Design and Implementation of a Distributed Dual Ascent Algorithm for the Steiner Problem in Graphs

The Steiner Problem in Graphs (SPG) is defined as follows. Given an undirected graph G = (V,E), positive edge costs c and a set T ⊆ V of terminal nodes, find a connected subgraph (V ′, E′) of G with T ⊆ V ′ minimizing ∑ e∈E′ ce. In other words, find a minimum cost tree containing all terminals, possibly also containing some other nodes. The Steiner Problem in Directed Graphs (SPDG) is the case where G is a directed graph and there is a special root terminal r ∈ T . The problem is to find a minimum cost directed tree containing paths from r to every other terminal. Both the SPG and the SPDG are NP-hard. If solutions must be obtained in short time, one must resort to heuristic algorithms like those surveyed in Voss [10].