CONTENTS: D.D. Dawson: Measure-valued Markov Processes.- B. Maisonneuve: Processus de Markov: Naissance, Retournement, Regeneration.- J. Spencer: Nine lectures on Random Graphs

In February 1992, I defended my doctoral thesis: Engineering Optimiza tion - selected contributions (IMSOR, The Technical University of Den mark, 1992, p. 92). This dissertation presents retrospectively my central contributions to the theoretical and applied aspects of optimization. When I had finished my thesis I became interested in editing a volume related to a new expanding area of applied optimization. I considered several approaches: simulated annealing, tabu search, genetic algorithms, neural networks, heuristics, expert systems, generalized multipliers, etc. Finally, I decided to edit a volume related to simulated annealing. My main three reasons for this choice were the following: (i) During the last four years my colleagues at IMSOR and I have car ried out several applied projects where simulated annealing was an essential. element in the problem-solving process. Most of the avail able reports and papers have been written in Danish. After a short review I was convinced that most of these works deserved to be pub lished for a wider audience. (ii) After the first reported applications of simulated annealing (1983- 1985), a tremendous amount of theoretical and applied work have been published within many different disciplines. Thus, I believe that simulated annealing is an approach that deserves to be in the curricula of, e.g. Engineering, Physics, Operations Research, Math ematical Programming, Economics, System Sciences, etc. (iii) A contact to an international network of well-known researchers showed that several individuals were willing to contribute to such a volume."

This book is about orthomorphisms and complete mappings of groups, and related constructions of orthogonal latin squares. It brings together, for the first time in book form, many of the results in this area. The aim of this book is to lay the foundations for a theory of orthomorphism graphsof groups, and to encourage research in this area. To this end, many directions for future research are suggested. The material in this book should be accessible to any graduate student who has taken courses in algebra (group theory and field theory). It will mainly be useful in research on combinatorial design theory, group theory and field theory.

This volume contains the 22 papers accepted for presentation at the Third Annual Symposium on Combinatorial Pattern Matching held April 29 to May 1, 1992, in Tucson, Arizona; it constitutes the first conference proceedings entirely devoted to combinatorial pattern matching (CPM). CPM deals withissues of searching and matching of strings and other more complicated patterns such as trees, regular expressions, extended expressions, etc. in order to derive combinatorial properties for such structures. As an interdisciplinary field of growing interest, CPM is related to research in information retrieval, pattern recognition, compilers, data compression, and program analysis as well as to results, problems and methods from combinatorial mathematics and molecular biology.

An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occaisionally mentioned.

One way to advance the science of computational geometry is to make a comprehensive study of fundamental operations that are used in many different algorithms. This monograph attempts such an investigation in the case of two basic predicates: the counterclockwise relation pqr, which states that the circle through points (p, q, r) is traversed counterclockwise when we encounter the points in cyclic order p, q, r, p, ...; and the incircle relation pqrs, which states that s lies inside that circle if pqr is true, or outside that circle if pqr is false. The author, Donald Knuth, is one of the greatest computer scientists of our time. A few years ago, he and some of his students were looking at amap that pinpointed the locations of about 100 cities. They asked, "Which ofthese cities are neighbors of each other?" They knew intuitively that some pairs of cities were neighbors and some were not; they wanted to find a formal mathematical characterization that would match their intuition.This monograph is the result.

This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new.

A famous theorem in the theory of linear spaces states that every finite linear space has at least as many lines as points. This result of De Bruijn and Erd-s led to the conjecture that every linear space with "few lines" canbe obtained from a projective plane by changing only a small part of itsstructure. Many results related to this conjecture have been proved in the last twenty years. This monograph surveys the subject and presents several new results, such as the recent proof of the Dowling-Wilsonconjecture. Typical methods used in combinatorics are developed so that the text can be understood without too much background. Thus the book will be of interest to anybody doing combinatorics and can also help other readers to learn the techniques used in this particular field.

