Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs

Feige, Uriel; Singh, Mohit

doi:10.1007/978-3-540-74208-1_8

Cited by 51 publications

(53 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This factor finally breaks the Θ(log n) barrier from Frieze et al [12] and subsequent improvements [3,16,11]. Our approach for ATSP has similarities with Christofides' algorithm; we first construct a spanning tree with special properties.…”

Section: Introductionmentioning

confidence: 99%

An O(log n/log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem

Asadpour¹,

Goemans²,

Mądry³

et al. 2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

102

160

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

An O(log n/log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem

Asadpour¹,

Goemans²,

Mądry³

et al. 2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

102

160

View full text Add to dashboard Cite

show abstract

“…This was improved to O(log n) by Chekuri and Pál [6], and the constant was further improved in [9]. The paper [9] also showed that a ρ-approximation algorithm for ATSP can be used to obtain an O(ρ)-approximation algorithm for ATSPP. All these results are combinatorial and do not bound integrality gap of ATSPP.…”

Section: Other Related Workmentioning

confidence: 99%

An Improved Integrality Gap for Asymmetric TSP Paths

2016

Self Cite

View full text Add to dashboard Cite

The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space (V, d) with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V .This problem is closely related to the Asymmetric TSP (ATSP), which seeks to find a tour (instead of an s-t path) visiting all the nodes: for ATSP, a ρ-approximation guarantee implies an O(ρ)-approximation for ATSPP. However, no such connection is known for the integrality gaps of the linear programming relaxations for these problems: the current-best approximation algorithm for ATSPP is O(log n/ log log n), whereas the best bound on the integrality gap of the natural LP relaxation (the subtour elimination LP) for ATSPP is O(log n).In this paper, we close this gap, and improve the current best bound on the integrality gap from O(log n) to O(log n/ log log n). The resulting algorithm uses the structure of narrow s-t cuts in the LP solution to construct a (random) tree spanning tree that can be cheaply augmented to contain an Eulerian s-t walk.We also build on a result of Oveis Gharan and Saberi and show a strong form of Goddyn's conjecture about thin spanning trees implies the integrality gap of the subtour elimination LP relaxation for ATSPP is bounded by a constant. Finally, we give a simpler family of instances showing the integrality gap of this LP is at least 2.

show abstract

“…Cycle covers are often used for designing approximation algorithms for the TSP [5,11,15]. A cycle cover of a graph is a set of vertex-disjoint cycles such that every vertex is part of exactly one cycle.…”

Section: Traveling Salesman Problemmentioning

confidence: 99%

On approximating multicriteria TSP

Manthey

2012

ACM Trans. Algorithms

View full text Add to dashboard Cite

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP).First, we devise randomized approximation algorithms for multi-criteria maximum traveling salesman problems (Max-TSP). For multi-criteria Max-STSP, where the edge weights have to be symmetric, we devise an algorithm with an approximation ratio of 2/3 − ε. For multi-criteria Max-ATSP, where the edge weights may be asymmetric, we present an algorithm with a ratio of 1/2 − ε. Our algorithms work for any fixed number k of objectives. Furthermore, we present a deterministic algorithm for bi-criteria Max-STSP that achieves an approximation ratio of 7/27.Finally, we present a randomized approximation algorithm for the asymmetric multi-criteria minimum TSP with triangle inequality (Min-ATSP). This algorithm achieves a ratio of log n + ε.

show abstract

Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs

Cited by 51 publications

References 14 publications

An O(log n/log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem

An O(log n/log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem

An Improved Integrality Gap for Asymmetric TSP Paths

On approximating multicriteria TSP

Contact Info

Product

Resources

About