation and testing

environment used for carrying out computational experiments. Chapter 4

briefly describes the implementation and origin of the algorithms being

tested. Many of these algorithms belong to the "classics" of stochastic pro-

gramming, but implementations are, except for a few extensions, due to the

author, and carried out in a testing environment which has been specifical-

ly developed to manage SLP problems. This model management system,

which also has been described in numerous scientific articles by the book

author and Peter Kall, is the topic of Chapter 5. The 6th and last chapter

finally contains an extensive report on computational experiments using test

problems from the literature as well as randomly generated and/or per-

turbed problems.

Overall, Meyer's book gives a well balanced introduction to stochastic

linear programming algorithms with emphasis on computational topics.

Although a revision of the author's Habilitationsschrift (postdoctoral

PAGE 10

degree) from the University of Ziirich, the text is accessible to any person

with some knowledge of mathematical (linear) programming, since the

emphasis has been put on computational comparison. However, it is not an

introductory stochastic programming textbook in the same sense as the pre-

viously mentioned books [1, 2, 3], since its scope is much too narrow in

comparison. A possible limitation is also that the scope of the book is not

development of new algorithms or solution methods, but rather a descrip-

tion and a comparison of already existing algorithms. This is also the

strength of the book. Probably one of the most useful assets of the book is

not actually a part of the book, but is the SLP-IOR model management sys-

tem utilized for performing the computational experiments, manipulating

model data and carrying out the testing. It should be mentioned that SLP-

IOR is freely available for academic use from the authors. Thus this

book/SLP-IOR may provide something which no textbook can do alone:

giving hands-on modeling experience in classroom teaching.

In short, I find the book useful, both for readers already familiar with

stochastic programming concepts -as it serves as a convenient (computa-

tional) documentation of algorithms and test problems which are otherwise

scattered around in the scientific literature -and for newcomers and poten-

tial users of SLP techniques who are looking for descriptions of algorithms

and their computational performance and characteristics and who do not

wish to start right away reading journal articles.

CLAUS C. CARE, COPENHAGEN

References

[1] J.R. Birge and F.V. Louveaux, Introduction to Stochastic

Programming (Springer-Verlag, New York, 1997).

[2] P Kall and S.W. Wallace, Stochastic Programming (Wiley-

Interscience, New York, 1994).

[3] A. Prekopa, Stochastic Programming (Kluwer Academic Publishers,

Dordrecht, 1995).

10PTIMA63

JANUARY 2000 PAGE 11

C o n f e r e n c e

) APMOD 2000

April 17-19, 2000,London,UK

URL:http://www.apmod.org.uk

) Seventh International Workshop on Project Management and Scheduling (PMS 2000)

April 17-19, 2000,University of Osnabrueck,Germany

URL: http://www.mathematik.uni-osnabrueck.de/research/OR/pms2000/

) Applied Mathematical Programming and Modelling Conference (APMOD 2000)

