Scalable Algorithms with Provable Optimality Bounds for the Multiple Watchman Route Problem

2026-04-16

AI Summary

This study addresses the multi-watcher route planning problem, which seeks to compute paths for multiple agents such that every location in a map is observed at least once while guaranteeing solution optimality or bounded suboptimality. To this end, the authors propose an optimal planner, MWRP-CP3, and a bounded-suboptimal algorithm, MxWA*, integrating state-space pruning, a weighted A* variant, efficient heuristics, and subproblem decomposition strategies. These techniques substantially reduce the search space and enable anytime optimization. Experimental results demonstrate that MWRP-CP3 compresses the search space by over 95% and achieves more than a 200-fold speedup over existing optimal methods. Meanwhile, the suboptimal algorithm scales to maps three times larger while maintaining strong guarantees on solution quality and computational efficiency.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this paper, we tackle the Multiple Watchman Route Problem (MWRP), which aims to find a set of paths that M watchmen can follow such that every location on the map can be seen by at least one watchman. First, we propose multiple methods to reduce the state space over which a search needs to be conducted by pruning map areas that are guaranteed to be seen en route to other areas. Next, we introduce MWRP-CP3, an efficient optimal planner that combines these methods with techniques that improve the quality and calculation time of existing heuristics. We present several suboptimal algorithms with bounds on solution quality, including MxWA*, a general variant of weighted A* for makespan problems. We also present anytime variations of our suboptimal algorithms, as well as techniques to improve an existing suboptimal solution by solving multiple decomposed sub-problems. We show that MWRP-CP3 can reduce the search space by more than 95% and runs more than 200x faster than existing optimal algorithms on 2D grid maps. We also show that our suboptimal algorithms solve maps 3x larger than those solvable by MWRP-CP3. See mwrp-cp3.github.io for the open source codebase and video demonstrations.

Problem

• Multiple Watchman Route Problem
• path planning
• visibility coverage
• multi-agent surveillance
• optimal routing

Innovation

• Multiple Watchman Route Problem
• state space pruning
• optimal planning
• bounded suboptimal search
• anytime algorithm