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An Approximation Algorithm for Minimum Certificate Dispersal Problems Hua ZHENG Shingo OMURA Koichi WADA Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E89-A No.2 pp.551-558 Publication Date: 2006/02/01 Online ISSN: 1745-1337 DOI: 10.1093/ietfec/e89-a.2.551 Print ISSN: 0916-8508 Type of Manuscript: PAPER Category: Graphs and Networks Keyword: public-key based security system, certificate dispersal, approximation algorithm, NP-Complete, Full Text: PDF(191.8KB)>>
Summary: We consider a network, where a special data called certificate is issued between two users, and all certificates issued by the users in the network can be represented by a directed graph. For any two users u and v, when u needs to send a message to v securely, v's public-key is needed. The user u can obtain v's public-key using the certificates stored in u and v. We need to disperse the certificates to the users such that when a user wants to send a message to the other user securely, there are enough certificates in them to get the reliable public-key. In this paper, when a certificate graph and a set of communication requests are given, we consider the problem to disperse the certificates among the nodes in the network, such that the communication requests are satisfied and the total number of certificates stored in the nodes is minimized. We formulate this problem as MINIMUM CERTIFICATE DISPERSAL (MCD for short). We show that MCD is NP-Complete, even if its input graph is restricted to a strongly connected graph. We also present a polynomial-time 2-approximation algorithm MinPivot for strongly connected graphs, when the communication requests satisfy some restrictions. We introduce some graph classes for which MinPivot can compute optimal dispersals, such as trees, rings, and some Cartesian products of graphs. | ||||||||||
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