Combining Approximation Algorithms for the Prize-Collecting TSP

TL;DR

This paper introduces a novel approximation algorithm for the prize-collecting TSP, achieving a 1.91457-approximation ratio by combining randomized rounding and primal-dual techniques.

Contribution

It presents the first known approximation algorithm with a ratio below 2 for the prize-collecting TSP, integrating two advanced algorithmic strategies.

Findings

Achieves a 1.91457-approximation ratio.

Combines randomized rounding with primal-dual methods.

Improves upon previous approximation bounds.

Abstract

We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and Williamson.