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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In this paper, we consider an interesting generalization of the weighted vertex cover problem, called the Facility Terminal Cover (FTC) problem. In the FTC problem, each vertex is associated with a positive weight, each edge is associated with a positive demand, and the objective is to determine a subset of vertices and a capacity for each selected vertex so that the demand of each edge is covered by the capacity of one of its two endpoints and the total weighted capacity of all selected vertices is minimized. The FTC problem is motivated by several key network optimization problems, such as the power assignment problem in ad hoc networks, and could be used as a subroutine to solve such problems. No quality-guaranteed solution is previously known for the FTC problem. In this paper, we present two linear time approximation algorithms for this problem. Our first algorithm achieves deterministically an approximation ratio of 8 by using an interesting rounding technique and a lower-bounding technique. Based on interesting randomization techniques, our second algorithm further improves the approximation ratio to 2e, where e is the natural logarithmic base. The second algorithm can be easily derandomized in quadratic time. Our algorithms are relatively simple and can be easily implemented for networking applications. Experiments show that the two algorithms behave rather similarly, especially in large-size graphs, indicating that the solutions yielded by one or both algorithms are much closer to the optimum. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(1), 118–126 2007