Algorithms and Order

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Springer Science & Business Media, 1989 - 498 pages
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This volume contains the texts of the principal survey papers presented at ALGORITHMS -and ORDER, held· at Ottawa, Canada from June 1 to June 12, 1987. The conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the University of Ottawa, and the Natural Sciences and Engineering Research Council of Canada. We are grateful for this considerable support. Over fifty years ago, the Symposium on Lattice Theory, in Charlottesville, U.S.A., proclaimed the vitality of ordered sets. Only twenty years later the Symposium on Partially Ordered Sets and Lattice Theory, held at Monterey, U.S.A., had solved many of the problems that had been originally posed. In 1981, the Symposium on Ordered Sets held at Banff, Canada, continued this tradition. It was marked by a landmark volume containing twenty-three articles on almost all current topics in the theory of ordered sets and its applications. Three years after, Graphs and Orders, also held at Banff, Canada, aimed to document the role of graphs in the theory of ordered sets and its applications. Because of its special place in the landscape of the mathematical sciences order is especially sensitive to new trends and developments. Today, the most important current in the theory and application of order springs from theoretical computer seience. Two themes of computer science lead the way. The first is data structure. Order is common to data structures.
 

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Table des matières

GRAPHICAL DATA STRUCTURES FOR ORDERED SETS
3
HOW TO DRAW THEM WITH A COMPUTER
33
A Computer Program for Orthomodular Lattices
59
COMPUTATIONAL COMPLEXITY
103
COMPUTATIONALLY TRACTABLE CLASSES OF ORDERED SETS
105
The Complexity of Orders
195
THE CALCULATION OF INVARIANTS FOR ORDERED SETS
231
SORTING AND SCHEDULING
281
DECISION MAKING
435
HUMAN DECISION MAKING AND ORDERED SETS
437
PROBLEM SESSIONS
467
INTRODUCTION
469
ORDERS PROBLEM LIST
471
SCHEDULING
475
THE DIAGRAM
477
LINEAR EXTENSIONS
481

Data Manipulations Based on Orderings
283
PREEMPTIVE SCHEDULING
307
ENUMERATION
325
ENUMERATION OF ORDERED SETS
327
LAWS IN LOGIC AND COMBINATORICS
353
GEOMETRY
385
PARTIAL ORDERS AND EUCLIDEAN GEOMETRY
387
ENUMERATION
483
SORTING
487
MISCELLANY
489
INDEX
493
Index
495
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