Journal ArticleDOI
Parallel algorithms for parity graphs
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TLDR
A parallel algorithm to recognize parity graphs and a parallel algorithm for finding the size of a maximum clique which runs in O(log2 n) time with n3log 2 n processors are presented.About:
This article is published in Journal of Algorithms.The article was published on 1991-01-02. It has received 11 citations till now. The article focuses on the topics: Chordal graph & Block graph.read more
Citations
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Journal ArticleDOI
Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition
TL;DR: It is shown that efficient parallel split decomposition induces an efficient parallel parity graph recognition algorithm, a consequence of the result of S. Cicerone and D. Di Stefano that parity graphs are exactly those graphs that can be split decomposed into cliques and bipartite graphs.
Journal ArticleDOI
On the extension of bipartite to parity graphs
TL;DR: In this paper, a different structural property of parity graphs is introduced: split decomposition returns exactly, as building blocks of parity graph, cliques and bipartite graph, and it can be used to provide optimum algorithms for both the recognition problem and the maximum weighted clique.
Journal ArticleDOI
Efficient parallel algorithms on distance hereditary graphs
TL;DR: This paper presents efficient parallel algorithms for finding a minimum weighted connected dominating set, a Minimum weighted Steiner tree, which take O(log n) time using O(n + m) processors on CRCW PRAM, where n and m are the number of vertices and edges of a given graph, respectively.
Journal ArticleDOI
P_4-Colorings and P_4-Bipartite Graphs
Chính T. Hoàng,Van Bang Le +1 more
TL;DR: The Strong Perfect Graph Conjecture (SPGC) for P_4-bipartite bipartite graphs was shown to be true for all P_3-free 2-colorable graphs with at most one color class meeting every P 4 at the midpoint as discussed by the authors.
P 4 -Free Colorings and P 4 -Bipartite Graphs
TL;DR: The Strong Perfect Graph Conjecture (SPGC) conjecture was introduced by Brown and Corneil as discussed by the authors, which states that a graph is perfect if and only if it has no induced cycle of odd length at least or the complement of such a cycle.
References
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Complement reducible graphs
TL;DR: It is shown that this family of graphs can be uniquely represented by a tree where the leaves of the tree correspond to the vertices of the graph.
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The Parallel Evaluation of General Arithmetic Expressions
TL;DR: It is shown that arithmetic expressions with n ≥ 1 variables and constants; operations of addition, multiplication, and division; and any depth of parenthesis nesting can be evaluated in time 4 log 2 + 10(n - 1) using processors which can independently perform arithmetic operations in unit time.
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A linear recognition algorithm for cographs
TL;DR: This paper presents a linear time algorithm for recognizing cographs and constructing their cotree representation, which is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general.
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Computing connected components on parallel computers
TL;DR: A parallel algorithm which uses n=2 processors to find the connected components of an undirected graph with n vertices in time in time O(n), which can be used to finding the transitive closure of a symmetric Boolean matrix.
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A simple parallel tree contraction algorithm
TL;DR: In this paper, a simple reduction from the tree contraction problem to the list ranking problem is presented, which takes O(log n) time for a tree with n nodes, using O( n log n ) EREW processors Thus tree contraction can be done as efficiently as list ranking.