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APPROX
2015
Springer

On Approximating Node-Disjoint Paths in Grids

7 years 11 months ago
On Approximating Node-Disjoint Paths in Grids
In the Node-Disjoint Paths (NDP) problem, the input is an undirected n-vertex graph G, and a collection {(s1, t1), . . . , (sk, tk)} of pairs of vertices called demand pairs. The goal is to route the largest possible number of the demand pairs (si, ti), by selecting a path connecting each such pair, so that the resulting paths are node-disjoint. NDP is one of the most basic and extensively studied routing problems. Unfortunately, its approximability is far from being wellunderstood: the best current upper bound of O( √ n) is achieved via a simple greedy algorithm, while the best current lower bound on its approximability is Ω(log1/2−δ n) for any constant δ. Even for seemingly simpler special cases, such as planar graphs, and even grid graphs, no better approximation algorithms are currently known. A major reason for this impasse is that the standard technique for designing approximation algorithms for routing problems is LP-rounding of the standard multicommodity flow relaxat...
Julia Chuzhoy, David H. K. Kim
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where APPROX
Authors Julia Chuzhoy, David H. K. Kim
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