Algorithms for Placing Monitors in a Flow Network

Authors:
Francis Chin;Marek Chrobak;Li Yan
Affiliations:
Department of Computer Science, The University of Hong Kong, Pokfulam, Hong Kong,;Department of Computer Science, University of California, Riverside, CA 92521;Department of Computer Science, University of California, Riverside, CA 92521
Venue:
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Year:
2009

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Abstract

In the Flow Edge-Monitor Problem, we are given an undirected graph G = (V ,E ), an integer k 0 and some unknown circulation *** on G . We want to find a set of k edges in G , so that if we place k monitors on those edges to measure the flow along them, the total number of edges for which the flow can be uniquely determined is maximized. In this paper, we first show that the Flow Edge-Monitor Problem is NP-hard, and then we give two approximation algorithms: a 3-approximation algorithm with running time O ((m + n )2) and a 2-approximation algorithm with running time O ((m + n )3), where n = |V | and m = |E |.