Distributed Computation of Graph Structures by Mobile Agents

Abstract

This thesis investigates how mobile agents with no centralised control can be employed in anonymous networks to perform efficient distributed graph computations. The network is modelled as a simple, undirected, anonymous graph with n nodes and m edges, where nodes are memoryless and indistinguishable, and edges represent bidirectional communication links or traversal paths for the agents. The mobile agents are uniquely identifiable, possess limited local memory, and operate under a local communication model, in which communication is restricted to agents colocated at the same node. Under this computational model, we explore how mobile agents can collaborate effectively to solve global network problems—including dispersion in the presence of crashes, the construction of spanning trees, the identification of dominating sets, and the analysis of sub-graph hierarchies. We study the time complexity and memory usage per agent required to solve the above problems. The first contributory chapter addresses the fault-tolerant dispersion problem, aiming to evenly spread mobile agents across an anonymous graph in the presence of crash faults, from two initial configurations: rooted, where all the agents start at a single node, and arbitrary, where agents are initially scattered across the graph in multiple clusters. This chapter explores how dispersion can be achieved under both settings, ensuring that each node eventually hosts at most one functional agent despite crashes. The next chapter presents the problem of computing dominating sets using mobile agents, where two different algorithms are introduced: one for computing minimal dominating sets in O(m) time when the agents are gathered at a single node, and another for scenarios where agents start from multiple clusters. Additionally, an ln ∆ approximation algorithm for the minimum dominating set problem is provided, where ∆ is the maximum degree of the graph. The subsequent chapter focuses on subgraph analytics using mobile agents dispersed across the nodes of a graph. We present algorithms for triangle counting (3-cycles) in general graphs and butterfly counting (4-cycles) in bipartite graphs. The triangle counting framework extends to related problems such as truss decomposition, triangle centrality, and local clustering coefficient. These methods enable the distributed identification of cohesive structures and dense subgraphs, with butterfly counting being of relevance to bipartite graphs commonly found in social network analysis and recommendation systems. The final chapter focuses on constructing tree structures, specifically BFS trees and minimum spanning trees, using mobile agents. These algorithms, which assume minimal prior knowledge, improve upon existing methods by achieving better time complexity and optimal memory usage. Throughout the thesis, these graph problems are explored through the lens of the mobile agent framework, focusing on minimising the time complexity of the algorithms and memory usage per agent.