A 4-Approximation Algorithm for k-Prize Collecting Steiner Tree Problems

TL;DR

This paper introduces a 4-approximation algorithm for the k-prize collecting Steiner tree problem, combining existing algorithms for related problems and extending applicability to certain traveling salesman problems.

Contribution

It presents a novel 4-approximation algorithm that generalizes previous approaches for related Steiner tree and spanning tree problems.

Findings

Achieves a 4-approximation ratio for the k-prize collecting Steiner tree problem.

Framework extends to specific k-prize collecting traveling salesman problems.

Utilizes two 2-approximation algorithms for related subproblems.

Abstract

This paper studies a 4-approximation algorithm for k-prize collecting Steiner tree problems. This problem generalizes both k-minimum spanning tree problems and prize collecting Steiner tree problems. Our proposed algorithm employs two 2-approximation algorithms for k-minimum spanning tree problems and prize collecting Steiner tree problems. Also our algorithm framework can be applied to a special case of k-prize collecting traveling salesman problems.