LP-based solution methods for the asymmetric TSP

نویسنده

  • Vardges Melkonian
چکیده

We consider an LP relaxation for ATSP. We introduce concepts of high-value and high-flow cycles in LP basic solutions and show that the existence of this kind of cycles would lead to constant-factor approximation algorithms for ATSP. The existence of high-flow cycles is motivated by computational results and theoretical observations. (

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Improved Integrality Gap for Asymmetric TSP Paths

The Asymmetric Traveling Salesperson Path (ATSPP) problem 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 visits all the vertices in V . This problem is closely related to the Asymmetric TSP (ATSP) problem, which seeks to find a tour (instead of an s-t path) visiting all the nodes: for ATSP, a ρ-approx...

متن کامل

Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations

Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman Problem (TSP) via LP relaxations. We first consider the s-t path graph-TSP, a critical special case of the metric s-t path TSP. We design a new simple LP-based algorithm for t...

متن کامل

A Small-Order-Polynomial-Sized Linear Program for Solving the Traveling Salesman Problem

We present a polynomial-sized linear program (LP) for the n-city TSP drawing upon “complex flow” modeling ideas by the first two authors who used an O(n)×O(n) model*. Here we have only O(n) variables and O(n) constraints. We do not model explicit cycles of the cities, and our modeling does not involve the city-to-city variables-based, traditional TSP polytope referred to in the literature as “T...

متن کامل

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...

متن کامل

How To Make a Greedy Heuristic for the Asymmetric Traveling Salesman Problem Competitive

It is widely confirmed by many computational experiments that a greedy type heuristics for the Traveling Salesman Problem (TSP) produces rather poor solutions except for the Euclidean TSP. The selection of arcs to be included by a greedy heuristic is usually done on the base of cost values. We propose to use upper tolerances of an optimal solution to one of the relaxed Asymmetric TSP (ATSP) to ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Inf. Process. Lett.

دوره 101  شماره 

صفحات  -

تاریخ انتشار 2007