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This research paper addresses the stability of search algorithms in complexnetworks when dealing with incomplete information or uncertainty. We propose atheoretical model to investigate whether a global search algorithm withincomplete prior information can be outperformed by a stochastic greedy searchon average. The model incorporates random variables to perturb edge weights inthe graph, thus capturing the uncertainty of available information. Ourfindings indicate that some graphs and uncertainty model parameters exist wherethe global search algorithm fails under uncertainty conditions, while therandom greedy search performs better. We derive a critical curve that separatesstable from unstable graphs for global search with incomplete information.Interestingly, the critical curve's behavior changes from monotonic tobell-shaped depending on the uncertainty parameters. We test our proposed modelthrough numerical simulations on various synthetic and real-world graphs withdifferent structures. Our results offer insights into the design andoptimization of search algorithms for network-based applications, such ascommunication networks, social networks, and biological networks. We alsodiscuss the study of memory and associative learning in miniature insects,highlighting the potential of efficient search and walking strategies for smallrobots or devices that operate in a limited area in space.

Prior Global Search Stability on Finite Graphs with Uncertainty. May Greedy Search Win?