Target Location Problem for Multi-commodity Flow

TL;DR

This paper introduces the target location problem for multi-commodity flow (LoMuF), analyzing its computational complexity and proposing algorithms for different network types, with implications for geo-distributed data analysis scheduling.

Contribution

It formalizes LoMuF, establishes its NP-hardness, and provides approximation and exact algorithms for undirected networks and trees, respectively.

Findings

LoMuF is NP-hard and APX-hard.

Approximation algorithm for general undirected networks.

Exact algorithm for undirected trees.

Abstract

Motivated by scheduling in Geo-distributed data analysis, we propose a target location problem for multi-commodity flow (LoMuF for short). Given commodities to be sent from their resources, LoMuF aims at locating their targets so that the multi-commodity flow is optimized in some sense. LoMuF is a combination of two fundamental problems, namely, the facility location problem and the network flow problem. We study the hardness and algorithmic issues of the problem in various settings. The findings lie in three aspects. First, a series of NP-hardness and APX-hardness results are obtained, uncovering the inherent difficulty in solving this problem. Second, we propose an approximation algorithm for general undirected networks and an exact algorithm for undirected trees, which naturally induce efficient approximation algorithms on directed networks. Third, we observe separations between directed networks and undirected ones, indicating that imposing direction on edges makes the problem strictly harder. These results show the richness of the problem and pave the way to further studies.