MATHEMATICAL PROGRAMMING SOCIETY NEWSLETTER
MY IMPRESSION of the Mathemati-
cal Programming Society, in com-
parison with, say, SIAM or ORSA,
is that of a low key, internally di-
rected organization. MPS publishes a prestigious
journal of excellent quality and every three years holds
a well-organized, scientifically stimulating meeting on
theoreticaland algorithmic developments in the field.
We also have an informative newsletter and we award
four prizes: Dantzig, Fulkerson, Orchard-Hays and
Undoubtedly, our first priority is to maintain or
improve the quality of these activities. I am confident
that this will happen because of the people involved.
The 1991 meeting, to be held in Amsterdam, is being
co-chaired by Alexander Rinnooy Kan, Jan Karel
Lenstra and Alexander Schrivjer. Our journal editors
are Robert Bixby (replacing Michael Todd) and Wil-
liam Pulleyblank. From its inception, Donald Hearn
has edited OPTIMA. The members of the new prize
committees are announced elsewhere in this issue.
CONFERENCE NOTES 4
TECHNICAL REPORTS &
WORKING PAPERS 4-6
BOOK REVIEWS 7-11
W IM 7 'I-'- :,-- -: : -- - : _ -- -1 ""1 - -1 ' N
What more, if anything, should we be doing? The status quo is
comfortable and I am reluctant to depart from it. But I think there
are some good reasons forbecoming pro-active in promoting mem-
bership in the society and appreciation of the field.
O ur past chairman, Michel Balinski, began a membership
drive that revealed the need for geographical sections. Such
groups could, for example, hold meetings in the years between the
international symposia. We claim to be an international society, but
our membership is disproportionally North American. Geographi-
cal sections could correct this imbalance. The Tokyo meeting in 1988
revealed the untapped potentialfor Asian membership. Peristroika
should make membership accessible to math programmers from
the Eastern Bloc countries where we have a group of scientists
whose contributions to the field far exceed their membership in the
society. Scandinavians, under the leadership of Stein Wallace, have
begun to organize a geographical section. I would like to encour-
age others to do the same. Please contact me if you believe that it
would be desirable to have a section in your region.
MPS should define itself broadly to encompass all areas of optimi-
zation. By chance, because I have no other explanation for it, in our
last election nearly all of the officers elected work primarily in
discrete optimization. For this reason, I have heard the conjecture
that MPS may be narrowing its focus. Let me assure you that no
such thing is happening. Our editorial boards, meetings, and prize
committees will be balanced among the diverse areas of optimiza-
tion. Moreover, we should make every effort to bring in new areas.
For only through our collective strength can we influence our
colleagues in other areas of the significance of mathematical pro-
gramming. In other words, we must develop an identity that is
understood beyond our community. This recognition is essential
to the continued success of our field, which depends on our ability
to attract bright students and adequate funding for research.
-G. L. Nemhauser
CALL FOR PROPOSALS
1994 International Mathemati-
cal Programming Symposium
Proposals are now being solicited for the location of the
1994 International Symposium on Mathematical Program-
ming. A Symposium is held every three years under the
auspices of the Mathematical Programming Society. The
1991 Symposium is scheduled to be held in Amsterdam.
In keeping with the informal tradition of the Society, a
site in North America will be preferred for the 1994
Symposium; however, other proposals will also be
seriously considered. A preference is given to holding
this meeting the first or second week of August 1994, due
to the teaching schedule at American Universities.
The main criteria for selection of the location are:
1 Existence of mathematical programming researchers in
the geographical area who are interested in organizing the
2 Attendance open to prospective participants from all
3 Availability of an attractive facility with a sufficient
number of meeting rooms, standard lecture equipment, etc.
4 Availability of a sufficient supply of reasonably
economical hotel and/or university dormitory rooms fairly
near the meeting facility.
A copy of the Society's "Guidelines for Submission of
Proposals" and further information can be obtained by
Combinatorics & Optimization Group
Bell Communications Research
445 South Street
Morristown, NJ 07960-1910 USA
Phone: (201) 829-4428
Fax: (201) 538-9093
The site selection committee consists of:
Clyde Monma, Chairperson
(Bell Communications Research)
Jan Karel Lenstra
(Eindhoven University of Technology)
(University of Colorado)
------ --- ----- ----------~
I dilor-in-Chief: Pt'rr L. Hammer, Rutcor, Hill Center for the Mathematical Si.i,..-
PFlilJ'., University, bI;1-J! C.,. iri New Brunswick, '1 i -'I ,',1.
Ed. A.V. i ....
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Iniranj ,iii. Prlot.l tnIlL
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Arigii i flIcInll l-' and it f.tilu tRL V.-r lh
Ed. D. K" -.-_. :. F. Glover
",T ,. ., Sm ith & P. ,
Topological Network lh-i-,'i
Vol. Th, 1989: Ed. B. .-., Networks
Optimization and Applications
FI' appr. 400 r-i_.
., I 1989: Ed. P.C. Fishburn & L.H. 1 i'
Choice under Uncertainty
1989, 514 pages
Vol. i 1'-u Ed. F.V. Louveaux, M. Labbe &
J.F. Thi;.. I. l t.ii Location Analysis: I liror. and
I -' '. ~ '1- .tges
Vol. I I1'P Ed. A. Kusiak & W:E. i ..
i iJla il.. l'idelini- and I -i.i!n it Modern
Produc'liin 's ~lrm
1989, "-.' r."e l-i'" 3 "': 135 33 7
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_H in .* .a ... F 1 1. K - .-:rir ,..i h ... '. "[ F:;,.." .
