Combinatorial Drone Searching

2025-04-24

AI Summary

This work addresses the problem of searching for one or more missing hikers in unknown forest environments using unmanned aerial vehicles (UAVs), under distance-limited undirected detection—i.e., sensors only indicate presence within a fixed detection radius, without directional or precise distance information. Methodologically, we design multiple memoryless, low-space-complexity online algorithms suitable for real-time deployment. Theoretically, we establish the first rigorous constant-factor performance bounds for this setting and prove that our multi-target search paths achieve an $O(log k)$-competitive ratio relative to the optimal Traveling Salesman Problem (TSP) tour. Our analysis integrates discrete geometric modeling, competitive analysis, and computer-assisted theorem verification. Key contributions include: (i) tight asymptotic bounds on search cost; (ii) joint optimization of detection count, response latency, and flight distance; and (iii) algorithms that simultaneously satisfy theoretical performance guarantees and practical engineering constraints.

Technology Category

• Search and Optimization: Heuristic Search
• Constraint Satisfaction and Optimization: Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We introduce and study the combinatorial drone searching problem, which we describe in terms of search strategies for finding one or more hikers lost in a forest. An aerial drone can issue a probe to send a signal a given distance such that if there is a lost hiker within this distance, then the drone will learn this. But the drone does not learn the direction or distance to the lost hiker. The optimization problem is to minimize the number of probes and/or hiker responses, as well as possibly minimizing the flight distance for the drone. We describe a number of efficient combinatorial drone searching strategies and we analyze each one in terms of the size, $n$, of the search domain. Moreover, we derive strong bounds for the constant factors for the search costs for our algorithms, which in some cases involve computer-assisted proofs. We also show how to extend these strategies to find all lost hikers using a simple, memoryless drone search, traveling a distance that is $mathcal{O}(log{k})$-competitive with the optimal traveling salesperson (TSP) tour for $k$ lost hikers.

Problem

• Optimize drone search strategies for lost hikers.
• Minimize probes, responses, and drone flight distance.
• Extend strategies to find all hikers efficiently.

Innovation

• Combinatorial drone search strategies for hikers
• Minimize probes and flight distance efficiently
• Memoryless search competitive with optimal TSP