17-19 April 2000, Brunel University, London

URL:http://www.apmod.org.uk

) INFORMS Spring 2000

May 7-10, 2000, Salt Lake City, Utah,USA

URL: http://www. informs.org/Conf/SaltLake2000/

) STOC 2000

May 21-23, 2000, Portland,Oregon,USA

URL:http://sigact.acm.org/stoc00

) Tenth SIAM Conference on Discrete Mathematics

June 12-15, 2000,Minneapolis,Minnesota,USA

URL:http://www.siam.org/meetings/dmOO/

I INFORMS/KORMS

June 18-21, 2000,Seoul, Korea

URL:http://informs.scu.edu/seoull

) SIAM Annual Meeting

July 10-14, 2000, Rio Grande, Puerto Rico

URL: http://www.siam.org/meetings/an00/

) ISMP 2000 17th International Symposium on Mathematical Programming

August 7-11, 2000,Georgia Institute of Technology, Atlanta,GA,USA

URL:http://www.isye.gatech.edulismp2000

) First SIAM Conference on Computational Science and Engineering

September 21-23, Washington,DC,USA

URL: http://www.siam.org/meetings/cse00/

) INFORMS Fall 2000

November 3-7, 2000, San Antonio, Texas,USA

URL:http://ie.tamu.edulinforms2000/

) IPCO 2001

Utrecht, The Netherlands

URL: http://www.cs.uu.nl/events/ipco2001/

JANUARY 2000

First Announcement and Call for Papers

HPOPT 2000

5th International Conference on High Performance Optimization Techniques

Rotterdam, The Netherlands

June 7-9, 2000

HPOPT 2000 will take place in the context of the

Dutch research project "High Performance

Models for Mathematical Optimization." In this

project, funded by the Dutch Organization for

Scientific Research (NWO), research teams

cooperate from four universities in the

Netherlands: Delft University of Technology,

Erasmus University, Eindhoven University of

Technology, and University of Utrecht.

The aim of the conference is to bring together

some of the most active researchers working on

the design and implementation of optimization

algorithms. We aim to cover the latest algorith-

mic developments, complexity results and imple-

mentation aspects, including the required tools

from numerical algebra. Much attention will be

given to the recent developments in semidefinite

optimization and its relevance for a wide range

of practical applications in fields such as combi-

natorial optimization, engineering design, matrix

inequalities in systems and control theory, and

matrix completion problems.

The meeting will consist of a one-day tutorial

and a two-day conference. Along with invited

presentations there will be sessions with con-

tributed lectures.

Conference Organizers: Dick den Hertog

(CQM, Eindhoven), Cor Hurkens (Eindhoven

University of Technology), Jan Karel Lenstra

(Eindhoven University of T.. I -..... ..'WI),

Leen Stougie (Eindhoven University of

Technology), and Tjark Vredeveld (Eindhoven

University of Technology).

Program Committee: Jan Brinkhuis (Erasmus

University Rotterdam), Dick den Hertog

(CQM, Eindhoven), Cor Hurkens (Eindhoven

of University Technology), Jan Karel Lenstra

(Eindhoven University of T.. I -..... ..'WI),

Kees Roos (Delft University of Technology),

Leen Stougie (Eindhoven University of

Technology), Henk van der Vorst (University of

Utrecht), and Tjark Vredeveld (Eindhoven

University of Technology).

Invited Speakers: Karen Aardal (University of

Utrecht, The Netherlands), Aharon Ben-Tal

(Technion, Haifa, Israel), N.G. de Bruijn

(Eindhoven University of Technology, The

Netherlands to be confirmed), Martin Dyer

(University of Leeds, Great Britain), Andrzej

Ruszczynski (Rutgers University, New

Brunswick, USA), Robert Vanderbei (Princeton

University, USA), and Maarten van der Vlerk

(University of Groningen, The Netherlands).

Submission of Papers: For contributed lectures,

authors are kindly requested to submit a one-

page abstract including title, author's name, affil-

iation, e-mail and postal address. Abstracts

should be sent in LaTeX format to

.

Registration: Pre-registration can be done

through the web site or by sending an e-mail

with your name and affiliation to

. Upon pre-registration you

will be kept up-to-date with any further

announcements about the conference.

Registration can be done in the same way as pre-

registration. Early registration is due on the 30th

of April 2000. The conference fees for early reg-

istration are: For the one-day seminar on

Wednesday, 7 June, Dgl 100; or the conference

on 8 and 9 June, Dgl 200; For both, Dgl 300.

For late registration, the fees for the two separate

parts are augmented with Dgl 50 and for the

three days with 100.

The conference fees include an abstract book,

free lunches in the restaurant of the World Trade

Center, coffee and tea with cookies during the

breaks, a get-together on Wednesday evening

and the conference dinner on Thursday evening.

Upon cancellation before the 30th of April

2000, your conference fee will be refunded com-

pletely, up to bank costs. Upon cancellation

before the 31st of May 2000, only half of your

fee will be refunded. After that date no refund-

ing is possible.

Important Dates: March 1, 2000 Deadlinefor

abstracts, March 31, 2000 Acceptance or rejection

notification; April 30, 2000 Deadline for early reg-

istration; June 7-9, 2000 HPOPT 2000.

Information: Information about the conference

can be found on the Conference Web Site:

mation can be obtained by sending an e-mail to:

.