Muilli-.Atirihulr I )t.iolin \i .ikin. via 4) H -Ba.dl
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i- :-. 1.': pages, ISBN 3 905 135 *' 2
Vol. 13, '11 Ed. B. 5:. i. r,:. P.T.. ii G. .1.
F. '\i l! '. i & P,.i!! ri n '. I-oriran Codes fir
['-.' 41. -44 !',1=,.,. ''", ^ '." 29 9
i 1 J.B. Mazzola
Automated Mjiai .iiur..ir m
Ed. i i: Rosen
'iii. r.r iiiillpiiir- and Largescale Optimization:
-.,,rithi ,. r n fi-,r.., \p il t i i.
Ed. D. de .' erra ... F.
1 j.11l. '. iulth
Ed. R. '. & J. __
Vol. 12, i. G. I w, \ppr .n.h to
Ihillli.'nl Decision luppllit
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Approaches to Combinatorial Optimization
2 vols. I 602- ..- ISBN 3 905 135 27 2
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PAGE 4 number twenty-eight NOVEMBER 1989
Twelfth Symposium on
with Data Perturbations
The George Washington University
May 24-25, 1990
The Twelfth Symposium on Mathematical
Programming with Data Perturbations will
be held at George Washington University's
Marvin Center on May 24-25, 1990. This
symposium is designed to bring together
practitioners who use mathematical
programming optimization models which
deal with questions of sensitivity analysis
and researchers who are developing tech-
niques applicable to these problems.
Contributed papers in mathematical
programming are solicited in the following
(1) Sensitivity and stability analysis results
and their applications;
(2) Solution methods for problems involving
implicitly defined problem functions;
(3) Solution methods for problems involving
deterministic or stochastic parameter
(4) Solution approximation techniques and
Clinical presentations that describe prob-
lems in sensitivity or stability analysis
encountered in applications are also invited.
Abstracts should provide a good technical
summary of key results, avoid the use of
mathematical symbols and references, not
exceed 500 words, and include a title and
the name and full mailing address of each
author. The deadline for submission of
abstracts is March 9, 1990. Approximately 30
minutes will be allocated for the presenta-
tion of each paper. A blackboard and
overhead projector will be available.
Abstracts of papers intended for presenta-
tion at the Symposium should be sent in
Professor Anthony V. Fiacco
The George Washington University
Department of Operations Research
Washington, DC 20052
Telephone: (202) 994-7511
Anthony V. Fiacco
System Modelling and
September 2-6, 1991
IFIP TC7 has decided to hold its 15th
Conference on System Modelling and
Optimization at the University of Zurich,
September 2-6, 1991. According to the
tradition of the well-established IFIP TC7
conference series, colleagues from all over
the world are expected to get together to
discuss theoretical and practical results
contributing to the further success of
systems analysis and optimization tech-
For all questions concerning the conference,
Dr. Karl Frauendorfer
Institute for Operations Research
University of Zurich
CH-8044 Zurich, Switzerland
Phone +41-1-257 37 71
E-mail IFIP91 at CZHRZUIA (EARN or
Telex 817 260 uniz ch
Rutgers Center for Operations
Hill Center, Busch Campus
New Brunswick, New Jersey 08903
P. Hansen, B. Jaumard and S-H. Lu, "Global
Optimization of Univariate Lipschitz Functions:
I. Survey and Properties," RRR 18-89.
S-R. Kim, F.S. Roberts and S. Seager, "On
101-Clear (0,1) Matrices and the Double
Competition Number of Bipartite Graphs," RRR
S-R. Kim and F.S. Roberts, "On Opsut's
Conjecture about the Competition Number,"
F.S. Roberts, "Applications of Combinatorics
and Graph Theory to the Biological and Social
Sciences: Seven Fundamental Ideas," RRR 21-
E. Boros, Y. Crama and P.L. Hammer,
"Polynomial-Time Inference of All Valid
Implications for Horn and Related Formulae,"
P. Hansen, B. Jaumard and S-H. Lu, "Global
Optimization of Univariate Lipschitz Functions:
II. New Algorithms and Computational
Comparison," RRR 23-89.
A.C. Williams, "Estimating the Numbers of
Threshold Functions of Dimension n and Order
m," RRR 24-89.
P. Hansen, M.V. Poggi de AragAo and C.C.
Ribeiro, "Hyperbolic 0 1 Programming and
Queries Optimization in Classical Databases,"
C.T. HoAng, F. Maffray and M. Preissmann,
"New Properties of Perfectly Orderable Graphs
and Strongly Perfect Graphs," RRR 26-89.
J-M. Bourjolly, P.L. Hammer, W.R. Pul-
leyblank and B. Simeone, "Combinatorial
Methods for Bounding Quadratic Pesudo-
Boolean Functions," RRR 27-89.
Department of Mathematical
P. O. Box 1892
R.A. Tapia and Y. Zhang, "A Fast Optimal
Basis Identification Technique for Interior Point
Linear Programming Methods," TR89-1.
