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An efficient algorithm to compute a Steiner set and Steiner tree on trapezoid graphs.(Report)

This paper presents an efficient algorithm to compute a minimum cardinality Steiner set and Steiner tree on trapezoid graphs. The algorithm takes O(m + n[square root of (log C)]) time for a trapezoid graph with n vertices and m edges, where cost of each arc is a non-negative integer number bounded by C.

Keywords and Phrases: Design and analysis of algorithms, Spanning tree, Steiner set, Steiner tree, Trapezoid graph.

1. Introduction

A trapezoid [T.sub.i] is defined by fore corner points [[a.sub.i], [b.sub.i], [c.sub.i], [d.sub.i]], where [a.sub.i]

[FIGURE 1 OMITTED]

graphs and the interval graphs (9). The permutation graphs are obtained in the case where [a.sub.i] = ...

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