These proceedings reflect the main activities of the Paris S minaire d'Alg bre 1989-1990, with a series of papers in Invariant Theory, Representation Theory and Combinatorics. It contains original works from J. Dixmier, F. Dumas, D. Krob, P. Pragacz and B.J. Schmid, as well as a new presentation of Derived Categories by J.E. Bj rk and as introduction to the deformation theory of Lie equations by J.F. Pommaret. J. Dixmier: Sur les invariants du groupe sym trique dans certaines repr sentations II.- B.J. Schmid: Finite groups and invariant theory.- J.E. Bj rk: Derived categories.- P. Pragacz: Algebro-Geometric applications of Schur S- and Q-polynomials.- F. Dumas: Sous-corps de fractions rationnelles des corps gauches de s ries de Laurent.- D. Krob: Expressions rationnelles sur un anneau.- J.F. Pommaret: Deformation theory of algebraic and Geometric structures.- M. van den Bergh: Differential operators on semi-invariants for tori and weighted projective spaces.

The AAECC conferences focus on the algebraic aspects of modern computer science, which includes the most up-to-date and advanced topics. The topic of error-correcting codes is one where theory and implementation are unifiedinto a subject both of mathematical beauty and of practical importance. Algebraic algorithms are not only interesting theoretically but also important in computer and communication engineering and many other fields. This volume contains the proceedings of the 9th AAECC conference, held in New Orleans, LA, in October 1991. Researchers from Europe, America, Japan and other regions of the world presented papers at the conference. The papers present new results of recent theoretical and application-oriented research in the field.

This book presents a selection of the papers presented at EUROCODE '90, the symposium on coding theory held in Udine, Italy, November 1990. It gives the state of the art on coding in Europe and ranges from theoretical top- ics like algebraic geometry and combinatorial coding to applications like modulation, real-space decoding and VLSI implementation. The book is divided into eight sections: - Algebraic codes - Combinatorial codes - Geometric codes - Protection of information - Convolutional codes - Information theory - Modulation - Applications of coding. Five of the sections are introduced by an invited contribution.

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the L vy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

Several geometric problems can be formulated in terms of the arrangement of a collection of curves in a plane, which has made this one of the most widely studied topics in computational geometry. This book, first published in 1991, presents a study of various problems related to arrangements of lines, segments, or curves in the plane. The first problem is a proof of almost tight bounds on the length of (n,s)-Davenport-Schinzel sequences, a technique for obtaining optimal bounds for numerous algorithmic problems. Then the intersection problem is treated. The final problem is improving the efficiency of partitioning algorithms, particularly those used to construct spanning trees with low stabbing numbers, a very versatile tool in solving geometric problems. A number of applications are also discussed. Researchers in computational and combinatorial geometry should find much to interest them in this book.

Parallelism or concurrency is one of the fundamental concepts in computer science. But in spite of its importance, theoretical methods to handle concurrency are not yet sufficiently developed. This volume presents a comprehensive study of Mazurkiewicz' trace theory from an algebraic-combinatorial point of view. This theory is recognized as an important tool for a rigorous mathematical treatment of concurrent systems. The volume covers several different research areas, and contains not only known results but also various new results published nowhere else. Chapter 1 introduces basic concepts. Chapter 2 gives a straight path to Ochmanski's characterization of recognizable trace languages and to Zielonka's theory of asynchronous automata. Chapter 3 applies the theory of traces to Petri nets. A kind of morphism between nets is introduced which generalizes the concept of synchronization. Chapter 4 provides a new bridge between the theory of string rewriting and formal power series. Chapter 5 is an introduction to a combinatorial theory of rewriting on traces which can be used as an abstract calculus for transforming concurrent processes.

This volume presents papers from the 2nd Scandinavian Workshop on Algorithm Theory. The contributions describe original research on algorithms and data structures, in all areas, including combinatorics, computational geometry, parallel computing, and graph theory. The majority of the papers focus on the design and complexity analysis of: data structures, text algorithms, and sequential and parallel algorithms for graph problems and for geometric problems. Examples of tech- niques presented include: - efficient ways to find approximation algorithms for the maximum independent set problem and for graph coloring; - exact estimation of the expected search cost for skip lists; - construction of canonical representations of partial 2-trees and partial 3-trees in linear time; - efficient triangulation of planar point sets and convex polygons.

