A 1.5-Approximation for Path TSP

05/10/2018
by   Rico Zenklusen, et al.
0

We present a 1.5-approximation for the Metric Path Traveling Salesman Problem (path TSP). All recent improvements on the path TSP crucially exploit a structural property shown by An, Kleinberg, and Shmoys [Journal of the ACM, 2015], namely that narrow cuts with respect to a Held-Karp solution form a chain. We significantly deviate from these approaches by showing the benefit to deal with larger s-t cuts, even though they are much less structured. More precisely, we show that a variation of the dynamic programming idea recently introduced by Traub and Vygen [SODA, 2018] is versatile enough to deal with larger size cuts, by exploiting a seminal result of Karger on the number of near-minimum cuts. This avoids a recursive application of dynamic programming as used by Traub and Vygen, and leads to a considerable simpler algorithm avoiding an additional error term in the approximation guarantee. Because we match the still unbeaten 1.5-approximation guarantee of Christofides' algorithm for TSP, any further progress on the approximability of the path TSP will also lead to an improvement for TSP.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

07/13/2018

Quantum Speedups for Exponential-Time Dynamic Programming Algorithms

In this paper we study quantum algorithms for NP-complete problems whose...
07/24/2019

Reducing Path TSP to TSP

We present a black-box reduction from the path version of the Traveling ...
04/23/2020

Dynamic Programming Approach to the Generalized Minimum Manhattan Network Problem

We study the generalized minimum Manhattan network (GMMN) problem: given...
06/04/2014

Improvement Tracking Dynamic Programming using Replication Function for Continuous Sign Language Recognition

In this paper we used a Replication Function (R. F.)for improvement trac...
12/08/2021

A PTAS for the Min-Max Euclidean Multiple TSP

We present a polynomial-time approximation scheme (PTAS) for the min-max...
11/04/2021

Average Sensitivity of Dynamic Programming

When processing data with uncertainty, it is desirable that the output o...
09/18/2020

Delay Optimization of Combinational Logic by And-Or Path Restructuring

We propose a dynamic programming algorithm that constructs delay-optimiz...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.