Improving on Best-of-Many-Christofides for T-tours

by   Vera Traub, et al.

The T-tour problem is a natural generalization of TSP and Path TSP. Given a graph G=(V,E), edge cost c: E →ℝ_≥ 0, and an even cardinality set T⊆ V, we want to compute a minimum-cost T-join connecting all vertices of G (and possibly containing parallel edges). In this paper we give an 11/7-approximation for the T-tour problem and show that the integrality ratio of the standard LP relaxation is at most 11/7. Despite much progress for the special case Path TSP, for general T-tours this is the first improvement on Sebő's analysis of the Best-of-Many-Christofides algorithm (Sebő [2013]).


page 1

page 2

page 3

page 4


Polynomial Integrality Gap of Flow LP for Directed Steiner Tree

In the Directed Steiner Tree (DST) problem, we are given a directed grap...

Threshold Rounding for the Standard LP Relaxation of some Geometric Stabbing Problems

In the rectangle stabbing problem, we are given a set of axis-aligned r...

Fast Approximations for Metric-TSP via Linear Programming

We develop faster approximation algorithms for Metric-TSP building on re...

Breaching the 2-Approximation Barrier for the Forest Augmentation Problem

The basic goal of survivable network design is to build cheap networks t...

A Small Improvement to the Upper Bound on the Integrality Ratio for the s-t Path TSP

In this paper we investigate the integrality ratio of the standard LP re...

Hardness of Minimum Barrier Shrinkage and Minimum Activation Path

In the Minimum Activation Path problem, we are given a graph G with edge...

Improving the dilation of a metric graph by adding edges

Most of the literature on spanners focuses on building the graph from sc...