DeepAI AI Chat
Log In Sign Up

Asymptotic Optimality of the Greedy Patching Heuristic for Max TSP in Doubling Metrics

by   Vladimir Shenmaier, et al.

The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. We prove that, in the case when the edge weights are induced by a metric space of bounded doubling dimension, asymptotically optimal solutions of the problem can be found by the simple greedy patching heuristic. Taking as a start point a maximum-weight cycle cover, this heuristic iteratively patches pairs of its cycles into one minimizing the weight loss at each step.


page 1

page 2

page 3

page 4


Efficient PTAS for the Maximum Traveling Salesman Problem in a Metric Space of Fixed Doubling Dimension

The maximum traveling salesman problem (Max TSP) is one of the intensive...

Matroidal Approximations of Independence Systems

Milgrom (2017) has proposed a heuristic for determining a maximum weight...

Algorithms for the Maximum Eulerian Cycle Decomposition Problem

Given an Eulerian graph G, in the Maximum Eulerian Cycle Decomposition p...

Analysis of a Greedy Heuristic for the Labeling of a Map with a Time-Window Interface

In this paper, we analyze the approximation quality of a greedy heuristi...

On the Constrained Least-cost Tour Problem

We introduce the Constrained Least-cost Tour (CLT) problem: given an und...

Iteratively reweighted greedy set cover

We empirically analyze a simple heuristic for large sparse set cover pro...

A New Quartet Tree Heuristic for Hierarchical Clustering

We consider the problem of constructing an an optimal-weight tree from t...