Approximation Algorithms for Stochastic k-TSP

TL;DR

This paper introduces approximation algorithms for the stochastic k-TSP problem, providing bounds on adaptivity gap and offering both adaptive and non-adaptive solutions with logarithmic approximation factors.

Contribution

It presents the first adaptive and non-adaptive approximation algorithms for stochastic k-TSP with provable guarantees and analyzes the adaptivity gap.

Findings

Adaptive algorithm achieves O(log k) approximation.

Non-adaptive algorithm achieves O(log^2 k) approximation.

The adaptivity gap is between e and O(log^2 k).

Abstract

We consider the stochastic $k$-TSP problem where rewards at vertices are random and the objective is to minimize the expected length of a tour that collects reward $k$. We present an adaptive $O(\log k)$-approximation algorithm, and a non-adaptive $O(\log^2k)$-approximation algorithm. We also show that the adaptivity gap of this problem is between $e$ and $O(\log^2k)$.