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In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…

Data Structures and Algorithms · Computer Science 2014-09-15 Lajos L. Pongrácz

This paper presents a parallelizable variant of the well-known Hierarchical Cooperative A* algorithm (HCA*) for the multi-agent path finding (MAPF) problem. In this variant, all agents initially find their shortest paths disregarding the…

Systems and Control · Electrical Eng. & Systems 2025-02-03 Sreenivasan Ganti , Visnu Srinivasan , Pallavi Ramicetty , Shravan Mohan , Milind Savagaonkar , Shubhashis Sengupta

We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some…

Computer Vision and Pattern Recognition · Computer Science 2017-02-06 Alexander Shekhovtsov , Paul Swoboda , Bogdan Savchynskyy

MAPF problem aims to find plans for multiple agents in an environment within a given time, such that the agents do not collide with each other or obstacles. Motivated by the execution and monitoring of these plans, we study Dynamic MAPF…

Artificial Intelligence · Computer Science 2026-01-14 Aysu Bogatarkan , Esra Erdem

Decentralized multi-agent path finding (MAPF) routes a team of agents on a shared grid, each acting from its own local view. The standard solution trains one shared neural policy with Proximal Policy Optimization (PPO), a popular on-policy…

Machine Learning · Computer Science 2026-05-13 Riad Ahmed

Existing multi-agent path finding (MAPF) solvers do not account for uncertain behavior of uncontrollable agents. We present a novel variant of Enhanced Conflict-Based Search (ECBS), for both one-shot and lifelong MAPF in dynamic…

Multiagent Systems · Computer Science 2025-07-31 Kegan J. Strawn , Thomy Phan , Eric Wang , Nora Ayanian , Sven Koenig , Lars Lindemann

We study Multi-Agent Path Finding for arrangements of labeled agents in the interior of a simply connected domain: Given a unique start and target position for each agent, the goal is to find a sequence of parallel, collision-free agent…

Computational Geometry · Computer Science 2024-09-11 Sándor P. Fekete , Ramin Kosfeld , Peter Kramer , Jonas Neutzner , Christian Rieck , Christian Scheffer

In this paper, we study the shortest path problem (SPP) with multiple source-destination pairs (MSD), namely MSD-SPP, to minimize average travel time of all shortest paths. The inherent traffic capacity limits within a road network…

Artificial Intelligence · Computer Science 2024-09-04 Jiaming Yin , Weixiong Rao , Yu Xiao , Keshuang Tang

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal…

Artificial Intelligence · Computer Science 2022-08-03 Qinghong Xu , Jiaoyang Li , Sven Koenig , Hang Ma

The Minimum Path Cover (MPC) problem consists of finding a minimum-cardinality set of node-disjoint paths that cover all nodes in a given graph. We explore a variant of the MPC problem on acyclic digraphs (DAGs) where, given a subset of…

Discrete Mathematics · Computer Science 2025-01-17 Nour ElHouda Tellache , Roberto Baldacci

Modern Multi-Agent Path Finding (MAPF) algorithms must plan for hundreds to thousands of agents in congested environments within a second, requiring highly efficient algorithms. Priority Inheritance with Backtracking (PIBT) is a popular…

Multiagent Systems · Computer Science 2026-03-25 Zixiang Jiang , Yulun Zhang , Rishi Veerapaneni , Jiaoyang Li

Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…

Data Structures and Algorithms · Computer Science 2020-02-19 Pratibha Choudhary

This paper introduces a new approach to solving a continuous-time version of the multi-agent path finding problem. The algorithm translates the problem into an extension of the classical Boolean satisfiability problem, satisfiability modulo…

Multiagent Systems · Computer Science 2023-12-18 Tomáš Kolárik , Stefan Ratschan , Pavel Surynek

This study extends the recently-developed LaCAM algorithm for multi-agent pathfinding (MAPF). LaCAM is a sub-optimal search-based algorithm that uses lazy successor generation to dramatically reduce the planning effort. We present two…

Artificial Intelligence · Computer Science 2023-05-08 Keisuke Okumura

We introduce and study the multi-agent stochastic shortest path (MSSP) problem, in which $k$ agents strive to reach a target state, aiming to minimize the expected time to reach the target by any agent. We analyze the computational and…

Multiagent Systems · Computer Science 2026-05-08 Martin Jonáš , Antonín Kučera , Vojtěch Kůr , Jan Mačák , Vojtěch Řehák

Multi-agent path finding (MAPF) is a task of finding non-conflicting paths connecting agents' specified initial and goal positions in a shared environment. We focus on compilation-based solvers in which the MAPF problem is expressed in a…

Artificial Intelligence · Computer Science 2022-12-15 Pavel Surynek

In multi-agent path finding (MAPF), the task is to find non-conflicting paths for multiple agents from their initial positions to given individual goal positions. MAPF represents a classical artificial intelligence problem often addressed…

Artificial Intelligence · Computer Science 2021-11-15 Martin Čapek , Pavel Surynek

Multi-agent pathfinding (MAPF) traditionally focuses on collision avoidance, but many real-world applications require active coordination between agents to improve team performance. This paper introduces Team Coordination on Graphs with…

Multiagent Systems · Computer Science 2025-09-10 Yanlin Zhou , Manshi Limbu , Xuesu Xiao

Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…

Optimization and Control · Mathematics 2020-12-01 Navid Rezazadeh , Solmaz S. Kia

We discuss milestones on the tour towards DPLL(MAPF), a multi-agent path finding (MAPF) solver fully integrated with the Davis-Putnam-Logemann-Loveland (DPLL) propositional satisfiability testing algorithm through satisfiability modulo…

Artificial Intelligence · Computer Science 2019-07-18 Pavel Surynek
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