Abstract
Trapezoid graphs are a superclass of permutation graphs and interval graphs. This paper presents first parallel algorithms for the independent domination, total domination, connected domination and domination problems in weighted trapezoid graphs. All these algorithms take O( log 2 n) time on a EREW PRAM. The number of processors required is O(max{ n 3 log 2n,n 2.376}) for the independent domination problem, and O(max{ nm 2 log 2n,m 2.376}) for the other domination problems, where m is the number of edges in a trapezoid graph of n vertices.
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