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Single-Sink Fractionally Subadditive Network Design

Authors Guru Guruganesh, Jennifer Iglesias, R. Ravi, Laura Sanita

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Guru Guruganesh
Jennifer Iglesias
R. Ravi
Laura Sanita

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Guru Guruganesh, Jennifer Iglesias, R. Ravi, and Laura Sanita. Single-Sink Fractionally Subadditive Network Design. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ESA.2017.46

Abstract

We study a generalization of the Steiner tree problem, where we are given a weighted network G together with a collection of k subsets of its vertices and a root r. We wish to construct a minimum cost network such that the network supports one unit of flow to the root from every node in a subset simultaneously. The network constructed does not need to support flows from all the subsets simultaneously.

We settle an open question regarding the complexity of this problem for k=2, and give a 3/2-approximation algorithm that improves over a (trivial) known 2-approximation. Furthermore, we prove some structural results that prevent many well-known techniques from doing better than the known O(log n)-approximation. Despite these obstacles, we conjecture that this problem should have an O(1)-approximation. We also give an approximation result for a variant of the problem where the solution is required to be a path.

Subject Classification

Keywords
  • Network design
  • single-commodity flow
  • approximation algorithms
  • Steiner tree

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