Résumé
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 N P-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 328 /325 in the bipartite case (resp. 17/15 −), unless P = N P, (resp. under UGC). We also show that, assuming ET H, there is no 2 o(√ 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.