Introduction to graph theory
Efficient parallel algorithms
Trapezoid graphs and their coloring
Discrete Applied Mathematics
A parallel algorithm for eliminating cycles in undirected graphs
Information Processing Letters
Dominations in trapezoid graphs
Information Processing Letters
An O(log n) parallel algorithm for constructing a spanning tree on permutation graphs
Information Processing Letters
A parallel algorithm for solving the coloring problem on trapezoid graphs
Information Processing Letters
A linear time algorithm for finding depth-first spanning trees on trapezoid graphs
Information Processing Letters
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Efficient parallel algorithms for some graph problems
Communications of the ACM
An optimal PRAM algorithm for a spanning tree on trapezoid graphs
The Korean Journal of Computational & Applied Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
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Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. An optimal parallel algorithm for finding a spanning tree on the trapezoid graph is given by Bera et al., it takes O(log n) time with O(n/log n) processors on the EREW (Exclusive-Read Exclusive-Write) PRAM. Bera et al.'s algorithm is very simple and elegant. Moreover, it can correctly construct a spanning tree when the graph is connected. However, their algorithm can not accept a disconnected graph as an input. Applying their algorithm to a disconnected graph, Concurrent-Write occurs once for each connected component, thus this can not be achieved on EREW PRAM. In this paper we present an O(log n) time parallel algorithm with O(n/log n) processors for constructing a spanning forest on trapezoid graph G on EREW PRAM even if G is a disconnected graph.