On fixed cost k-flow problems

Mohammadtaghi Hajiaghayi, Rohit Khandekar, Guy Kortsarz, Zeev Nutov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In the Fixed Cost k -Flow problem, we are given a graph G = (V,E) with edge-capacities {u e |e ∈E} and edge-costs {c e |e ∈E}, source-sink pair s,t ∈ V, and an integer k. The goal is to find a minimum cost subgraph H of G such that the minimum capacity of an st-cut in H is at least k. We show that Group Steiner is a special case of Fixed Cost k -Flow, thus obtaining the first polylogarithmic lower bound for the problem; this also implies the first non constant lower bounds for the Capacitated Steiner Network and Capacitated Multicommodity Flow problems. We then consider two special cases of Fixed Cost k -Flow. In the Bipartite Fixed-Cost k -Flow problem, we are given a bipartite graph G = (A ∪ B,E) and an integer k > 0. The goal is to find a node subset S ⊆ A ∪ B of minimum size |S| such G has k pairwise edge-disjoint paths between S ∩ A and S ∩ B. We give an O(√k log k) approximation for this problem. We also show that we can compute a solution of optimum size with Ω(k/polylog(n)) paths, where n = |A| + |B|. In the Generalized-P2P problem we are given an undirected graph G = (V,E) with edge-costs and integer charges {b v :v ∈ V}. The goal is to find a minimum-cost spanning subgraph H of G such that every connected component of H has non-negative charge. This problem originated in a practical project for shift design [10]. Besides that, it generalizes many problems such as Steiner Forest, k -Steiner Tree, and Point to Point Connection. We give a logarithmic approximation algorithm for this problem. Finally, we consider a related problem called Connected Rent or Buy Multicommodity Flow and give a log3+ε n approximation scheme for it using Group Steiner techniques.

Original languageEnglish (US)
Title of host publicationApproximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers
PublisherSpringer Verlag
Pages49-60
Number of pages12
ISBN (Print)9783319080000
DOIs
StatePublished - 2014
Event11th International Workshop on Approximation and Online Algorithms, WAOA 2013 - Sophia Antipolis, France
Duration: Sep 5 2013Sep 6 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8447 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Workshop on Approximation and Online Algorithms, WAOA 2013
Country/TerritoryFrance
CitySophia Antipolis
Period9/5/139/6/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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