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OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. ..."
Abstract

Cited by 11 (2 self)
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A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
Optimal Independent Spanning Trees on Hypercubes
, 2004
"... Two spanning trees rooted at some vertex r in a graph G are said to be independent if for each vertex v of G, v ≠ r, the paths from r to v in two trees are vertexdisjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. A set of independent spanning trees is ..."
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Cited by 3 (1 self)
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Two spanning trees rooted at some vertex r in a graph G are said to be independent if for each vertex v of G, v ≠ r, the paths from r to v in two trees are vertexdisjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. A set of independent spanning trees is optimal if the average path length of the trees is the minimum. Any kdimensional hypercube has k independent spanning trees rooted at an arbitrary vertex. In this paper, an O(kn) time algorithm is proposed to construct k optimal independent spanning trees on a kdimensional hypercube, where n = 2 k is the number of vertices in a hypercube.
Parallel Construction of Independent Spanning Trees on Multidimensional Tori
 THE 24TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... A set of spanning trees rooted at vertex r in G is called independent spanning trees (IST) if for each vertex v in G, v = r, the paths from v to r in any two trees are different and vertexdisjoint. If the connectivity of G is k, the IST problem is to construct k IST rooted at each vertex. The IST ..."
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A set of spanning trees rooted at vertex r in G is called independent spanning trees (IST) if for each vertex v in G, v = r, the paths from v to r in any two trees are different and vertexdisjoint. If the connectivity of G is k, the IST problem is to construct k IST rooted at each vertex. The IST problem has found applications in faulttolerant broadcasting, but it is still open for general graph with connectivity greater than four. Obokata et al. [IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E79A (1996) 1894–1903] have proved that the IST problem can be solved on multidimensional tori. However, their construction algorithm forbids the possibility of parallel processing. In this paper, we shall propose a parallel algorithm that is based on the Latin square scheme to solve the IST problem on multidimensional tori.