Efficient Algorithms for the Minimum Connected Domination on Trapezoid Graphs

Abstract

Given the trapezoid diagram, the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in O(m+ n) time [7]; the results is recently improved to be O(n) time by Kohler [5]. For the (vertex) weighted case, finding the minimum weighted connected dominating set in trapezoid graphs can be solved in O(m + n log n) time [11]. Here n (m) denotes the number of vertices (edges) of the trapezoid graph.In this paper, we show a different approach for finding the minimum cardinality connected dominating set in trapezoid graphs using O(n) time. For finding the minimum weighted connected dominating set, we show the problem can be efficiently solved in O(n log log n) time.KeywordsCorner PointPriority QueueMinimum CardinalityPermutation GraphAggregate WeightThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.