Ebook: Algorithms and Order

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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Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Graphical Data Structures for Ordered Sets....Pages 3-31
Lattices in Data Analysis: How to Draw Them with a Computer....Pages 33-58
A Computer Program for Orthomodular Lattices....Pages 59-102
Front Matter....Pages 103-103
Computationally Tractable Classes of Ordered Sets....Pages 105-193
The Complexity of Orders....Pages 195-230
The Calculation of Invariants for Ordered Sets....Pages 231-279
Front Matter....Pages 281-281
Data Manipulations Based on Orderings....Pages 283-306
Preemptive Scheduling....Pages 307-323
Front Matter....Pages 325-325
Enumeration of Ordered Sets....Pages 327-352
Laws in Logic and Combinatorics....Pages 353-383
Front Matter....Pages 385-385
Partial Orders and Euclidean Geometry....Pages 387-434
Front Matter....Pages 435-435
Human Decision Making and Ordered Sets....Pages 437-465
Front Matter....Pages 467-467
Introduction....Pages 469-469
Order’s Problem List....Pages 471-474
Scheduling....Pages 475-476
The Diagram....Pages 477-479
Linear Extensions....Pages 481-482
Enumeration....Pages 483-486
Sorting....Pages 487-487
Miscellany....Pages 489-491
Back Matter....Pages 493-498

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Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Graphical Data Structures for Ordered Sets....Pages 3-31
Lattices in Data Analysis: How to Draw Them with a Computer....Pages 33-58
A Computer Program for Orthomodular Lattices....Pages 59-102
Front Matter....Pages 103-103
Computationally Tractable Classes of Ordered Sets....Pages 105-193
The Complexity of Orders....Pages 195-230
The Calculation of Invariants for Ordered Sets....Pages 231-279
Front Matter....Pages 281-281
Data Manipulations Based on Orderings....Pages 283-306
Preemptive Scheduling....Pages 307-323
Front Matter....Pages 325-325
Enumeration of Ordered Sets....Pages 327-352
Laws in Logic and Combinatorics....Pages 353-383
Front Matter....Pages 385-385
Partial Orders and Euclidean Geometry....Pages 387-434
Front Matter....Pages 435-435
Human Decision Making and Ordered Sets....Pages 437-465
Front Matter....Pages 467-467
Introduction....Pages 469-469
Order’s Problem List....Pages 471-474
Scheduling....Pages 475-476
The Diagram....Pages 477-479
Linear Extensions....Pages 481-482
Enumeration....Pages 483-486
Sorting....Pages 487-487
Miscellany....Pages 489-491
Back Matter....Pages 493-498
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