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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GRAPHICAL DATA STRUCTURES FOR ORDERED SETS
HOW TO DRAW THEM WITH A COMPUTER
A Computer Program for Orthomodular Lattices
COMPUTATIONALLY TRACTABLE CLASSES OF ORDERED SETS
The Complexity of Orders
THE CALCULATION OF INVARIANTS FOR ORDERED SETS
SORTING AND SCHEDULING
HUMAN DECISION MAKING AND ORDERED SETS
ORDERS PROBLEM LIST
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2-dimensional partial orders antichain atoms binary bipartite block canonical decomposition chain characterization circle order class of posets cograph comparability graph complexity components composition concept lattice construction contains corresponding covering graph crossing number data structures defined denote dfgreedy digraph dimension disjoint edge diagram elements equivalent example Figure finite Fishburn FO sentence formula functions given graded posets greedy linear extension Habib implicit data structure induced integer intersect interval graphs interval orders interval posets isomorphism jump number labeled asymptotic probability Lemma line diagram linear extensions logic lower bound maximal maximal elements minimal Möhring N-free partial orders nodes NP-complete number of linear obtained orientation pair partially ordered sets permutation permutation graphs planar points polynomial precedence constraints preemptive scheduling prime proof properties prove relational structures result Rival satisfy scheduling problems semigroup sequence series—parallel partial orders subset substitution decomposition subtrees Theorem theory transitive unlabelled vertex vertices width