在距离之和以下路由多个智能体
Routing Multiple Agents Below the Sum of Distances
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中文总结 AI 辅助
研究瞬态多智能体路径规划，以距离之和与完工时间差距及智能体数为参数，证明组合参数固定参数可处理，并刻画了各参数下的复杂性边界。
中文摘要 AI 辅助
我们研究瞬态多智能体路径规划问题，这是经典多智能体路径规划问题的一个变体，其中一组智能体必须在不发生碰撞的情况下，从指定的起始顶点路由到图中指定的目标顶点。我们在参数化复杂性的上界与下界保证范式内分析该问题。特别地，我们考虑自然上界 \\(L\\)，由智能体终端对之间的最短路径距离之和给出（对应于智能体的顺序路由）。参数化由该界与目标完工时间 \\(\lambda\\) 之间的差距 \\(\zeta = L - \lambda\\) 以及智能体数量 \\(k\\) 共同给出。我们的主要结果确立了组合参数 \\(k + \zeta\\) 的固定参数可处理性。匹配的下界表明，仅以 \\(k\\) 为参数时问题是 W[1] 难的，且当终端不要求互异时，仅以 \\(\zeta\\) 为参数时问题也是 W[1] 难的。在正面方面，如果所有终端互异，则仅以 \\(\zeta\\) 为参数时问题变为固定参数可处理。最后，我们表明瞬态多智能体路径规划在以 \\(k + \zeta\\) 为参数时不太可能承认多项式核。总之，我们的结果为所考虑参数下问题的参数化复杂性图景提供了几乎完整的刻画。
英文摘要
We study Transient Multiagent Pathfinding, a variant of the classical Multi-Agent Pathfinding problem in which a set of agents must be routed without collisions from designated start vertices to designated destination vertices in a graph. We analyze the problem within the above-and-below-guarantee paradigm of parameterized complexity. In particular, we consider the natural upper bound \(L\), given by the sum of the shortest-path distances between pairs of agents' terminals (corresponding to sequential routing of the agents). The parameterization is given by the gap \(ζ= L - λ\) between this bound and the target makespan \(λ\), together with the number \(k\) of agents. Our main result establishes fixed-parameter tractability for the combined parameter \(k + ζ\). Matching lower bounds show that parameterization by \(k\) alone is W[1]-hard, and that parameterization by \(ζ\) alone is W[1]-hard when terminals are not required to be distinct. On the positive side, if all terminals are distinct, the problem becomes fixed-parameter tractable when parameterized solely by \(ζ\). Finally, we show that Transient Multiagent Pathfinding is unlikely to admit a polynomial kernel when parameterized by \(k + ζ\). Together, our results provide an almost complete characterization of the parameterized complexity landscape of the problem for the considered parameters.
发表机构
- TU Berlin（柏林工业大学）
- Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
- University of Bergen（卑尔根大学）
机构由 AI 辅助整理，请以论文原文为准。