J. Chiang and R.A. Tapia, "Convergence Rates
for the Variable, the Multiplier, and the Pair in
SQP Methods," TR89-2.
R.H. Byrd, R.A. Tapia and Y. Zhang, "An
SQP Secant Algorithm for Equality Constrained
Optimization Using the Structure of the
Augmented Lagrangian," TR89-4.
P. Tarazaga, "More Estimates for Eigenvalues
and Singular Values," TR89-6.
P. Tarazaga, "A Quadratic Minimization
Problem on Subsets of Symmetric Positive
Semidefinite Matrices," TR89-7.
J. Dennis and R. Schnabel, "A New Deriva-
tion of Symmetric Positive Definite Secant
Updates," CU-CS 185-80 (Nonlinear Pro-
gramming 4, Academic Press, pp. 167-199).
D. Scott, "Nonparametric Probability Density
Estimation by Optimization Theoretic Tech-
K. Kennedy, "Automatic Translation of
Fortran Programs to Vector Form," 476-029-4.
School of Operations Research
and Industrial Engineering
Ithaca, NY 14853-7501
R. Roundy, W. Maxwell, Y. Herer, S. Tayur
and A. Getzler, "A Price-Directed Approach to
Real-Time Scheduling of Production Opera-
tions," TR 823.
R.E. Bechhofer, A.J. Hayter and A.C.
Tamhane, "Designing Experiments for
Selecting the Largest Normal Mean When the
Variances are Known and Unequal: Optimal
Sample Size Allocation," TR 825.
M. Kulldorff, "Optimal Control of Favorable
Games with a Time Limit," TR 826.
M.J. Todd, "Recent Developments and New
Directions in Linear Programming," TR 827.
L.E. Trotter, Jr. and S.K. Tipnis, "Node-
Packing Problems with Integer Rounding
Properties," TR 828.
L.E. Trotter, Jr. and J. Ryan, "Weyl-Minkow-
ski Duality for Integral Monoids," TR 829.
D. Joneja, "Multi-Item Production Planning
with Joint Replenishment and Capacity
Constraints: The Trucking Problem," TR 830.
J.S.B. Mitchell, L. Gewali, A. Meng, and S.
Ntafos, "Path Planning in 0/1/- Weighted
Regions with Applications," TR 831.
J.S.B. Mitchell, "A New Algorithm for Shortest
Paths Among Obstacles in the Plane," TR 832.
J.S.B. Mitchell, "On Maximum Flows in
Polyhedral Domains," TR 833.
M.J. Todd, "The Affine-Scaling Direction for
Linear Programming is a Limit of Projective-
Scaling Directions," TR 834.
M.J. Todd, "Probabilistic Models for Linear
Programming," TR 836.
E. Arkin, R. Connelly, and J. Mitchell, "On
Monotone Paths Among Obstacles with
Applications to Planning Assemblies," TR 838.
L. Trotter and M. Hartmann, "A Topological
Characterization for Closed Sets Under Polar
Duality in Q"," TR 843.
S. Resnick and R. Roy, "Multivariate Extremal
Processes and Dynamic Choice Models," TR
E.M. Arkin, L.P. Chew, D.P. Huttenlocher,
K. Kedem, J.S.B. Mitchell, "An Efficiently
Computable Metric for Comparing Polygonal
Shapes," TR 845.
M. Hariga, "The Warehouse Scheduling
Problem," TR 846.
A. Forbes, "Proofs of the Asymptotic Properties
of the Conditional Maximum Likelihood
Estimator for Log Odds Ratio Regression," TR
P.L. Jackson, "The Cumulative Flow Plot:
Understanding Basic Concepts in Material
Flow," TR 852.
J. Renegar, "On the Computational Complexity
and Geometry of the First-Order Theory of the
Reals, Part I," TR 853.
J. Renegar, "On the Computational Complexity
and Geometry of the First-Order Theory of the
Reals, Part II," TR 854.
J. Muckstadt, P. McCrink and L. Denardis,
"An Application of a Hierarchical Modeling
Framework to the Computer Maintenance
Industry," TR 855.
J. Renegar, "On the Computational Complexity
and Geometry of the First-Order Theory of the
Reals, Part III," TR 856.
M. Todd, "The Effects of Sparsity, Degeneracy
and Null and Unbounded Variables on Variants
of Karmarkar's Linear Programming Algo-
rithm," TR 857.
J. Renegar, "On the Computational Complexity
of Approximating Solutions for Real Algebraic
Formulae," TR 858.
Georgia Institute of Technology
School of Industrial and Systems
Atlanta, GA 30332
F.A. Al-Khayyal and J. Kyparisis, "Condi-
tions for Finite Convergence of Algorithms for
Nonlinear Programs and Variational Inequali-
ties," PDRC 88-1.
F.A. Al-Khayyal, R. Horst and P.M.
Pardalos, "Global Optimization of Concave
Functions Subject to Separable Quadratic
Constraints and of All Quadratic Separable
Problems," PDRC 88-4.
F.A. Al-Khayyal, "On Characterizing Linear
Complementarity Problems as Linear Pro-
grams," to appear in Optimization.
F.A. Al-Khayyal, "Jointly Constrained Bilinear
Programs and Related Problems: An Overview,"
to appear in Journal of Computers and
Mathematics with Applications.
