Evacuation of rectilinear polygons

TL;DR

This paper studies evacuation planning for grid polygon buildings, providing algorithms for confluent and non-confluent strategies, analyzing their complexity, and comparing their efficiency bounds.

Contribution

It introduces polynomial algorithms for confluent evacuation plans with two exits and a pseudo-polynomial algorithm for non-confluent plans, along with complexity analysis.

Findings

Polynomial algorithms for confluent evacuation with two exits

Pseudo-polynomial algorithm for non-confluent evacuation

Bound on the efficiency difference between confluent and non-confluent plans

Abstract

We investigate the problem of creating fast evacuation plans for buildings that are modeled as grid polygons, possibly containing exponentially many cells. We study this problem in two contexts: the ``confluent'' context in which the routes to exits remain fixed over time, and the ``non-confluent'' context in which routes may change. Confluent evacuation plans are simpler to carry out, as they allocate contiguous regions to exits; non-confluent allocation can possibly create faster evacuation plans. We give results on the hardness of creating the evacuation plans and strongly polynomial algorithms for finding confluent evacuation plans when the building has two exits. We also give a pseudo-polynomial time algorithm for non-confluent evacuation plans. Finally, we show that the worst-case bound between confluent and non-confluent plans is 2-2/(k+1).