Given a simple graph G = (V, E), the goal is to find a smallest set F of new edges such that G = (V, E union F) is k-edge-connected and simple. Very recently this problem was shown to be NP-hard by the second author. In this paper we prove that if OPTPk is high enough - depending on k only - then OPTSk = OPTPk holds, where OPTSk (OPTPk) is the size of an optimal solution of the augmentation problem with (without) the simplicity-preserving requirement, respectively. Furthermore, OPTSk-OPTPk≤g(k) holds for a certain (quadratic) function of k. Based on these results an algorithm is given which computes an optimal solution in time O(n4) for any fixed k. Most of these results are extended to the case of non-uniform demands, as well.
|Number of pages||10|
|Journal||Annual Symposium on Foundations of Computer Science - Proceedings|
|Publication status||Published - Dec 1 1997|
|Event||Proceedings of the 1997 38th IEEE Annual Symposium on Foundations of Computer Science - Miami Beach, FL, USA|
Duration: Oct 20 1997 → Oct 22 1997
ASJC Scopus subject areas
- Hardware and Architecture