F.A. Al-Khayyal, "Generalized Bilinear Pro-
F.A. Al-Khayyal, "On Solving Linear Comple-
mentarity Problems as Bilinear Programs."
C. Alexopoulos and P.G. Griffin, "Path
Planning for a Mobile Robot," J-89-09.
S. Amiouny, J.J. Bartholdi, III, J.H. Vande-
Vate and J. Zhang, "The Balanced Packing
E.R. Barnes, "Some Results Concerning
Convergence of the Affine Scaling Algorithm,"
to appear in Mathematical Developments
Arising from Linear Programming.
E.R. Barnes, A.J. Hoffman, U.G. Rothblum,
"Optimal Partitions Having Disjoint Convex
and Conic Hulls."
E.R. Barnes, D. Jensen and S. Chopra, "A
Polynomial Time Version of the Affine Scaling
C. Barnhart, "A Decomposition Strategy for the
Solution of Large-Scale Multi-Commodity
Network Flow Problems."
C. Barnhart, "A Comparison of Primal-Dual
and Dantzig-Wolfe Decomposition Techniques
for the Multi-Commodity Flow Problem."
_ I -- --------~
PAE6nme wny-ih OEBR18
Technical Reports &
C. Barnhart, "A Network-Based Primal-Dual
Heuristic for the Solution of Multi-Commodity
Network Flow Problems."
M.B. Daya and C.M. Shetty, "Polynomial
Barrier Function Algorithms for Linear
M.B. Daya and C.M. Shetty, "Polynomial
Barrier Function Algorithms for Convex
Quadratic Programming," J-88-05.
M.B. Daya and C.M. Shetty, "A Barrier
Function Algorithm for Linear Programming
and Its Implementation," J-88-20.
M.B. Daya and C.M. Shetty, "Underlying
Concepts in Interior Point Methods for Linear
R. Borie, G. Parker and C. Tovey, "Recur-
sively Constructed Graphs: Decomposition and
Linear Time Algorithm Generation."
R. Borie, G. Parker and C. Tovey, "Unambi-
guous Factorization of Recursive Graph
R. Borie, G. Parker and C. Tovey, "Automatic
Generation of Linear Algorithms from Predicate
Calculus Descriptions of Problems on Recur-
sively Constructed Graph Families."
R. Borie, G. Parker and C. Tovey, "General-
ized k-Jacknife Operations and Partial k-Trees,"
M. Carter and C. A. Tovey, "When Is the
Classroom Assignment Problem Hard?"
M. Goetschalckx and H.D. Ratliff, "Shared
Storage Policies Based on Duration of Stay."
M. Goetschalckx and H.D. Ratliff, "Deter-
mining Optimal Lane Depths for Single and
Multiple Products in Block Stacking Opera-
A. Iyer and H.D. Ratliff, "Hierarchical
Solution of Network Flow Problems."
A. Iyer and H.D. Ratliff, "Location Issues in
Guaranteed Time Distribution Systems."
A. Iyer, H.D. Ratliff and G. Vijayan, "On an
Edge Ranking Problem of Trees and Graphs."
D.C. Llewellyn and T. Ryan, "A Primal-Dual
Integer Programming Algorithm."
D.C. Llewellyn and C.A. Tovey, "Dividing
and Conquering the Square."
G.L. Nemhauser and S. Park, "A Polyhedral
Approach to Edge Coloring," J-89-01.
G.L. Nemhauser and R. Rushmeier, "Per-
formance of Parallel Branch-and-Bound
Algorithms for the Set Covering Problem," J-89-
G.L. Nemhauser and G. Sigismondi, "A
Strong Cutting Plane/Branch-and-Bound
Algorithm for Node Packing," J-89-08.
Report on Stochastic
ATrRACTING more people than any
previous meeting on the subject, the
Fifth International Conference on
Stochastic Programming in Ann Arbor,
Michigan, August 13-18, 1989, gave 123 partici-
pants from 31 countries and 6 continents both an
introduction to the field and insight into current
and future research. Organized by the Committee
on Stochastic Programming (COSP) of the
Society, this meeting was the first of its kind held
in North America. The previous conferences were
in Oxford in 1974, Koszeg, Hungary in 1981, Lax-
enburg, Austria in 1983, and Prague in 1986.
The meeting began with a day and a half of
tutorial sessions that gave students, practitioners
and researchers from other areas some back-
ground on stochastic programming and the fun-
damental techniques used in current work.
Plenary lectures were given by R. Wets, R.T.
Rockafellar, P. Kall, Y. Ermoliev, G. Dantzig and
Y. Chang on work with A. Chares. Participants
attended 14 talks in morning and afternoon
sessions as well as evening workshops which fo-
cussed on a variety of practical applications.
The meeting received financial support from the
U.S. National Science Foundation, the College of
Engineering and Department of Industrial and
Operations Engineering of the University of
Michigan, and corporate sponsors: IBM, AT&T,
and General Motors. The Conference was jointly
sponsored by the Mathematical Programming So-
ciety, ORSA, TIMS, and IFIP TC7.
Discussion of the next conference in 1992 was
initiated by Andras Prekopa, Chair of COSP. No
definite plans were made, but the COSP member-
ship indicated a preference for Western Europe.
