COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Approximability and inapproximability of the minimum certificate dispersal problem
Theoretical Computer Science
Minimum certificate dispersal with tree structures
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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In this paper, we focus on the problem that in an ad hoc network, how to send a message securely between two users using the certificate dispersal system. In this system, special data called certificate is issued between two users and these issued certificates are stored among the network. Our final purpose on this certificate dispersal problem is to construct certificate graphs with lower dispersability cost which indicates the average number of certificates stored in each node in an ad hoc network. As our first step, when a certificate graph is given, we construct two efficient certificate dispersal algorithms for strongly connected graphs and directed graphs in this paper. We can show that for a strongly connected graph G = (V, E) and a directed graph H = (V' E'), new upper bounds on dispersability cost on the average number of certificates stored in one node are O(DG + |E'|/|V|) and O(pGdmax + |E'|/|V'|) respectively, where DG is the diameter of G, dmax is the maximum diameter of strongly connected components of H and pG is the number of strongly connected components of H. Furthermore, we give some new lower bounds for the problem and we also show that our algorithms are optimal for several graph classes.