BTPG-max: Achieving Local Maximal Bidirectional Pairs for Bidirectional Temporal Plan Graphs

2025-08-06

AI Summary

To address path conflicts in multi-agent path finding (MAPF) caused by agent execution delays, this paper proposes BTPG-max: the first algorithm to generate locally optimal bidirectional pairs—i.e., maximal subgraphs admitting no additional bidirectional edges—within the Bidirectional Temporal Planning Graph (BTPG) framework. Our method integrates time-agnostic dependency modeling with dynamic relaxation strategies, significantly enhancing execution robustness and fault tolerance. Experimental results demonstrate that BTPG-max substantially increases the number of bidirectional edges compared to baseline approaches, achieving higher success rates at all time steps and markedly improved delay tolerance. These advances provide both theoretical guarantees and practical optimization pathways for real-world MAPF deployment.

Technology Category

Multiagent Systems: Multiagent PlanningPlanning, Routing, and Scheduling: Temporal PlanningHumans and AI: Planning and Decision Support for Human-Machine Teams

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Agentic searchResponsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Multi-Agent Path Finding (MAPF) requires computing collision-free paths for multiple agents in shared environment. Most MAPF planners assume that each agent reaches a specific location at a specific timestep, but this is infeasible to directly follow on real systems where delays often occur. To address collisions caused by agents deviating due to delays, the Temporal Plan Graph (TPG) was proposed, which converts a MAPF time dependent solution into a time independent set of inter-agent dependencies. Recently, a Bidirectional TPG (BTPG) was proposed which relaxed some dependencies into ``bidirectional pairs" and improved efficiency of agents executing their MAPF solution with delays. Our work improves upon this prior work by designing an algorithm, BPTG-max, that finds more bidirectional pairs. Our main theoretical contribution is in designing the BTPG-max algorithm is locally optimal, i.e. which constructs a BTPG where no additional bidirectional pairs can be added. We also show how in practice BTPG-max leads to BTPGs with significantly more bidirectional edges, superior anytime behavior, and improves robustness to delays.

Problem

• Enhancing bidirectional pairs in Bidirectional Temporal Plan Graphs
• Improving robustness to delays in Multi-Agent Path Finding
• Achieving local optimality in BTPG-max algorithm design

Innovation

• BTPG-max algorithm finds more bidirectional pairs
• Locally optimal BTPG construction method
• Enhances robustness to delays in execution