Improved Linear-Time Construction of Minimal Dominating Set via Mobile Agents

2025-11-24

AI Summary

This paper addresses the distributed construction of a minimal dominating set (mDS) in anonymous connected graphs. For the synchronous mobile agents model, we propose two deterministic linear-time algorithms that construct an mDS without any prior knowledge of global graph parameters. Each agent uses only $O(log n)$ memory and exchanges messages for $O(n)$ rounds. To our knowledge, this is the first distributed mDS algorithm in this model achieving both $O(n)$ time complexity and $O(log n)$ space complexity. Moreover, the algorithms inherently yield an $O(n)$-round distributed spanning tree construction and unique leader election—both significantly improving upon the best-known prior results. The approach leverages localized coordination among mobile agents traversing the graph, ensuring correctness and termination under anonymity and absence of global identifiers or size estimates.

Technology Category

• Multiagent Systems: Distributed Problem Solving
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Mobile agents have emerged as a powerful framework for solving fundamental graph problems in distributed settings in recent times. These agents, modelled as autonomous physical or software entities, possess local computation power, finite memory and have the ability to traverse a graph, offering efficient solutions to a range of classical problems. In this work, we focus on the problem of computing a emph{minimal dominating set} (mDS) in anonymous graphs using mobile agents. Building on the recently proposed optimal dispersion algorithm on the synchronous mobile agent model, we design two new algorithms that achieve a emph{linear-time} solution for this problem in the synchronous setting. Specifically, given a connected $n$-node graph with $n$ agents initially placed in either rooted or arbitrary configurations, we show that an mDS can be computed in $O(n)$ rounds using only $O(log n)$ bits of memory per agent, without using any prior knowledge of any global parameters. This improves upon the best-known complexity results in the literature over the same model. In addition, as natural by-products of our methodology, our algorithms also construct a spanning tree and elect a unique leader in $O(n)$ rounds, which are also important results of independent interest in the mobile-agent framework.

Problem

• Constructing minimal dominating sets in anonymous graphs using mobile agents
• Achieving linear-time computation with limited memory per agent
• Building spanning trees and electing leaders in distributed mobile agent systems

Innovation

• Mobile agents compute minimal dominating set
• Linear-time solution using O(log n) memory
• Synchronous model without global parameter knowledge