Given a connected graph G=(V,E) with n vertices, a subgraph G' is an approximate t-spanner of G if, for every u, /spl nu//spl isin/V, the distance between, u and /spl nu/ in G' is at most f(t) times longer than the distance in G, where f(t) is a polynomial function of t and t/spl les/f(t)n. In this paper parallel algorithms for finding approximate t-spanners on both unweighted graphs and weighted graphs with f(t)=O(t/sup k+1/) and f(t)=O(Dt/sup k+1/) respectively are given, where D is the maximum edge weight of a minimum spanning tree of G, k is a fixed constant integer, and 1/spl les/k/spl les/log/sub t/n. Also, an NC algorithm for finding a 2t-spanner on a weighted graph G is presented. The algorithms are for a CRCW PRAM model.
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机译：给定与N顶点的连接图G =（v，e），子图G'是G如果每个U，/ SPL NU // SPL ISIN / V，u和/之间的距离G的近似T扳手SPL NU / IN g'是大多数比G的距离更长的f（t）时间，其中f（t）是t和t / spl les / f（t）> n的多项式函数。在本文中，并行算法用于在两个未加权的图表和具有F（t）= O（t / sup k + 1 /）和f（t）= o（dt / sup k + 1 /）的加权图）上找到近似的t型横向算法给出，其中D是G，K的最小跨度树的最大边缘重量，K是固定恒定整数，1 / SPL LES / K / SPL LES / LOG / SUB T / N.此外，呈现了一种用于在加权图G上找到2T扳手的NC算法。该算法用于CRCW PRAM模型。
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