Approximation and Heuristic Algorithms for Probabilistic Physical Search on General Graphs

TL;DR

This paper introduces the first approximation and heuristic algorithms for probabilistic physical search problems on general graphs, addressing cost and success probability trade-offs in applications like exploration missions.

Contribution

It presents novel approximation algorithms and heuristics for probabilistic physical search on general graphs, along with hardness results and practical evaluation.

Findings

Algorithms achieve effective success probability optimization

Heuristics perform well in simulations on real and synthetic graphs

Hardness results establish computational limits

Abstract

We consider an agent seeking to obtain an item, potentially available at different locations in a physical environment. The traveling costs between locations are known in advance, but there is only probabilistic knowledge regarding the possible prices of the item at any given location. Given such a setting, the problem is to find a plan that maximizes the probability of acquiring the good while minimizing both travel and purchase costs. Sample applications include agents in search-and-rescue or exploration missions, e.g., a rover on Mars seeking to mine a specific mineral. These probabilistic physical search problems have been previously studied, but we present the first approximation and heuristic algorithms for solving such problems on general graphs. We establish an interesting connection between these problems and classical graph-search problems, which led us to provide the approximation algorithms and hardness of approximation results for our settings. We further suggest several heuristics for practical use, and demonstrate their effectiveness with simulation on real graph structure and synthetic graphs.