A note on two source location problems

Guy Kortsarz, Zeev Nutov

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We consider Source Location (SL) problems: given a capacitated network G = (V, E), cost c (v) and a demand d (v) for every v ∈ V, choose a min-cost S ⊆ V so that λ (v, S) ≥ d (v) holds for every v ∈ V, where λ (v, S) is the maximum flow value from v to S. In the directed variant, we have demands din (v) and dout (v) and we require λ (S, v) ≥ din (v) and λ (v, S) ≥ dout (v). Undirected SL is (weakly) NP-hard on stars with r (v) = 0 for all v except the center. But, it is known to be polynomially solvable for uniform costs and uniform demands. For general instances, both directed an undirected SL admit a (ln D + 1)-approximation algorithms, where D is the sum of the demands; up to constant this is tight, unless P = NP. We give a pseudopolynomial algorithm for undirected SL on trees with running time O (| V | Δ3), where Δ = maxv ∈ V d (v). This algorithm is used to derive a linear time algorithm for undirected SL with Δ ≤ 3. We also consider the Single Assignment Source Location (SASL) where every v ∈ V should be assigned to a single node s (v) ∈ S. While the undirected SASL is in P, we give a (ln | V | + 1)-approximation algorithm for the directed case, and show that this is tight, unless P = NP.

Original languageEnglish (US)
Pages (from-to)520-525
Number of pages6
JournalJournal of Discrete Algorithms
Volume6
Issue number3
DOIs
StatePublished - Sep 1 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Approximation
  • Flow
  • Location
  • Source

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