Balanced Dispersion on Time-Varying Dynamic Graphs

TL;DR

This paper introduces the k-balanced dispersion problem on dynamic graphs, integrating load balancing principles with mobile agents to ensure more equitable distribution across nodes, addressing limitations of previous static graph models.

Contribution

It defines and studies the k-balanced dispersion problem on dynamic graphs, bridging dispersion and load balancing with a focus on mobile agents and balanced distribution.

Findings

Proposes a new formulation of dispersion with load balancing constraints.

Establishes theoretical bounds for balanced dispersion on dynamic graphs.

Connects dispersion and load balancing through mobile agents in dynamic environments.

Abstract

We aim to connect two problems, namely, dispersion and load balancing. Both problems have already been studied over static as well as dynamic graphs. Though dispersion and load balancing share some common features, the tools used in solving load balancing differ significantly from those used in solving dispersion. One of the reasons is that the load balancing problem is introduced and studied heavily over graphs where nodes are the processors and work under the message passing model, whereas dispersion is a task for mobile agents to achieve on graphs. To bring the (load) balancing aspect in the dispersion problem, we say, mobile agents move to balance themselves as equally as possible across the nodes of the graph, instead of stationary nodes sharing loads in the load balancing problem. We call it the \emph{$k$-balanced dispersion} problem and study it on dynamic graphs. This is equivalent to the load balancing problem considering movable loads in form of the agents. Earlier, on static graphs, the \emph{$k$-dispersion} problem [TAMC 2019] aimed for the same by putting an upper bound on the number of agents on each node in the final configuration; however, the absence of a lower bound on the number of agents in their problem definition hampers the load-balancing aspect, as some nodes may end up with no agents in the final configuration. We take care of this part in our \emph{$k$-balanced dispersion} problem definition and thus produce a stronger connection between the two domains.