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This paper resolves a long-standing open problem on whether the concurrent write capability of parallel random access machine (PRAM) is essential for solving fundamental graph problems like connected components and minimum spanning trees in <italic>O</italic>(log<italic>n</italic>) time. Specifically, we present a new algorithm to solve these problems in(More)
In this paper we consider the problem of computing the connected components of the complement of a given graph. We describe a simple sequential algorithm for this problem, which works on the input graph and not on its complement, and which for a graph on n vertices and m edges runs in optimal O(n+m) time. Moreover, unlike previous linear co-connectivity(More)
In this paper we present a new parallel algorithm for finding the connected components of an undirected graph. On a graph with n vertices and m edges, the algorithm runs in O(log n loglog n) time using n + m processors on an EREW (exclusive-read and exclusive-write) PRAM. Prior to our work, the best known exclusive-write algorithm for this problem requires(More)
The problem of finding the minimum bicon-netted spanning subgraph of an undirected graph is NP-hard. A lot of effort has been made to find biconnected spanning subgraphs that approximate to the minimum one as close as possible. Recently, new polynomial-time (sequential) approximation algorithms have been devised to improve the approximation factor from 2 to(More)