PAGE 12

Call for Papers for Theme

Issue of The Arabian Journal

for Science and Engineering

on Optimization Theory and

Applications

The Editorial Board of the Arabian

Journal for Science and Engineering

(AJSE) plans to publish, in June 2000, a

Theme Issue in Optimization Theory

and Applications. The AJSE hopes to

bring together in a single issue research

papers that represent the state of the art

in this vast and rapidly growing area.

The scope of this theme issue encom-

passes, but is not limited to, the follow-

ing areas: linear programming; interior

and exterior methods; quadratic pro-

gramming; large scale optimization; sto-

chastic programming; nonsmooth opti-

mization; nonconvex programming;

semidefinite programming; integer and

combinatorial optimization; LCP; varia-

tional inequalities; heuristic-based opti-

mization; and industrial applications.

Guest Editors Professor Katta G.

Murty, Department of Industrial and

Operations Engineering, University of

Michigan; Professor Hanif D. Sherali,

Department of Industrial and Systems

Engineering, Virginia Polytechnic

Institute and State University.

Publication Schedule

Deadline forsubmission of manu-

scripts: January 10, 2000; Notification

of acceptance of papers: March 31,

2000; Publication of the theme issue:

June 2000.

Note to Authors: Four copies of the

manuscript should be submitted to:

Professor Harry Mavromatis, Managing

Editor, The Arabian Journal for Science

and Engineering, King Fahd University

of Petroleum & Minerals KFUPM, Box

5033, Dhahran 31261, Saudi Arabia;

Telephone: (+966) 3 8605418; Fax:

(+966) 3 8605458; e-mail:

.

Authors may obtain details of the for-

mat and style adopted by the AJSE by

contacting the Managing Editor at the

above address or by e-mail.

10PTIMA63

JANUARY 2000

Call for Nominations:

Optimization Prize for

Young Researchers

Principal Guideline The Optimization Prize

for Young Researchers, established in 1998 and

administered by the Optimization Section

(OS) within the Institute for Operations

Research and Management Science

(INFORMS), is awarded annually at the

INFORMS Fall National Meeting to one (or

more) young researchers for the most outstand-

ing paper in optimization that is submitted to

or published in a refereed professional journal.

The prize serves as an esteemed recognition of

promising colleagues who are at the beginning

of their academic or industrial career.

Description of the Award The optimization

award includes a cash amount of US$1,000

and a citation certificate. The award winners

will be invited to give a one-hour lecture of the

winning paper at the INFORMS Fall National

Meeting in the year the award is made. It is

expected that the winners will be responsible

for the travel expenses to present the paper at

the INFORMS meeting.

Eligibility The authors and paper must satisfy

the following three conditions to be eligible for

the prize:

(a) The paper must either be published in a

refereed professional journal no more than

three years before the closing date of

nomination, or be submitted to and

received by a refereed professional journal

no more than three years before the clos-

ing date of nomination;

(b) All authors must have been awarded their

terminal degree within five years of the

closing date of nomination;

(c) The topic of the paper must belong to the

field of optimization in its broadest sense.

Nomination Nominations should be sent

before July 15, 2000 to

Robert J. Vanderbei

Dept. of Operations Research and Financial

Engineering

Princeton University

Princeton, NJ 08544

Nominations should be accompanied by

a supporting letter.

PAGE 13

Second Announcement

Seventh DIMACS Implementation Challenge

Semidefinite and Related Optimization Problems

The workshop of the Seventh DIMACS Challenge has been postponed to

September 13-15, 2000. We have received many excellent proposals (see

the web site address below), but also a fair number of requests to allow

more time for projects which were otherwise unlikely to finish before

January. New proposals are still welcome.

For up-to-date information on the workshop, please see the Challenge

web site at . For the collection of test

problems, visit .

FARID ALIZADEH, DAVID JOHNSON, GABOR PATAKI

NEOS

Version 2 of the NEOS Server was de-com-

missioned on March 4, 1999, after having

processed 39,900 submissions. Version 3 of

the NEOS Server (NEOS 99) went into

operation the same day, and is continually

being improved. The new server can be

found at .

