A framework for distributed discrete evacuation strategies
Piotr Borowiecki, Dariusz Dereniowski, Łukasz Kuszner
TL;DR
The paper tackles distributed discrete evacuation on graphs where agents know topology and exits but not others' positions, aiming to minimize evacuation time under synchronous, collision-free movement. It introduces a general framework built on $B$-partitions and zone graphs to decompose the graph into manageable zones and schedule phase-based evacuations, allowing both internal (self-sufficient) and cross-zone strategies. A central result bounds the evacuation time by $s=6\sum_{j=1}^{p} d_j 2^j$ with $p=\lceil\log_2 OPT\rceil$, ensuring a finite, scalable strategy, and shows that grids admit a constant-competitive evacuation due to a $\Theta(1)$-colorable zone graph. The framework’s core novelty lies in its partitioning approach, the zone-graph abstraction, and the phased, color-based coordination that remains valid without full knowledge of other agents. Practically, this yields efficient, distributed evacuation plans for grid-like environments and offers directions for extending to other lattice topologies and dynamic/heterogeneous settings.
Abstract
Consider the following discrete evacuation model. The evacuation terrain is modeled by a simple graph $G=(V,E)$ whose certain vertices $X\subseteq V$ are called \emph{exits}. Initially, each vertex is either \emph{empty} or \emph{occupied} by an agent. We assume that each vertex has a unique \emph{id} (and therefore the agents do have unique ids), each agent has finite but arbitrarily large memory, and the graph is initially stored in the memory of each agent. In other words, the agents do know the topology of the network along with the locations of the exits, but they do not know the initial positions nor the quantity of other agents. The time is divided into \emph{steps}; in each step any pair of agents present at vertices at a distance of at most two can exchange an arbitrary number of messages, and then each agent can either make a move or stay put. The agents should make moves in a collision-free manner, i.e., no two agents can be located at the same vertex in the same step. At the end of each step, any agent located at an exit \emph{evacuates}, i.e., it is removed from the graph. The goal is to provide an algorithm to the agents (referred to as an evacuation strategy) that ensures the evacuation of all agents and minimizes the number of steps. This work provides an algorithmic framework that allows constructing valid evacuation strategies for arbitrary input graphs. Specifically, we focus on the properties of the input graphs that lead to evacuation strategies with constant competitive ratios. In particular, we describe an application of the above framework that gives an asymptotically optimal evacuation for grids (and by extension hexagonal or triangular grids as well).