Minsum Problem for Discrete and Weighted Set Flow on Dynamic Path Network

TL;DR

This paper introduces a modified minsum flow problem for dynamic path networks that accounts for groups with different importance levels and proposes an approximation algorithm for its solution.

Contribution

It extends the minsum flow problem to handle discrete, weighted sets and provides a 2-approximation algorithm for path networks with uniform capacity.

Findings

The modified problem better models real evacuation scenarios.

A 2-approximation algorithm is developed for the problem.

The algorithm operates in pseudo-polynomial time.

Abstract

In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during emergencies such as earthquakes. However, previous approaches often assume that individuals are separable and identical, which does not adequately account for the fact that some groups of people, such as families, need to move together and that some groups may be more important than others. To address these limitations, we modify the minsum flow problem to support flows represented as discrete and weighted sets. We also propose a 2-approximation pseudo-polynomial time algorithm to solve this modified problem for path networks with uniform capacity.