The fields of integer programming and combinatorial optimization continue to be areas of great vitality, with an ever increasing number of publications and journals appearing. A classified bibliography thus continues to be necessary and useful today, even more so than it did when the project, of which this is the fifth volume, was started in 1970 in the Institut fur Okonometrie und Operations Research of the University of Bonn. The pioneering first volume was compiled by Claus Kastning during the years 1970 - 1975 and appeared in 1976 as Volume 128 of the series Lecture Notes in Economics and Mathematical Systems published by the Springer Verlag. Work on the project was continued by Dirk Hausmann, Reinhardt Euler, and Rabe von Randow, and resulted in the publication of the second, third, and fourth volumes in 1978, 1982, and 1985 (Volumes 160, 197, and 243 of the above series). The present book constitutes the fifth volume of the bibliography and covers the period from autumn 1984 to the end of 1987. It contains 5864 new publications by 4480 authors and was compiled by Rabe von Randow. Its form is practically identical to that of the first four volumes, some additions having been made to the subject list.

The central theme of this volume is commutative algebra, with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra. Most of the papers have partly survey character, but are research-oriented, aiming at classification and structural results.

This book contains a selection of papers presented at a Symposium on coding theory: "3 Journees sur le Codage," held November 24-26, 1986, in Cachan near Paris, France. It gives an account of the state of the art of research in France on Coding, ranging from rather theoretical topics like algebraic geometry and combinatorial coding to applications like modulation, real-space decoding and implementation of coding algorithms on microcomputers. The symposium was the second one of this type. With its broad spectrum, it was a unique opportunity for contacts between university and industry on the topics of information and coding theory.

This volume contains the papers which were presented at the second workshop "Computer Science Logic" held in Duisburg, FRG, October 3-7, 1988. These proceedings cover a wide range of topics both from theoretical and applied areas of computer science. More specifically, the papers deal with problems arising at the border of logic and computer science: e.g. in complexity, data base theory, logic programming, artificial intelligence, and concurrency. The volume should be of interest to all logicians and computer scientists working in the above fields.

The problem of uniform distribution of sequences initiated by Hardy, Little wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.

This volume presents the proceedings of the 14th International Workshop on Graph-Theoretic Concepts in Computer Science (WG '88), held from June 15 to 17, 1988 in Amsterdam, The Netherlands. It contains 31 papers on new or current developments in the area of graph-based algorithms. The topics covered include e.g. structural graph theory, parallel graph algorithms, graph-based modeling (in database theory and VLSI), computational geometry and applied graph theory. The book contains the revised versions of all the papers presented at the workshop. The revisions are based on comments and suggestions received by the authors during and after the workshop.

This volume presents the proceedings of the 2nd International Workshop on Distributed Algorithms, held July 8-10, 1987, in Amsterdam, The Netherlands. It contains 29 papers on new developments in the area of the design and analysis of distributed algorithms. The topics covered include, e.g. algorithms for distributed consensus and agreement in networks, connection management and topology update schemes, election and termination detection protocols, and other issues in distributed network control.

This text is an attempt to outline the basic facts concerning KekulEURO structures in benzenoid hydrocarbons: their history, applica tions and especially enumeration. We further pOint out the numerous and often quite remarkable connections between this topic and various parts of combinatorics and discrete mathematics. Our book is primarily aimed toward organic and theoretical chemists interested in the enume ration of Kekule structures of conjugated hydrocarbons as well as to scientists working in the field of mathematical and computational chemistry. The book may be of some relevance also to mathematicians wishing to learn about contemporary applications of combinatorics, graph theory and other branches of discrete mathematics. In 1985, when we decided to prepare these notes for publication, we expected to be able to give a complete account of all known combi natorial formulas for the number of Kekule structures of benzenoid hydrocarbons. This turned out to be a much more difficult task than we initially realized: only in 1986 some 60 new publications appeared dealing with the enumeration of Kekule structures in benzenoids and closely related topics. In any event, we believe that we have collec ted and systematized the essential part of the presently existing results. In addition to this we were delighted to see that the topics to*which we have been devoted in the last few years nowadays form a rapidly expanding branch of mathematical chemistry which attracts the attention of a large number of researchers (both chemists and mathematicians).

This volume contains the presentations of the Fifth Symposium on Theoretical Aspects of Computer Science (STACS 88) held at the University of Bordeaux, February 11-13, 1988. In addition to papers presented in the regular program the volume contains abstracts of software systems demonstrations which were included in this conference series in order to show applications of research results in theoretical computer science. The papers are grouped into the following thematic sections: algorithms, complexity, formal languages, rewriting systems and abstract data types, graph grammars, distributed algorithms, geometrical algorithms, trace languages, semantics of parallelism.