Polytopes, permutation shapes and bin packing

Authors:
Marguerite A. Eisenstein-Taylor
Affiliations:
Department of Mathematics, Brandeis University, Waltham, MA
Venue:
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Year:
2003

Citing 5
Cited 0

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Abstract

We define a partition of the unit hypercube into polytopes. These polytopes correspond to arrangements of a sequence of objects into bins in the NEXT FIT solution to the one-dimensional bin packing problem. The probability that an arrangement appears is given by the volume of the corresponding polytope in the partition. We show that this volume can be calculated as the solution to a problem of permutation enumeration and apply this technique to analyze the behavior of the NEXT FIT algorithm.