相关论文: Lift-and-Project Integrality Gaps for the Travelin…
We study the ATSP (Asymmetric Traveling Salesman Problem), and our focus is on negative results in the framework of the Sherali-Adams (SA) Lift and Project method. Our main result pertains to the standard LP (linear programming) relaxation…
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…
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…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the metric Travelling Salesman Problem (TSP) has been an open problem for over thirty years, with little progress made. It is known that $4/3 \leq \alpha \leq 3/2$, and a…
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…
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…
We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant…
We study integrality gap (IG) lower bounds on strong LP and SDP relaxations derived by the Sherali-Adams (SA), Lovasz-Schrijver-SDP (LS+), and Sherali-Adams-SDP (SA+) lift-and-project (L&P) systems for the t-Partial-Vertex-Cover (t-PVC)…
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 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…
We show that the classical LP relaxation of the asymmetric traveling salesman path problem (ATSPP) has constant integrality ratio. If $\rho_{\text{ATSP}}$ and $\rho_{\text{ATSPP}}$ denote the integrality ratios for the asymmetric TSP and…
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 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…
We address the classical Dantzig - Fulkerson - Johnson formulation of the symmetric metric Traveling Salesman Problem and study the integrality gap of its linear relaxation, namely the Subtour Elimination Problem (SEP). This integrality gap…
The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs.…
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 consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP) that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation…
In Asymmetric A Priori TSP (with independent activation probabilities) we are given an instance of the Asymmetric Traveling Salesman Problem together with an activation probability for each vertex. The task is to compute a tour that…
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…
We study the integrality gap of the natural linear programming relaxation for the \textit{Bounded Color Matching} (BCM) problem. We provide several families of instances and establish lower bounds on their integrality gaps and we study how…