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Given an undirected graph G = (V,E) with positive edge weights and two vertices s and t, the next-to-shortest path problem is to find an st-path which length is minimum among all st-paths of lengths strictly larger than the shortest path length. In this paper we give an O(|V|log|V| + |E|) time algorithm for this problem, which improves the previous result of O(|V|2) time for sparse graphs.
Undirected double-loop networks G(n; ± s1, ± s2), where n is the number of its nodes, s1 and s2 are its steps, 1 ≤ s1 < s2 < n / 2 and gcd(n, s1, s2)=1, are important interconnection networks. In this paper, by using the four parameters of the L-shape tile and a solution (x̄,ȳ) of a congruence equation s...
Given a graph G = (V, E) with |V| = n, |E| = m, and a source node s, we consider the problem of finding two disjoint paths from s to two destination nodes t1 and t2 with minimum total length, for every pair nodes t1, t2 ∈ V–{s}. One efficient solution is to transform this problem into the problem of finding shortest pairs of disjoint paths, and use the Suurablle-Tarjan...
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