Subcubic Cost Algorithms for the All Pairs Shortest Path Problem
نویسندگان
چکیده
منابع مشابه
On the Exponent of the All Pairs Shortest Path Problem
The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even for the very special case of directed graphs with uniform edge lengths. In this paper we give an algor...
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The objective of this paper is to advance the view that solving the all-pairs shortest path (APSP) problem for a chordal graph G is a two-step process: the first step is determining vertex pairs at distance two (i.c., computing C’) and the second step is finding the vcrtcx pairs at distance three or more. The main technical result here is that the APSP problem for a chordal graph can be solved ...
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This paper uses the isoeeciency metric to analyze the scalability of several parallel algorithms for nding shortest paths between all pairs of nodes in a densely connected graph. Parallel algorithms analyzed in this paper have either been previously presented elsewhere or are small variations of them. Scalability is analyzed with respect to mesh, hypercube and shared-memory architectures. We de...
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This paper presents experiences from the implementation of parallel algorithms for the all-pairs shortest path problem. A brief survey of the problem is given and efficient techniques for exploiting the memory hierarchy of parallel computers are described. Comparing the algorithms at a practical level, the importance of issues such as synchronisation and data locality is established.
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In this paper we deal with a directed graph G = (V,E) with non-negative integer edge costs where the edge costs are bounded by c and |V | = n and m = |E|. We show the all pairs shortest path (APSP) problem can be solved in O(mn+ n log(c/n))) time with the data structure of cascading bucket system. The idea for speed-up is to share a single priority queue among n single source shortest path (SSS...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 1998
ISSN: 0178-4617
DOI: 10.1007/pl00009198