Covering problems in edge- and node-weighted graphs

Fukunaga, Takuro

doi:10.1016/j.disopt.2016.03.001

Cited by 10 publications

(2 citation statements)

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“…Let us mention that the idea on formulating our LP relaxation is potentially useful for other covering problems. The author pointed out in his recent work [6] that a natural LP relaxation has a large integrality gap for many covering problems in node-weighted graphs. He also presented several tight approximation algorithms using the LP relaxations designed based on the idea we propose in the present paper.…”

Section: Lp Relaxationmentioning

confidence: 99%

“…Note: In [6], the author applied a similar idea of lifting LP relaxations for solving several covering problems in edge-and node-weighted graphs. He defined a new LP relaxation by replacing edge variables by variables corresponding to pairs of edges and constraints, and showed that the new LP relaxation has better integrality gap than the original one.…”

Section: Lp Relaxation For Prize-collecting Augmentation Problemmentioning

confidence: 99%

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Spider covers for prize-collecting network activation problem

Fukunaga

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the network activation problem, each edge in a graph is associated with an activation function that decides whether the edge is activated from weights assigned to its end nodes. The feasible solutions of the problem are node weights such that the activated edges form graphs of required connectivity, and the objective is to find a feasible solution minimizing its total weight. In this paper, we consider a prize-collecting version of the network activation problem and present the first nontrivial approximation algorithms. Our algorithms are based on a new linear programming relaxation of the problem. They round optimal solutions for the relaxation by repeatedly computing node weights activating subgraphs, called spiders. For the problem with element-and nodeconnectivity requirements, we also present a new potential function on uncrossable biset families and use it to analyze our algorithms. v∈V w(v), denoted by w(V ). We assume throughout the paper that G is undirected even though the problem

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Section: Lp Relaxationmentioning

confidence: 99%

Section: Lp Relaxation For Prize-collecting Augmentation Problemmentioning

confidence: 99%