Approximation Algorithms for the Directed k-Tour and k-Stroll Problems

We consider two natural generalizations of the Asymmetric Traveling Salesman problem: the k-Stroll and the k-Tour problems. The input to the k-Stroll problem is a directed n-vertex graph with nonnegative edge lengths, an integer k, and two special vertices s and t. The goal is to find a minimum-length s-t walk, containing at least k distinct vertices. The k-Tour problem can be viewed as a special case of k-Stroll, where s = t. That is, the walk is required to be a tour, containing some pre-specified vertex s. When k = n, the k-Stroll problem becomes equivalent to Asymmetric Traveling Salesman Path, and k-Tour to Asymmetric Traveling Salesman. Our main result is a polylogarithmic approximation algorithm for the k-Stroll problem. Prior to our work, only bicriteria (O(log2 k), 3)-approximation algorithms have been known, producing walks whose length is bounded by 3OPT, while the number of vertices visited is (k/ log2 k). We also show a simple O(log2 n/ log log n)-approximation algorithm ...

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: MohammadHossein Bateni, Julia Chuzhoy
• Keywords: Algorithms, APPROX 2010, Asymmetric Traveling Salesman, K-Stroll Problem, K-tour Problem