1Steady State Resource Allocation Analysis for Stochastic Diffusion Search
Title: 1Steady State Resource Allocation Analysis for Stochastic Diffusion Search
Abstract: This research article presents an analysis of the long-term behavior of Stochastic Diffusion Search (SDS), a distributed agent-based system designed for best-fit pattern matching. SDS operates by allocating simple agents to different regions of the search space, where they independently propose hypotheses about the presence of a pattern and its potential distortion. Agents that pose mutually consistent hypotheses support each other and inhibit agents with inconsistent hypotheses, leading to the emergence of a stable agent population identifying the desired solution. Positive feedback through diffusion of information between agents significantly contributes to the speed with which the solution population forms.
The study characterizes the SDS model using interacting Markov Chains, enabling the analysis of agent allocation and resource usage. It focuses on the steady-state probability distribution of agent activity, which leads to the characterization of the solution population in terms of its similarity to the target pattern.
Keywords: Generalized Ehrenfest Urn model, interacting Markov Chains, nonstationary processes, resource allocation, best-fit search, distributed agent-based computation
Introduction: The research aims to investigate the steady-state behavior of Stochastic Diffusion Search (SDS), a generic, distributed, agent-based method for solving the best-fit matching problem. Many fundamental problems in computer science, artificial intelligence, and bioinformatics can be formulated as pattern matching or search problems. The study explores various variations of these problems, including different distances used for determining similarity between patterns and the allowance for a pre-specified number of errors.
The study discusses the classical exact string matching problem and its extension to tree matching, with algorithms adapted from string matching methods. It highlights the increased interest in heuristic search methods as alternatives to deterministic methods, mentioning examples like Genetic Algorithms, Evolutionary Strategies, Ant Colony Optimization, and Simulated Annealing. These methods rely on random sampling of the search space by a population of computational agents, with sampling bias determined by coupling mechanisms between the agents.
The research notes that while these heuristic search methods have wide applications, they lack a standard formal framework for theoretical analysis. However, it argues that randomness in computation has also been employed in more classical computational schemes, like Randomized Algorithms.
Methodology: The study characterizes the SDS model using interacting Markov Chains, enabling the analysis of agent allocation and resource usage. It focuses on the steady-state probability distribution of agent activity, which leads to the characterization of the solution population in terms of its similarity to the target pattern.
Results: The research presents an analysis of the long-term behavior of SDS, focusing on the steady-state probability distribution of agent activity. This characterization leads to the formation of a stable agent population identifying the desired solution.
Implications: The study suggests that positive feedback through diffusion of information between agents significantly contributes to the speed with which the solution population forms. It also highlights the importance of developing a standard formal framework for theoretical analysis of heuristic search methods, which could help improve our understanding of these methods and their applications.
Link to Article: https://arxiv.org/abs/0202007v1 Authors: arXiv ID: 0202007v1