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It has already been shown that the problem of obtaining an optimal strategy for a general query on a distributed database system is NP-hard. On the other hand, simple queries have been known as one class of queries for which an optimal strategy can be obtained efficiently. So far, it has been shown that if the topology of a computer network is a complete graph, then a strategy with the minimum response time for simple queries can be obtained in O(n²), where n is the number of sites of the network. This paper discusses the problem of obtaining a strategy with the minimum response time for simple queries when the topology of a computer network is a star (in brief, problem RT). We assume that each communication channel of a star network has equal communication capacity, and that each site has an equal capability for data processing. Here, we also assume that the center of a star network is capable of performing so-called broadcasting. In this paper, we present an algorithm called RT of O(n²) time for solving problem RT. Algorithm RT constructs a schedule graph that represents an optimal strategy by using the dynamic programming method. [ABSTRACT FROM AUTHOR]

One of the interesting issues in the management of large computer networks is to partition the network into clusters and then to perform the management for each cluster. This paper presents a basic discussion on the initial clustering problem for a given network. The initial clustering problem C is defined as follows. Given a graphic representation G(V,E), V-n of a network and a set of nodes G-(c)1≤ r ≤ m) &epsive; 1, the graph G is to be partitioned into m connected subgraphs Gi = (Vi, Ei) (1≦i≦m) of G satisfying the following conditions: &o1; V, O C= (c), &o2; V, ≦K (a positive integer); and &o3; the distance between v&epsive; V, and Cx&epsive; C is minimum when x = i. The following results were obtained for the time complexity of the problem C: (1) the initial clustering problem C is in general NP-hard; and (2) the sub-problem obtained by deleting the condition &o2; can be solved in O(n⊃). [ABSTRACT FROM AUTHOR]