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Journal of Combinatorial Optimization

, Volume 35, Issue 3, pp 895–905 | Cite as

Complexity and inapproximability results for the Power Edge Set problem

  • Sonia Toubaline
  • Claudia D’Ambrosio
  • Leo Liberti
  • Pierre-Louis Poirion
  • Baruch Schieber
  • Hadas Shachnai
Article

Abstract

We consider the single channel PMU placement problem called the Power Edge Set problem. In this variant of the PMU placement problem, (single channel) PMUs are placed on the edges of an electrical network. Such a PMU measures the current along the edge on which it is placed and the voltage at its two endpoints. The objective is to find the minimum placement of PMUs in the network that ensures its full observability, namely measurement of all the voltages and currents. We prove that PES is NP-hard to approximate within a factor (1.12)-\(\epsilon \), for any \(\epsilon > 0\). On the positive side we prove that PES problem is solvable in polynomial time for trees and grids.

Keywords

PMU placement problem Power Edge Set NP-hardness Inapproximability 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Sonia Toubaline
    • 1
    • 2
  • Claudia D’Ambrosio
    • 2
  • Leo Liberti
    • 2
  • Pierre-Louis Poirion
    • 2
  • Baruch Schieber
    • 3
  • Hadas Shachnai
    • 4
  1. 1.Université Paris-Dauphine, PSL Research UniversityCNRS, LAMSADEParisFrance
  2. 2.CNRS LIX, Ecole PolytechniquePalaiseauFrance
  3. 3.IBM T.J. Watson Research CenterNYUSA
  4. 4.Computer Science DepartmentTechnionHaifaIsrael

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