Efficient Approximate Algorithms for the Beacon Placement and its Dual Problem (Abstract)
Jiexun Wang, Jaeseong Gim, Masahiro Sasaki, Liang Zhao, Hiroshi Nagamochi · 2009
Given a graph and an integer L ¿ 0, the beacon placement problem (BPP) asks to find a minimum set B of nodes such that for all edges e, at least one of the two endpoints of e can be reached from some node (called an L-beacon) in B using at most L edges. In particular, it reduces to the vertex cover problem if L = 0. This problem arises from link-monitoring in computer networks. Generalizing the works of Horton and Lopez-Ortiz (2003) and Kumar and Kaur (2006), Sasaki, Zhao and Nagamochi (2008) formulated the BPP and showed the NP-hardness for all L. They also provided an exact and an approximate algorithm for this problem. In this paper, we first generalize the problem to a robust covering formulation which, for all edges e, asks whether there exist at least reL-beacons that can reach at least one of the two endpoints of e, where re¿ ¿+is a given robustness requirement. Then we propose efficient approximate algorithms for this and its dual problem. Studies on large-scale computer networks show that the proposed algorithms are quite efficient and accurate in practice.