Algorithms and Order

1. Front Matter

   Pages i-x

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2. Graphical Data Structures

   1. Front Matter

      Pages 1-1

      PDF

   2. Graphical Data Structures for Ordered Sets

      • Ivan Rival

      Pages 3-31

   3. Lattices in Data Analysis: How to Draw Them with a Computer

      • Rudolf Wille

      Pages 33-58

   4. A Computer Program for Orthomodular Lattices

      • William David Miller

      Pages 59-102

3. Computational Complexity

   1. Front Matter

      Pages 103-103

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   2. Computationally Tractable Classes of Ordered Sets

      • Rolf H. Möhring

      Pages 105-193

   3. The Complexity of Orders

      • M. D. Atkinson

      Pages 195-230

   4. The Calculation of Invariants for Ordered Sets

      • V. Bouchitte, M. Habib

      Pages 231-279

4. Sorting and Scheduling

   1. Front Matter

      Pages 281-281

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   2. Data Manipulations Based on Orderings

      • J. Ian Munro

      Pages 283-306

   3. Preemptive Scheduling

      • N. W. Sauer, M. G. Stone

      Pages 307-323

5. Enumeration

   1. Front Matter

      Pages 325-325

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   2. Enumeration of Ordered Sets

      • Mohamed H. El-Zahar

      Pages 327-352

   3. Laws in Logic and Combinatorics

      • Kevin J. Compton

      Pages 353-383

6. Geometry

   1. Front Matter

      Pages 385-385

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   2. Partial Orders and Euclidean Geometry

      • Jorge Urrutia

      Pages 387-434

7. Decision Making

   1. Front Matter

      Pages 435-435

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   2. Human Decision Making and Ordered Sets

      • Peter C. Fishburn

      Pages 437-465

8. Problem Sessions

   1. Front Matter

      Pages 467-467

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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.

• Scheduling
• algorithms
• ants
• combinatorics
• complexity
• data structures
• geometry
• logic
• sets
• sorting

• Departments of Computer Science and Mathematics, University of Ottawa, Ottawa, Canada

  Ivan Rival

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