Computational Graph Theory

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2 Computing Supplementum 7 G. Tinhofer, E. Mayr, H. Noltemeier, M. M. Syslo (eds.) in cooperation with R. Albrecht Computational Graph Theory Springer-Verlag Wien New York

3 Prof. Dr. G. Tinhofer Institut flir Mathematik Technische Universitiit Miinchen Federal Republic of Germany Prof. Dr. E. Mayr Department of Computer Science Stanford University Calif., U.S.A. Prof. Dr. M. M. Syslo Institute of Computer Science University ofwroclaw Poland Prof. Dr. Rudolf Albrecht Institut flir Informatik Universitiit Innsbruck Austria Prof. Dr. H. Noltemeier lnstitut flir Informatik Universitiit Wiirzburg Federal Republic of Germany This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically those oftransiation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks by Springer-Verlag/Wien With 68 Figures ISSN ISBN 13: e-isbn-13 : DOl: / Printed on acid-free paper

4 Preface One ofthe most important aspects in research fields where mathematics is "applied is the construction of a formal model of a real system. As for structural relations, graphs have turned out to provide the most appropriate tool for setting up the mathematical model. This is certainly one of the reasons for the rapid expansion in graph theory during the last decades. Furthermore, in recent years it also became clear that the two disciplines of graph theory and computer science have very much in common, and that each one has been capable of assisting significantly in the development of the other. On one hand, graph theorists have found that many of their problems can be solved by the use of computing techniques, and on the other hand, computer scientists have realized that many of their concepts, with which they have to deal, may be conveniently expressed in the language of graph theory, and that standard results in graph theory are often very relevant to the solution of problems concerning them. As a consequence, a tremendous number of publications has appeared, dealing with graphtheoretical problems from a computational point of view or treating computational problems using graph theoretical concepts. Due to these facts, graph theory and computer science have become so strongly connected that it seems no overstatement to say that in our days a good deal of modern graph theory is part of computer science or, on the other hand again, to say that computer science is at least partially based on graph theory. The purpose ofthis supplementary volume is to draw attention to problems and applications which represent the strong connection between the two disciplines. It contains a collection of invited papers, each devoted to a particular class of graphtheoretical problems and their solution by computational techniques. Although the papers are all written on an expert and not on a teaching level they are supposed to be suitable for a first contact with the contents. The collected papers cover a broad spectrum of graphtheoretical topics. Techniques for hard graph problems, problems on planar graphs, path problems, coloring problems, graphs and orders and several other topics are discussed, as well as computational aspects like data structures, the probabilistic behaviour of algorithms, the design and analysis of parallel algorithms and VLSI-structures. No claim for completeness is made, however, we believe that the collection is representative in the sense that all the main topics of "computational graph theory" are included. February 1990 The Editors

5 Contents Proskurowski, A., Syslo, Mo Mo: Efficient Computations in Tree-Like Graphs 1 Mohring, R. Ho: Graph Problems Related to Gate Matrix Layout and PLA Folding Nishizeki, To: Planar Graph Problems Mayr, Eo Wo: Basic Parallel Algorithms in Graph Theory Helmbold, Do, Mayr, Eo Wo: Applications of Parallel Scheduling Algorithms to Families of Perfect Graphs Faigle, u., Schrader, R.: Orders and Graphs Noltemeier, Ho: Dynamic Partial Orders and Generalized Heaps Faigle, u., Turan, Go: Communication Complexity Rote, Go: Path Problems in Graphs Werra, Do de: Heuristics for Graph Coloring Frieze, A. Mo: Probabilistic Analysis of Graph Algorithms Tinhofer, Go: Generating Graphs Uniformly at Random Monien, B., Sudborough, Ho: Embedding one Interconnection Network in Another