NEOS 99 is a major improvement. This

version is portable, faster, more reliable,

allows submissions from the local file space,

and accepts compressed data. We have also

added a considerable number of new

solvers. In particular, for integer program-

ming: MINLP (Roger Fletcher and Sven

Leyffer), XPRESS-MP/INTEGER (Dash

Associates and Dash Optimization); for

complementarity problems: MILES

(GAMS Development Corporation and T

Rutherford), PATH (GAMS Development

Corporation and S. Dirkse, M. Ferris and

T Munson); for nonlinearly constrained

optimization: DONLP2 (Hans Mittelmann

and Peter Spellucci), FILTER (Roger

Fletcher and Sven L. .II. . LANCELOT

(Andy Conn, Nick Gould and Philippe

Toint), LOQO (Robert Vanderbei),

MINOS (Bruce Murtagh and Michael

Saunders), SNOPT (Philip Gill, Walter

Murray and Michael Saunders); for bound-

constrained optimization: L-BFGS-B

(Ciyou Zhu, Richard Byrd, Peihuang Lu,

and Jorge Nocedal), TRON (Chih-Jen Lin

and Jorge More); and for positive semidefi-

nite programming: DSDP (Steve Benson,

Yinyu Ye, and Xiong Zhang). Many of the

solvers accept input in AMPL format, and

we have recently added solvers that accept

input in GAMS format.

We welcome comments and suggestions.

In particular, we are seeking comments

from NEOS users who support our contin-

uing effort to offer this service to the pub-

lic. The easiest way to provide user feedback

is by sending e-mail to

.

LIZ DOLAN AND JORGE MORE FOR THE

NEOS GROUP

0S MA63

IANU "i; l

jJ rJUiW 0"

1'..1. .

riilll

SThe deadline >i [he neX\ Issue of OPTINIA is Nihl\ 5. 200.

For the electronic version of OPTIMA, please see:

http://www.ise.ufl.edu/~optima/

Application for Membership

I wish to enroll as a member of the Society.

My subscription is for my personal use and not for the benefit of any library or institution.

O I will pay my membership dues on receipt of your invoice.

E I wish to pay by credit card (Master/Euro or Visa).

CREDITCARD NO.

FAMILY NAME

MAILING ADDRESS

EXPIRY DATE

TELEPHONE NO. TELEFAX NO.

EMAIL

SIGNATURE

Mail to:

Mathematical Programming Society

3600 University City Sciences Center

Philadelphia PA 19104-2688 USA

Cheques or money orders should be made

payable to The Mathematical Programming

Society, Inc. Dues for 1999, including sub-

scription to the journal Mathematical

Programming, are US $75.

Student applications: Dues are one-half the

above rate. Have a faculty member verify your

student status and send application with dues

to above address.

Faculty verifying status

Institution

10SP I M A 6 3

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O P T I M A

MATHEMATICAL PROGRAMMING SOCIETY

UNIVERSITY OF

FLORIDA

Center for Applied Optimization

371 Weil

PO Box 116595

Gainesville FL 32611-6595 USA

FIRST CLASS MAIL

EDITOR:

Karen Aardal

Department of Computer Science

Utrecht University

PO Box 80089

3508 TB Utrecht

The Netherlands

e-mail: aardal@cs.ruu.nl

URL: http://www.cs.ruu.nl/staff/aardal.html

AREA EDITOR, DISCRETE OPTIMIZATION:

Sebastian Ceria

417 Uris Hall

Graduate School of Business

Columbia University

New York, NY 10027-7004

USA

e-mail: sebas@cumparsita.gsb.columbia.edu

URL: http://www.columbia.edu/~sc244/

BOOK REVIEW EDITOR:

Robert Weismantel

Universitat Magdeburg

Fakultat fur Mathematik

Universitatsplatz 2

D-39106 Magdeburg

Germany

e-mail: weismant@math.uni-magdeburg.de

Donald W. Hearn, FOUNDING EDITOR

Elsa Drake, DESIGNER

PUBLISHED BYTHE

MATHEMATICAL PROGRAMMING SOCIETY &

GATOREngineeringo PUBLICATION SERVICES

University of Florida

Journal contents are subject to change by thepublisher.