Fast estimation of diameter and shortest paths (without matrix multiplication)
- Stanford Univ., CA (United States)
Consider the problem of computing all-pairs shortest paths (APSP) in an unweighted, undirected graph G with n vertices and m edges. The recent work of Alon, Galil, and Margalit, Alon, Galil, Margalit, and Naor, and Seidel has led to dramatic progress in devising fast algorithms for this problem. These algorithm are based on formulating the problem in terms of matrices with small integer entries and using fast matrix multiplications. They achieve a time bound of O(n{sup {omega}}){sup 1} where {omega} denotes the exponent in the running time of the matrix multiplication algorithm used. The current best matrix multiplication algorithm is due to Coppersmith and Winograd [CW90] and has {omega} = 2.376. In contrast, the naive algorithm for APSP performs breadth-first searches from each vertex, and requires time {Theta}(nm).
- OSTI ID:
- 416840
- Report Number(s):
- CONF-960121--
- Country of Publication:
- United States
- Language:
- English
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