Related papers: Karp's patching algorithm on dense digraph

We consider the following question. We are given a dense digraph $D$ with minimum in- and out-degree at least $\alpha n$, where $\alpha>1/2$ is a constant. The edges of $D$ are given edge costs $C(e),e\in E(D)$, where $C(e)$ is an…

We consider the following question. We are given a dense digraph $D_0$ with minimum in- and out-degree at least $\alpha n$, where $\alpha>0$ is a constant. We then add random edges $R$ to $D_0$ to create a digraph $D$. Here an edge $e$ is…

Starting with M(a), an n X n asymmetric cost matrix, Jonker and Volgenannt transformed it into a 2n X 2n symmetric cost matrix, M(s)where M(s) has unusual properties. One such property is that an optimal tour in M(s) yields an optimal tour…

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.…

We prove that any polynomial-time $\alpha(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(\alpha(C))$-approximation algorithm for the mixed and windy Capacitated Arc…

We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation…

We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related {\em maximum path cover} problem, which asks for a collection of vertex disjoint paths that include the maximum number of…

A well-studied continuous model of graphs, introduced by Dearing and Francis [Transportation Science, 1974], considers each edge as a continuous unit-length interval of points. For $\delta \geq 0$, we introduce the problem $\delta$-Tour,…

Let $D$ be a directed graph cellularly embedded in a surface together with non-negative cost on its arcs. Given any integer circulation in $D$, we study the problem of finding a minimum-cost non-negative integer circulation in $D$ that is…

We describe a $\frac{4}{3}$-approximation algorithm for the traveling salesman problem in which the distances between points are induced by graph-theoretical distances in an unweighted graph. The algorithm is based on finding a minimum cost…

Let $H$ be a $k$-graph on $n$ vertices, with minimum codegree at least $n/k + cn$ for some fixed $c > 0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in $H$ or a certificate that none exists.…

We are given a set of points $p_1,\ldots , p_n$ and a symmetric distance matrix $(d_{ij})$ giving the distance between $p_i$ and $p_j$. We wish to construct a tour that minimizes $\sum_{i=1}^n \ell(i)$, where $\ell(i)$ is the {\em latency}…

Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…

It is well-known and easy to show that even the following version of the directed travelling salesman problem is NP-complete: Given a strongly connected complete digraph $D=(V,A)$, a cost function $w: A\rightarrow \{0,1\}$ and a natural…

In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…

The aim of the paper is to compare different approximation algorithms for the travelling salesperson problem. We pick the most popular and widespread methods known in the literature and contrast them with a novel approach (the polygonal…

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 consider the algorithmic decision problem that takes as input an $n$-vertex $k$-uniform hypergraph $H$ with minimum codegree at least $m-c$ and decides whether it has a matching of size $m$. We show that this decision problem is fixed…

Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local…

The symmetric circulant TSP is a special case of the traveling salesman problem in which edge costs are symmetric and obey circulant symmetry. Despite the substantial symmetry of the input, remarkably little is known about the symmetric…