Node-weighted Steiner Tree Problem Research Articles

A Nearly Best-Possible Approximation Algorithm for Node-Weighted Steiner Trees

We give the first approximation algorithm for the node-weighted Steiner tree problem. Its performance guarantee is within a constant factor of the best possible unless P̃ ⊇ NP. ( P̃ stands for the complexity class deterministic quasi-polynomial time, or DTIME[ n polylog n ].) Our algorithm generalizes to handle other network-design problems.

The node‐weighted steiner tree problem

AbstractThe general Node‐Weighted Steiner Tree problem is an extension of the standard Steiner Tree problem by the addition of node‐associated weights. This article analyzes a special case of that problem, where the set of nodes, which must be included in the solution tree, consists of a single node, and all node weights are negative. The special case is shown to be NP‐Complete, its integer programming formulation is presented, and heuristic procedures are proposed. Using Lagrangian relaxation and subgradient optimization, tight lower bounds were derived and utilized by a branch and bound algorithm. The effectiveness of the developed procedures is demonstrated by a set of computational experiments.