Algorithms for Placing Monitors in a Flow Network

TL;DR

This paper studies the problem of optimally placing a limited number of flow monitors in a network to maximize flow identifiability, proving NP-hardness and providing approximation algorithms.

Contribution

It establishes NP-hardness of the Flow Edge-Monitor Problem and introduces two approximation algorithms with proven performance guarantees.

Findings

NP-hardness of the Flow Edge-Monitor Problem

3-approximation algorithm with O((m+n)^2) runtime

2-approximation algorithm with O((m+n)^3) runtime

Abstract

In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k > 0 and some unknown circulation \psi on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow along them, the total number of edges for which the flow can be uniquely determined is maximized. In this paper, we first show that the Flow Edge-Monitor Problem is NP-hard, and then we give two approximation algorithms: a 3-approximation algorithm with running time O((m+n)^2) and a 2-approximation algorithm with running time O((m+n)^3), where n = |V| and m=|E|.