Probabilistic search on optimized graph topologies

Abstract

This thesis investigates how the performance of a mobile searcher is affected by altering the search environment. We model the search environment as a simple connected, undirected graph. By adding new edges to the graph, we change the search environment. Our objective is to optimize search performance, that is, to minimize the (expected) time needed to find the target, in the context of probabilistic search. We first analyze two different methods to generate random connected graphs, then evaluate a number of methods to augment the graph, typically by considering the algebraic connectivity of the graph and its associated (Fiedler) eigenvector. Extensive simulation studies and resulting statistical and theoretical models show that adding a few wisely chosen edges to a sparse graph is sufficient to dramatically increase search performance. Further, we propose a novel method for incorporating prior information about the target's likely location by defining a subgraph on which the presented approach is performed, resulting in even greater improvements in search performance.