Asymmetric Traveling Salesman Problem on Graphs with Bounded Genus

نویسندگان

  • Shayan Oveis Gharan
  • Amin Saberi
چکیده

The symmetric traveling salesman problem (STSP) is a special case of ATSP in which the cost function is symmetric (i.e. c(u, v) = c(v, u)). Christofides in 1976 [6] discovered a 3/2approximation algorithm for STSP. No better approximation algorithm has since been found for the general symmetric metric case. However, polynomial-time approximation schemes have been found when the distances are shortest paths in a planar graph [13, 1] or a bounded-genus graph [7].

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

A near-optimal approximation algorithm for Asymmetric TSP

5 We present a near-optimal polynomial-time approximation algorithm for the asymmetric 6 traveling salesman problem for graphs of bounded orientable or non-orientable genus. Our al7 gorithm achieves an approximation factor of O(f(g)) on graphs with genus g, where f(n) is the 8 best approximation factor achievable in polynomial time on arbitrary n-vertex graphs. In par9 ticular, the O(log n/ log...

متن کامل

Approximation Algorithms via Contraction DecompositionA preliminary version of this paper appears in Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, January 2007

We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number k of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound depends on k). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained in [Bak94, Epp00, DDO04, DHK05], and it generalizes a...

متن کامل

Approximation algorithms for the traveling salesman problem

We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the in...

متن کامل

An Approximation Algorithm for the Curvature-Constrained Traveling Salesman Problem

We present an approximation algorithm for the Traveling Salesman Problem when the vehicle is constrained to move forward along paths with bounded curvature (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turning radius and Dmin is the minimum E...

متن کامل

Approximation Algorithms for the Dubins' Traveling Salesman Problem

We present an approximation algorithm for the traveling salesman problem when the vehicle is constrained to move forward along paths with bounded curvatures (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turn radius and Dmin is the minimum Euc...

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:
  • CoRR

دوره abs/0909.2849  شماره 

صفحات  -

تاریخ انتشار 2009