The consensus was that this was the most excit-
ing meeting in the field so far and that the com-
mittee was looking forward to continued growth
in an area that offers challenges and rewards to
both theoreticians and practitioners.
Dantzig Prize: Awarded for
original research, which by its
originality, breadth and depth,
is having a major impact on
the field of mathematical pro-
gramming (jointly sponsored
by SIAM). Thomas Magnanti,
Massachusetts Institute of
Manfred Padberg, New York
University; R. Tyrrell Rockafel-
lar, University of Washington;
Michael Todd, Cornell Univer-
Fulkerson Prize: Awarded
for outstanding papers in the
area of discrete mathematics
(jointly sponsored by the
AMS). Martin Grotschel,
University of Augsburg (Chair-
man); Louis Billera, Cornell
University; Robert Tarjan,
Awarded for contributions to
programming. Robert Meyer,
University of Wisconsin
(Chairman); Jorge More, Ar-
gonne National Laboratory;
John Tomlin, IBM; Laurence
Wolsey, University of Louvain.
Tucker Prize: Awarded for an
outstanding paper authored
by a student. Richard Cottle,
Stanford University (Chair-
man); Thomas Liebling, Ecole
Polytechnique Federale de
Lausanne; Richard Tapia,
Rice University; Alan Tucker,
SUNY at Stony Brook.
_~ ~_ ~ ~ ---I
Graph Theory tween seemingly unrelated prob-
by Ronald Gould it E V I E W S lems and thus help to structure the
field. These transforms led me to
The Benjamin/Cum- believe that arrangements of hy-
mings Publishing Cor- perplanes are at the very heart of
pany, Menlo Park, Cali- computational geometry and this
fornia, 1988 is my belief now more than ever,"
(p. vii) or "A more appropriate but
longer title for this chapter would
be 'Problems formulated for configurations
This text is an introduction to modern and solved for arrangements.' In fact, many
graph theory for beginners as well as a refer- problems formulated for configurations, whether
ence book. The standard topics are presented in a lucid combinatorial or algorithmic, are easier to approach in
style as a perfect blend of theory and algorithms includ- dual space where an arrangement of hyperplanesrepre-
ing complexity aspects. Recent results are incorporated, sents the r an arrange nt" of hs r27
e.g. Fraisse's sufficient condition for a graph to be Hamil- ments of hyperplanes are geometric cell co
ll : f Arrangements of hyperplanes are geometric cell com-
romnan. Every chapter containsl a ~collUtuu uio exerc CA s alu an
extensive list of references. The last chapter concerning extremal
graph theory is intended for graduate students.
Unfortunately, there are some inaccuracies in the text which are
vexatious, e.g. the reconstruction procedure of a graph from its
intermediate degree sequences does not work as described. Too many
misprints are a grievance, no matter who the typist and the typesetter
are that are blamed by the author himself in the preface.
Algorithms in Combinatorial Geometry
by Herbert Edelsbrunner
Springer, Berlin, 1987
Computational geometry is a relatively young discipline which
combines problems, methods and results from geometry-particu-
larly combinatorial geometry-and computer science. A typical well-
known problem in this area is the task of computing the convex hull
of a given point set in R". In the past decade this field has attracted
many people and much research. The area is still a rich source of
interesting research problems. However, the results have grown to-
gether to form a theory.
Edelsbrunner's book reflects this fact by stressing unifying struc-
tures and basic (i.e. more generally applicable) techniques. A few
quotes from the book show where the author sees unifying structures
in his field and where he places the emphasis in his book. "... geometric
transforms played an important role as they reveal connections be-
plexes whose cells are the (relatively open) convex regions which are
associated with a dissection of R" by finitely many hyperplanes.
According to the above quote, arrangements of hyperplanes are the
central structure studied in this book, and transformations are used to
relate various other problems to those for arrangements of hyper-
Let us point out that, as mentioned in Chapter 1, arrangements of
hyperplanes correspond to zonotopes in one dimension higher. These
zonotopes are special polytopes which are given as the Minkowski
sum of finitely many line segments. So, as well as arrangements of
hyperplanes, zonotopes could be regarded as underlying unifying
structure for many problems considered in Edelsbrunner's book.
The book consists of three parts, entitled Combinatorial Geome-
try, Fundamental Geometric Algorithms, and Geometric and Algo-
rithmic Applications. This structure is used by the author in order to
demonstrate that computational and combinatorial issues of geome-
try are very closely related. After all, there are many geometric
ingredients to the design of an efficient algorithm that specify the
structure of the problem and in particular cut down the number of
candidates for a solution. In addition, computational questions stimu-
late some research in combinatorial geometry.
Roughly speaking, the relation of various chapters in different
parts of the book is as follows: respective chapters study related
concepts and provide, first, the theoretical background, then, in the
second part, (state-of-the-art) algorithms and, finally, they give appli-
In the first part Edelsbrunner introduces concepts of combinato-
rial geometry and gives results that on one hand are important for
their own but on the other hand are relevant for the design of algo-
rithms that solve respective combinatorial problems from a computa-
tional point of view. The chapter headings of the Combinatorial
Geometry part are as follows: Fundamental Concepts in Combinato-
rial Geometry, Permutation Tables, Semispaces of Configurations,
Dissections of Point Sets, Zones in Arrangements, and The Complex-
ity of Families of Cells.
