Compact Formulations of the Steiner Traveling Salesman Problem and Related Problems

TL;DR

This paper adapts compact integer programming formulations from the classic TSP to the Steiner TSP, enabling more efficient solutions for sparse network routing problems.

Contribution

It introduces polynomial-sized formulations for the Steiner TSP by adapting existing compact TSP formulations, extending their applicability.

Findings

Compact formulations reduce computational complexity.

Adaptations are effective for sparse networks.

Potential for improved solving efficiency.

Abstract

The Steiner Traveling Salesman Problem (STSP) is a variant of the Traveling Salesman Problem (TSP) that is particularly suitable when dealing with sparse networks, such as road networks. The standard integer programming formulation of the STSP has an exponential number of constraints, just like the standard formulation of the TSP. On the other hand, there exist several known {\em compact} formulations of the TSP, i.e., formulations with a polynomial number of both variables and constraints. In this paper, we show that some of these compact formulations can be adapted to the STSP. We also briefly discuss the adaptation of our formulations to some closely-related problems.