Constructing minimal spanning/Steiner trees with bounded path length

This paper presents an exact algorithm and two heuristics for solving the Bounded path length Minimal Spanning Tree (BMST) problem. The exact algorithm which is based on iterative negative-sum-exchange(s) has polynomial space complexity and is hence more practical than the method presented by Gabow. The first heuristic method (BKRUS) is based on the classical Kruskal MST construction. For any given value of parameter ε, the algorithm constructs a routing tree with the longest interconnection path length at most (1+ε).R, and empirically with cost at most 1.19 times cost (BMST*) where R is the length of the direct path from the source to the farthest sink and BMST* is the optimal bounded path length MST. The second heuristic combines BKRUS and negative-sum-exchange(s) of depth 2 to improve results. Extensions of these techniques to the bounded path length Minimal Steiner Trees, using the Elmore delay model are presented as well. Empirical results demonstrate the effectiveness of these algorithms on a large benchmark set