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ICALP
2011
Springer

Steiner Transitive-Closure Spanners of Low-Dimensional Posets

13 years 2 months ago
Steiner Transitive-Closure Spanners of Low-Dimensional Posets
Given a directed graph G = (V, E) and an integer k ≥ 1, a Steiner k-transitive-closure-spanner (Steiner k-TC-spanner) of G is a directed graph H = (VH , EH ) such that (1) V ⊆ VH and (2) for all vertices v, u ∈ V , the distance from v to u in H is at most k if u is reachable from v in G, and ∞ otherwise. Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners of directed acyclic graphs or, equivalently, partially ordered sets. We study the relationship between the dimension of a poset and the size, denoted Sk, of its sparsest Steiner k-TC-spanner. We present a nearly tight lower bound on S2 for d-dimensional directed hypergrids. Our bound is derived from an explicit dual solution to a linear programming relaxation of the 2-TC-spanner problem. We also give an efficient construction of Steiner 2-TC-spanners, of size matching the lower bound, for all low-dimensional posets. Finally, we present a nearly tight lower ...
Piotr Berman, Arnab Bhattacharyya, Elena Grigoresc
Added 29 Aug 2011
Updated 29 Aug 2011
Type Journal
Year 2011
Where ICALP
Authors Piotr Berman, Arnab Bhattacharyya, Elena Grigorescu, Sofya Raskhodnikova, David P. Woodruff, Grigory Yaroslavtsev
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