On the Metric $s$--$t$ Path Traveling Salesman Problem

On the metric s-t path Traveling Salesman Problem

We study the metric s-t path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing 5 3 -approximation factor and presented an algorithm that achieves an approximation factor of 1+ √ 5 2 ≈ 1.61803. Later [Sebő, IPCO 2013] further improved the approximation factor to 85 . We present a simple, self-contained analysis that unifies both results; our m...

2 Metric Traveling Salesman

The traveling salesman problem is a classical NP-hard problem, and also hard to approximate at all under the assumption P 6= NP. Definition 1. A vertex tour of a graph G is a path which visits all vertices and returns to its starting vertex. This is another name for a Hamiltonian cycle on G. Traveling salesman problems involve finding a tour of undirected graph G with edge weights d(·), which w...

Approximation Algorithms for the Metric Asymmetric Traveling Salesman Problem

The traveling salesman problem (TSP) is a well-known, commonly studied, and very important NP-hard optimization problem in theoretical computer science. It consists of finding a cyclic (i.e., start and stop on the same vertex) tour of minimum cost of a graph G that visits each vertex exactly once; i.e., a Hamiltonian cycle. The undirected or directed graph G has non-negative weights associated ...

The traveling salesman problem

Traveling salesman path problems

In the traveling salesman path problem, we are given a set of cities, traveling costs between city pairs and fixed source and destination cities. The objective is to find a minimum cost path from the source to destination visiting all cities exactly once. In this paper, we study polyhedral and combinatorial properties of a variant we call the traveling salesman walk problem, in which the object...