Complexity and inapproximability results for the Power Edge Set problem

Sonia Toubaline, Claudia D’Ambrosio, Leo Liberti, Pierre Louis Poirion, Baruch Schieber, Hadas Shachnai

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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)-ϵ, for any ϵ> 0. On the positive side we prove that PES problem is solvable in polynomial time for trees and grids.

Original languageEnglish (US)
Pages (from-to)895-905
Number of pages11
JournalJournal of Combinatorial Optimization
Issue number3
StatePublished - Apr 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


  • Inapproximability
  • NP-hardness
  • PMU placement problem
  • Power Edge Set


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