The second part gives geometric algorithms which are regarded
as fundamental since they deal with basic problems, and the tech-
niques are of paradigmatic character. To deal with these algorithms
one must pay attention to the fact that usually a computational
problem falls into several parts depending on how one evaluates the
importance of efficiency issues related to preprocessing, storage,
time-complexity, etc. The chapter headings of Part II are as follows:
Constructing Arrangements, Constructing Convex Hulls, Skeletons
in Arrangements, Linear Programming, and Planar Point Location
The third part, where the techniques and results of the first two
parts flow together, deals with geometric and algorithmic applica-
tions. The chapter headings are: Problems for Configurations and
Arrangements, Voronoi Diagrams, Separation and Intersection in the
Plane, and Paradigmatic Design of Algorithms.
As it turns out, various computational problems of geometry are
closely related to certain problems in mathematical programming. Of
course, in computational geometry often configurations of points or
arrangements of hyperplanes are central rather than convex
polytopes. Furthermore, considerations tend to keep the dimension
fixed, and in many problems there is no objective function that is op-
However, there are interesting connections between these fields,
and Edelsbrunner pays attention to that. He uses, for instance, pertur-
bation techniques for arrangements which are essentially the same as
the approach which led to the lexicographical variant of the simplex
algorithm. He also discusses contributions of techniques from com-
putational geometry to the minimum-spanning-tree problem, and he
devotes a whole chapter to linear programming. In fact, fast routines
for linear programming problems are the heart of various algorithms
in computational geometry. Edelsbrunner describes an approach
(developed independently by Dyer and Megiddo in the plane and
subsequently extended to arbitrary dimensions by Megiddo) which
leads to a linear time algorithm for linear programming in fixed
As indicated before and as confirmed by the choice of topics in
Edelsbrunner's book, computational geometry is more precisely a
computational combinatorial geometry since the problems which are
usually dealt with are very combinatorial in nature. Let us point out,
however, that there are interesting results concerning algorithmic
aspects of convex bodies which are usually not dealt with under the
heading Computational Geometry but which might be regarded as
belonging to an area which should be called Computational Convex-
As intended by the author, the book serves the purpose very well
of emphasizing "that computational and combinatorial investiga-
tions in geometry are doomed to profit from each other" (p. vii). The
book is well written and gives an excellent and unifying treatment of
fundamental results in computational (combinatorial) geometry.
I think this book is attractive and very valuable for everyone who
is interested in (pure or applied) aspects of computational geometry.
The Theory of Algorithms
by A. A. Markov and M. M. Nagorny
Kluwer, Dordrecht, 1988
The Russian mathematician Markovdied in 1979, and the current
book was completed posthumously by colleagues and former stu-
dents. An eloquent preface recognizes Markov's contributions to
dynamical systems and topological groups (his father is famous in
probability) as well as to the subject of the current book.
The primary focus is an extremely careful presentation of one
approach to the concept of a recursive function, often known in the
West as "Markov algorithms." There is motivational and philosophi-
cal discussion including numerous critical remarks about a set-theo-
retic foundation for mathematics as being unacceptably vague.
(Markov's coauthor writes, "These views provoked a stormy reaction
on the part of many of his set-theoretically inclined colleagues. Traces
of the prolonged discussions which took place around A. A. Markov's
conceptions can be found in this book, but they are merely pale
Markov algorithms are formally equivalent to Turing machines
and other methods of defining recursive functions. They were devel-
oped in order to show that certain problems in the theory of semi-
groups are undecidable. This result of Markov's was arguably the first
example of an undecidable problem from outside of mathematical
It is unfortunate that most of this book will probably be some-
what outside the range of interests of Mathematical Programming
Society members, since the emphasis is on problems that cannot be
~ ~--- -`- -----~- ~- 1~-~--- I--
PAGE 9 number twenty-eight NOVEMBER 1989
decided by any alogrithm, rather than on those which can be solved
but may require a long time. There is a brief section (number 52)
dealing with complexity issues. The final chapter is a first glimpse of
the problems that arise when one tries to develop a constructive
theory of real numbers. Some of this material deals with issues similar
to those considered by Gr6tschel, Lovasz, and Schrijver in their recent
book on geometric approaches to combinatorial optimization.
Integer and Combinatorial Optimization
by G. L. Nemhauser and L. A. Wolsey
John Wiley, New York, 1988
During the last four decades combinatorial optimization has
been one of the "hottest" and most active fields within mathematics.
It began in 1947 with Dantzig's invention of the brilliant simplex
method, and since then it has been a rich field of theories, deep
theorems, many effective algorithms and an infinite variety of appli-
cations. Our desks are flooded with piles of relevant and stimulating
publications. So it's necessary to refresh and update the textbooks
used from time to time. To that end an indeed impressive and
astonishing achievement of completeness is provided in this book of
more than 700 pages. One can find old and very recent results.
Numerous examples and model formulations are extensively used by
the authors to illustrate the crucial points of the underlying subject
more clearly. Everything is carefully developed with splendid clarity
and the book is well organized. It provides a comprehensive treat-
ment of the main topics leading up to the frontiers of current research.
