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

（1） It is considered the Updating Minimum Spanning Tree Problem （UMP）， that is， the problem to update the Minimum-weight Spanning Tree （MST） in res\to topology change of network。分布式算法被提议在多个链接被删除和添加后重新构建MST。它的消息复杂性及其理想时间复杂性为0 （m+n·log （t+f））和0 （n+n·log （t+f））相应地，其中n是网络中处理器的数目， t （响应. f）是添加的链接的数目（回答。the number of the old MST）， and m=t+n if f=0， m=e （i. e. e.拓扑变化后网络中的链接数量（其他）。而分布式算法也提出了与处理器删除和添加的交易，如良好的链接。（2） The leader election problem （LEP） in asynchronous complete networks with undetectable fail-stop failures is considered。特别是，它被讨论了当一个全局意义的方向影响的LEP的信息复杂性在故障网络中。对于一个完整的网络，在k处理器的算法自发地启动，并且在f （<n/2）处理器是错误的，如果LEP的消息复杂性是rheta （n+ k. f），则完整的网络具有全球意义的方向。它已经知道LEP需要欧米茄（n.）log k + k·f） message exchanges， if the complete network has no global sense of direction。因此，这个结果表明，LEP的消息复杂性可以被大大减少，因为使用一个全球意义上的方向在错误网络中很好地作为可靠的网络。

(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.