A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Orienteering and Discounted-Reward TSP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A Recursive Greedy Algorithm for Walks in Directed Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
Mathematics of Operations Research
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved approximations for buy-at-bulk and shallow-light k-steiner trees and (k,2)-subgraph
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
An improved integrality gap for asymmetric TSP paths
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
| Hi-index | 0.00 |
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 Ω(k/ log2 k). We also show a simple O(log2 n/ log log n)-approximation algorithm for the k-Tour problem. The best previously known approximation algorithms achieved min(O(log3 k),O(log2 nċlog k/ log log n))-approximation in polynomial time, and O(log2 k)-approximation in quasipolynomial time.