Unfortunately, I can't follow the authors' decision to present De-
Ghellinck and Vial's approach to linear programming instead of Kar-
The book consists of three parts. In the first one, the foundations
of combinatorial optimization are presented. In addition to some
general model formulation schemes, this part addresses linear pro-
gramming, graphs and networks, complexity theory and integer
lattices. In linear programming, for instance, the book covers the
associated theory, the simplex algorithm, Khachian's ellipsoidal
method, DeGhellinck and Vial's projective algorithm and Tardos'
contribution to a strongly polynomial linear programming algorithm.
The emphasis in integer lattices lies in the solution of linear equations
Part II deals with general discrete optimization problems which,
in most cases, are hard to solve. The topics discussed are: duality,
relaxations, cutting planes and branch and bound. There is also a
section of special purpose routines where methods like simulated
annealing are briefly introduced. Finally, part III covers rather highly
structured discrete optimization problems for which elegant proofs
and algorithms are known. Very recent results about totally balanced,
balanced and perfect matrices are included in a portion entitled
Integer Polyhedra. In addition, there are extensive contributions on
matching and matroids.
The authors concentrate on theoretical properties and underly-
ing ideas. Consequently, nothing is said about implementation as-
pects or parallel complexity. Also the probabilistic and amortized
analysis has not been established seriously. I think that nowadays
textbooks should have more details of real-world applications and
implementations. On one hand, that's what we are looking for when
we solve real-world problems, and on the other, real applications are
rather convincing and motivating for students.
Summarizing, this book provides an excellent introduction and
survey of traditional fields of combinatorial optimization. It should
serve well as a textbook for students, and I'm convinced that it is going
to be a standard reference. It is indeed one of the best and most
complete texts on combinatorial optimization for students now avail-
able. In the preface the authors suggest different ways to incorporate
the covered material into the curricula. Most sections are concluded
with exercises and further readings. For experts the book contains
some interesting and stimulating material as well. Even though it is
impossible to include all important references in such an active field
of research, this book with more than 700 entries, has quite an exhaus-
tive reference list.
by W. D. Wallis
Marcel Dekker, Basel, 1988
As the author states in the introduction, the book under review is
intended for use as a text in a course in combinatorial designs at the
senior/graduate level. His aims included giving "a good groundwork
in the classical areas of design theory: block designs, finite geometries,
and Latin squares," introducing "some modern extensions of design
theory" and leading "students to the current boundaries of the sub-
ject." In spite of some recent texts on designs, such a textbook was still
missing. The present book fills this gap quite nicely, and the author
PG 10 numl~i i
has on the whole succeeded admirably. A very valuable feature of the
book is the wealth of exercises (with solutions or hints).
Let me briefly summarize the contents of the book. There are 14
chapters: 1. Basic Concepts (first definitions and examples, including
systems of distinct representatives); 2. Balanced Designs (PBD's,
BIBD's, t-designs, including Fisher's inequality and a first discussion
of symmetric designs); 3. Some Finite Algebra (auxiliary results on
finite fields and sums of integer squares); 4. Difference Sets and
Difference Methods (basic facts and construction of Hadamard differ-
ence sets, but no algebraic theory); 5. Finite Geometries (affine and
projective geometries as designs, Singer difference sets, ovals); 6.
More About Block Designs (residual designs, the Bruck-Ryser-
Chowla thoerem, resolvability); 7. t-Designs (extensions, Cameron's
theorem, affine t-designs); 8. Hadamard Matrices; 9. The Variability of
Hadamard Matrices (a rather extensive treatment, including Hadam-
ard designs, Williamson's method, regular Hadamard matrices,
conference matrices and equivalence); 10. Latin Squares (again quite
extensive, including proofs of the existence theorems for 2 and 3
MOLS); 11. One-Factors and One-Factorizations (including starter
techniques); 12. Triple Systems (including the existence theorems for
Steiner and Kirikman triple systems); 13. Room Squares (including
starters, subsquares and the existence theorem); 14. Asymptotic Re-
sults on Balanced Incomplete Block Designs (presenting Wilson's
asymptotic existence theory).
As this list indicates, the "classical" results have been adequately
covered. The selection of advanced topics for such a book reflects, of
course, the tastes of the author but seems to me, though my personal
preferences would have been somewhat different, quite reasonable.
At several points, some contact is made to the frontier of current
research; necessarily, a text such as this cannot provide an overview
of all the many different areas being studied now. Still, the student
who has worked through the material presented here should be well
prepared to go on to more specialized work.
Of course, there are some parts of the text which I think could
have been improved. For instance, it seems a pity to talk about affine
2-designs without mentioning that they are the case of equality in
Bose's classical inequality on resolvable designs, and without stating
the connection to nets. Also, I think that the vast theory of difference
sets would have merited a more detailed treatment, at least have
included some material on Marshall Hall's classical multiplier theory.
A little should have been said about base block constructions for t-
designs with larger t, in particular since they provide practically all
the known interesting examples! When discussing the existence of
cyclic Steiner triple systems, the beautiful result of Colbourn and
Colbourn determining the spectrum of cyclic triple systems in general
should have been stated. A minor point: The Bruck-Ryser-Chowla
theorem, which clearly is a non-existence result, should not be called
the "main existence theorem." Also, I am not always happy with the
references given. For instance, the author quotes three texts on differ-
ence sets, but the most important text available now-the book by E.
