Optimizing mixing in pervasive networks: a graph-theoretic perspective
ESORICS'11 Proceedings of the 16th European conference on Research in computer security
Optimizing mix-zone coverage in pervasive wireless networks
Journal of Computer Security - Research in Computer Security and Privacy: Emerging Trends
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The facility terminal cover problem is a generalization of the vertex cover problem. The problem is to “cover” the edges of an undirected graph G = (V,E) where each edge e is associated with a non-negative demand de. An edge e = u,v is covered if at least one of its endpoint vertices is allocated capacity of at least de. Each vertex v is associated with a non-negative weight wv. The goal is to allocate capacity cv ≥ 0 to each vertex v so that all edges are covered and the total allocation cost, $\sum\limits_{v\in V}w_{v}c_{v}$, is minimized. A recent paper by Xu et al. [Networks 50 (2007), 118-126], studied this problem, and presented a 2e- approximation algorithm for this problem for e the base of the natural logarithm. We generalize here the facility terminal cover problem to the multi-integer set cover, and relate that problem to the set cover problem, which it generalizes, and the multi-cover problem. We present a Δ-approximation algorithm for the multi-integer set cover problem, for Δ the maximum coverage. This demonstrates that even though the multi-integer set cover problem generalizes the set cover problem, the same approximation ratio holds. In the special case of the facility terminal cover problem this yields a 2-approximation algorithm, and with run time dominated by the sorting of the edge demands. This approximation algorithm improves considerably on the result of Xu et al. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009