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arXiv 2412.09433cs.CCcs.AI
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在高度集中化网络上求解多智能体路径规划

Solving Multiagent Path Finding on Highly Centralized Networks

Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague(理论计算机科学系,信息科技学院,捷克技术大学)

Foivos Fioravantes, Dušan Knop, Jan Matyáš Křišťan, Nikolaos Melissinos, Michal Opler, Tung Anh Vu

AI总结:

本文通过参数化复杂度视角研究多智能体路径规划(MAPF)问题,证明了其在星型拓扑和11叶子树上的NP-hard性,并提出了一种适用于高度集中化网络(有界距离到团)的可扩展精确FPT算法。

摘要:

多智能体路径规划(MAPF)问题旨在确定一组智能体在给定网络中为尽快到达各自目标地且互不碰撞而应遵循的轨迹。我们旨在最小化任意智能体到达目标所需的最长时间,以确保最优路径长度。在本研究中,我们通过参数化复杂度视角,补充了近期旨在系统研究该问题算法行为的一系列成果。首先,我们证明了当给定网络具有星型拓扑(有界顶点覆盖数)或是具有 $11$ 个叶子的树时,MAPF 是 NP-hard 的。这两项结果填补了我们对这一问题可处理性理解上的重要空白,这些空白在 [Fioravantes et al. Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology. AAAI'24] 的近期工作中未被处理。然而,我们的主要贡献是提出了一种当给定网络拓扑高度集中化(有界距离到团)时,能随输入规模良好扩展的精确算法(FPT)。该参数意义重大,因为它反映了现实世界的网络。在这样的环境中,一群中心枢纽(例如,处理区域)仅连接到少数外围节点。

英文摘要:

The Mutliagent Path Finding (MAPF) problem consists of identifying the trajectories that a set of agents should follow inside a given network in order to reach their desired destinations as soon as possible, but without colliding with each other. We aim to minimize the maximum time any agent takes to reach their goal, ensuring optimal path length. In this work, we complement a recent thread of results that aim to systematically study the algorithmic behavior of this problem, through the parameterized complexity point of view. First, we show that MAPF is NP-hard when the given network has a star-like topology (bounded vertex cover number) or is a tree with $11$ leaves. Both of these results fill important gaps in our understanding of the tractability of this problem that were left untreated in the recent work of [Fioravantes et al. Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology. AAAI'24]. Nevertheless, our main contribution is an exact algorithm that scales well as the input grows (FPT) when the topology of the given network is highly centralized (bounded distance to clique). This parameter is significant as it mirrors real-world networks. In such environments, a bunch of central hubs (e.g., processing areas) are connected to only few peripheral nodes.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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