Abstract
Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.
Highlights
Given a simple connected graph G with n vertices, the spanning tree problem is to find a tree that connects all the vertices of G
Wang et al proposed optimal parallel algorithms for some problems including the spanning tree problem on interval graphs that can be executed in O time with O ( n log n ) processors on the EREW
We propose a parallel algorithm for spanning tree problem on a proper circle trapezoid graph
Summary
Given a simple connected graph G with n vertices, the spanning tree problem is to find a tree that connects all the vertices of G. Wang et al proposed optimal parallel algorithms for some problems including the spanning tree problem on interval graphs that can be executed in O ( log n ) time with O ( n log n ) processors on the EREW. Honma et al developed parallel algorithms for finding a spanning tree on circular permutation graphs [7] and circular trapezoid graphs [8] Both of them take in O ( log n ) time using O ( n log n ). We propose a parallel algorithm for spanning tree problem on a proper circle trapezoid graph. It can run in O ( log n ) time with O ( n log n ).
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