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Journal Articles Theoretical Computer Science Year : 2004

Computational aspects of the 2-dimension of partially ordered sets

Abstract

A well-known method to represent a partially ordered set P (order for short) consists in associating to each element of P a subset of a ?xed set S = {1, . . . , k} such that the order relation coincides with subset inclusion. Such an embedding of P into 2S (the lattice of all subsets of S) is called a bit-vector encoding of P. In this article, we focus on computational complexity results. After a synthesis of known results, we come back on the NP-completeness by detailing a proof and enforcing the conclusion with non-approximability ratios. Besides this general result, we investigate the complexity of the 2-dimension for the class of trees. We describe a 4-approximation algorithm for this class. It uses an optimal balancing strategy which solves a conjecture of [KVH97]. Several interesting open problems are listed.

Domains

Other [cs.OH]

Dates and versions

inria-00099966 , version 1 (26-09-2006)

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Michel Habib, Lhouari Nourine, Olivier Raynaud, Eric Thierry. Computational aspects of the 2-dimension of partially ordered sets. Theoretical Computer Science, 2004, 312 (2-3), pp.401-431. ⟨10.1016/j.tcs.2003.10.029⟩. ⟨inria-00099966⟩
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