TY - JOUR

T1 - Algorithms for generalized vertex-rankings of partial k-trees

AU - Kashem, Md Abul

AU - Zhou, Xiao

AU - Nishizeki, Takao

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000/6/17

Y1 - 2000/6/17

N2 - A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. A c-vertex-ranking is optimal if the number of labels used is as small as possible. We present sequential and parallel algorithms to find an optimal c-vertex-ranking of a partial k-tree, that is, a graph of treewidth bounded by a fixed integer k. The sequential algorithm takes polynomial-time for any positive integer c. The parallel algorithm takes O(log n) parallel time using a polynomial number of processors on the common CRCW PRAM, where n is the number of vertices in G.

AB - A c-vertex-ranking of a graph G for a positive integer c is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. A c-vertex-ranking is optimal if the number of labels used is as small as possible. We present sequential and parallel algorithms to find an optimal c-vertex-ranking of a partial k-tree, that is, a graph of treewidth bounded by a fixed integer k. The sequential algorithm takes polynomial-time for any positive integer c. The parallel algorithm takes O(log n) parallel time using a polynomial number of processors on the common CRCW PRAM, where n is the number of vertices in G.

KW - Algorithm

KW - Partial k-tree

KW - Separator tree

KW - Treewidth

KW - Vertex-ranking

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U2 - 10.1016/S0304-3975(99)00240-6

DO - 10.1016/S0304-3975(99)00240-6

M3 - Article

AN - SCOPUS:0347269374

VL - 240

SP - 407

EP - 427

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 2

ER -