Related papers: An Improved Approximation Algorithm for TSP in the…
We study the structure of solutions to linear programming formulations for the traveling salesperson problem (TSP). We perform a detailed analysis of the support of the subtour elimination linear programming relaxation, which leads to…
The subtour relaxation of the traveling salesman problem (TSP) plays a central role in approximation algorithms and polyhedral studies of the TSP. A long-standing conjecture asserts that the integrality gap of the subtour relaxation for the…
A long-standing conjecture for the traveling salesman problem (TSP) states that the integrality gap of the standard linear programming relaxation of the TSP is at most 4/3. Despite significant efforts, the conjecture remains open. We…
We study the metric $s$-$t$ path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing $\frac{5}{3}$-approximation factor and presented an algorithm that achieves an approximation factor of…
In this paper, we study the integrality gap of the subtour LP relaxation for the traveling salesman problem in the special case when all edge costs are either 1 or 2. For the general case of symmetric costs that obey triangle inequality, a…
We consider the integrality gap of the subtour LP relaxation of the Traveling Salesman Problem restricted to circulant instances. De Klerk and Dobre conjectured that the value of the optimal solution to the subtour LP on these instances is…
We present a new approximation algorithm for the (metric) prize-collecting traveling salesperson problem (PCTSP). In PCTSP, opposed to the classical traveling salesperson problem (TSP), one may not include a vertex of the input graph in the…
Among various variants of the traveling salesman problem, the s-t-path graph TSP has the special feature that we know the exact integrality ratio, 3/2, and an approximation algorithm matching this ratio. In this paper, we go below this…
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…
We show that for some $\epsilon > 10^{-36}$ and any metric TSP instance, the max entropy algorithm returns a solution of expected cost at most $\frac{3}{2}-\epsilon$ times the cost of the optimal solution to the subtour elimination LP. This…
In the Traveling Salesperson Problem (TSP) we are given a list of locations and the distances between each pair of them. The goal is to find the shortest possible tour that visits each location exactly once and returns to the starting…
Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of the…
We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured…
We design a new LP-based algorithm for the graphic $s$-$t$ path Traveling Salesman Problem (TSP), which achieves the best approximation factor of 1.5. The algorithm is based on the idea of narrow cuts due to An, Kleinberg, and Shmoys. It…
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.…
We study a semidefinite programming relaxation of the traveling salesman problem introduced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unbounded integrality gap. In particular, we give a family of…
In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for instances with $n$ nodes, where $n$…
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the $(1,2)$-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on…