Light Spanner and Monotone Tree

TL;DR

This paper introduces an efficient algorithm for constructing light spanners in bounded catwidth graphs, utilizing a new data structure called monotone tree, with applications in metric TSP.

Contribution

The paper extends previous work on light spanners from bounded pathwidth graphs to bounded catwidth graphs using monotone trees.

Findings

Developed an efficient algorithm for light spanners in bounded catwidth graphs.

Extended the applicability of monotone trees to broader graph classes.

Enhanced approximation techniques for metric TSP problems.

Abstract

In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem). We have developed an efficient algorithm for light spanners in bounded pathwidth graphs, based on an intermediate data structure called monotone tree. In this paper, we extended the results to include bounded catwidth graphs.