A linear time algorithm to construct a tree 4-spanner on trapezoid graphs

In a graph G, a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in networks and distributed environments. In this paper, we present an algorithm to find a tree 4-spanner on trapezoid graphs in O(n) time, where n is the number of vertices.

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