Improved Complexity for Power Edge Set Problem

  • Benoit DartiesEmail author
  • Annie Chateau
  • Rodolphe Giroudeau
  • Matthias Weller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10765)


We study the complexity of Power Edge Set (PES), a problem dedicated to the monitoring of an electric network. In such context we propose some new complexity results. We show that PES remains \(\mathcal {NP}\)-hard in planar graphs with degree at most five. This result is extended to bipartite planar graphs with degree at most six. We also show that PES is hard to approximate within a factor lower than Open image in new window in the bipartite case (resp. \(17/15-\epsilon \)), unless \(\mathcal {P}=\mathcal {NP}\), (resp. under \(\mathcal {UGC}\)). We also show that, assuming \(\mathcal {ETH}\), there is no \(2^{o(\sqrt{n})}\)-time algorithm and no \(2^{o(k)}n^{O(1)}\)-time parameterized algorithm, where n is the number of vertices and k the number of PMUs placed. These results improve the current best known bounds.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Le2i FRE2005, CNRS, Arts et MétiersUniversity of Bourgogne Franche-ComtéDijonFrance
  2. 2.LIRMM - CNRS UMR 5506MontpellierFrance

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