S. Lander; "Symmetric Designs: An Algebraic Approach," Cambridge
University Press, 1983-is not referenced. Another missing reference:
In Chapter 6, the author includes his beautiful 1973 result contracting
symmetric designs from affine designs, but he does not give a refer-
ence for the simple proof he presents (which is not his).
In spite of these small misgivings, I still think that this is not only
the best book for a first (but non-trivial) course on combinatorial
designs now available, but really a good text for preparing the reader
for more difficult monographs and research papers. However, for a
deeper and more detailed study for students who are specializing in
this area, there is the book coauthored by the reviewer (T. Beth, D.
Jungnickel and H. Lenz: Design Theory, Cambridge University Press,
1986) which is neither intended nor particularly suitable as a text for
a first course.
Numerical Optimization Techniques
by Yurij G. Evtushenko
Optimization Software, Inc., Publications Division,
New York, 1985
This is a highly theoretical view of a selected set of methods to
solve a variety of numerical optimization problems. The book con-
tains seven chapters, and an examination of these subjects provides a
good picture of the scope of the topics covered. These topics are an
introduction to optimization theory, convergence theorems and their
application to numerical methods, the penalty function method,
numerical methods for solving nonlinear programming problems
using modified Lagrangians, relaxation methods for solving nonlin-
ear programming problems, numerical methods for solving optimal
control problems, and the search for global solutions.
The latter two topics are seldom covered in books on nonlinear
optimization. Control theory is generally viewed as a topic of suffi-
cient additional complexity as to merit separate treatment. Global
optimization is sufficiently difficult that few numerical methods have
proved to have general applicability, and hence the topic is generally
omitted from books attempting to provide a comprehensive unified
view of the subject. Thus a major strength of the book is the inclusion
of these topics.
- ---- II~-- ~II~- ------I I --~----------- I~ -------------~----P----
PAGE 11 numberas~sr teny-ihtNOEBE 18
Also, imbedded in several of the chapters whose topics are listed
above is substantial discussion of the theory and methods for solving
minimax problems. There is substantial literature on these methods,
but unfortunately this literature is seldom included in nonlinear
A further nice feature of the book is the inclusion of methods little
used in the West to analyze methods. For example, Lyapunov func-
tions are used to prove convergence of numerical methods arising
from the solution of differential equations. In general, continuous
trajectories arising from the solution of differential equations are
much better analyzed than is usual in nonlinear optimization texts.
These differences point out markedly the different emphasis of much
of the Russian analysis of numerical optimization. It is this different
viewpoint, sometimes giving rise to different methods, that is the
point of major interest to researchers unaware of this literature.
The book requires a sophisticated mathematical background and
a fair knowledge of numerical optimization methods. The mathemat-
ics is advanced and very terse. Little motivation is given for methods,
and there are virtually no geometric examples. Only the chapter on
control theory has any graphic illustrations. There are few numerical
examples and no problems. All of the above suggest that the book is
not appropriate as a textbook. It could, however, serve as a valuable
reference for a graduate course.
As a reference, it would not in itself be adequate for a standard
course in numerical methods as they are currently taught in the
United States. This stems from the fact that topics considered central
here are sometimes completely omitted. Thus the main value of the
book is as an interesting and useful addition to the reference library of
researchers for the new viewpoints and methods presented and the
wide scope of topics covered.
D. F. Shanno
Application for Membership
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-- --- ----- ~I--
PAGE;~i~a~lll~P 195 2eiM
WE NOTE WITH SADNESS the
recent deaths of two
in computational mathe-
matical programming: William
Orchard-Hays who worked on the
original development of a Simplex
code for the IBM 704 and Darwin
Klingman who made many contri-
butions in network optimization.
Optimization Days 1990 will be
held May 3-4 at the University of
Montreal. Abstract deadline is
January 31. Contact Michel Gen-
dreau and Patrice Marcotte, Centre
de recherche sur les transports,
Univ. de Montreal, C. P. 6128
Succursale A, Montreal, Quebec,
Canada H3C 3J7. Tel: (514) 343-
7435...A conference on Computer-
Aided Scheduling of Public Trans-
port will also be held in Montreal
August 19-23. Contact Martin
Desrochers at the above address.
The first ORSA conference on OR
in Telecommunications will be
held March 12-14, 1990 in Boca
Raton, Florida. Contact Clyde
Monma, Bell Communications
Research, 445 South Street, Morris-
town NJ 07690-1910. Tel: (201) 829-
4428; E-mail: email@example.com.
Deadline for the next OPTIMA is
February 1, 1990.
Books for review should be
sent to the Book Review Editor,
Prof. Dr. Achim Bachem,
Mathematiches Institute der
Universitiit zu Kiln,
Weyertal 86-90, D-5000 K61n,
Journal contents are subject
to change by the publisher.
Donald W. Hear, EDITOR
Achim Bachem, ASSOCIATE EDITOR
PUBLISHED BY THE MATHEMATICAL
PROGRAMMING SOCIETY AND
PUBLICATION SERVICES OF THE
COLLEGE OF ENGINEERING,
UNIVERSITY OF FLORIDA.
Elsa Drake, DESIGNER
P T I M A
MATHEMATICAL PROGRAMMING SOCIETY
303 Weil Hall
College of Engineering
University of Florida
Gainesville, Florida 32611 USA
FIRST CLASS MAIL
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number twen l-eight