Study of Co-operative Problem Solving Methods in Distributed Network Environment

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(1) It is considered the Updating Minimum Spanning Tree Problem (UMP), that is, the problem to update the Minimum-weight Spanning Tree (MST) in response to topology change of network. The distributed algorithm is proposed which reconstructs the MST after several links are deleted and added. Its message complexity and its ideal-time complexity are 0 (m+n・log (t+f)) and 0 (n+n・log (t+f)) respectively, where n is the number of processors in the network, t (resp. f) is the number of added links (resp. the number of deleted links of the old MST), and m=t+n if f=0, m=e (i. e. the number of links in the network after topology change) otherwise. And the distributed algorithms is also proposed which deals with deletion and addition of processors as well as links.(2) The leader election problem (LEP) in asynchronous complete networks with undetectable fail-stop failures is considered. Especially, it is discussed whether presence of a global sense of direction affects the message complexity of LEP in faulty networks. For a complete network of n processors where k processors start the algorithm spontaneously and at most f (<n/2) processors are faulty, the message complexity of LEP is rheta (n+k.f) if the complete network has a global sense of direction. It is already known that LEP requires OMEGA (n. log k + k・f) message exchanges, if the complete network has no global sense of direction. Therefore, this result implies that the message complexity of LEP can be greatly reduced by using a global sense of direction in faulty networks as well as in reliable networks.