# Replica Placement on Bounded Treewidth Graphs

## TL;DR

This paper studies the replica placement problem on graphs with bounded treewidth, providing an approximation algorithm whose performance depends linearly on the treewidth, improving understanding of the problem's complexity.

## Contribution

It introduces an O(t)-approximation algorithm for the replica placement problem on graphs with treewidth t, advancing approximation techniques for this class of graphs.

## Key findings

- The problem is NP-hard to approximate within o(log n).
- An O(t)-approximation algorithm is developed for graphs with treewidth t.
- The approximation ratio scales linearly with the treewidth t.

## Abstract

We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get served and there is a maximum limit (capacity) on the amount of request a replica can serve. The problem falls under the general framework of capacitated set covering. It admits an O(\log n)-approximation and it is NP-hard to approximate within a factor of $o(\log n)$. We study the problem in terms of the treewidth $t$ of the graph and present an O(t)-approximation algorithm.