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arxiv: 2603.26684 · v2 · submitted 2026-03-11 · 💻 cs.MA · cs.RO

Decoupling Geometric Planning and Execution in Scalable Multi-Agent Path Finding

Fernando Salanova , Eduardo Montijano , Cristian Mahulea This is my paper

Pith reviewed 2026-05-15 12:56 UTC · model grok-4.3

classification 💻 cs.MA cs.RO
keywords multi-agent path findingMAPFgeometric planningdecentralized controlprioritized planningconflict resolutionscalable algorithmsA* search
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The pith

Separating geometric path planning from timed execution scales multi-agent path finding to 1000 agents with near-linear runtime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a hybrid prioritized framework for multi-agent path finding that first computes spatially non-conflicting geometric paths using sequential inflated-cost A* search and then resolves timing conflicts locally during execution. This decoupling avoids constructing large time-expanded graphs that cause poor scaling in centralized solvers. The first stage inflates costs for vertices already used by higher-priority agents to encourage spatial detours. The second stage uses per-vertex FIFO authorization queues to insert waits and prevent vertex and edge conflicts. A reader would care because the approach delivers 100 percent success on geometrically feasible benchmark instances while runtime grows near-linearly with agent count up to 1000.

Core claim

The central claim is that decoupling geometric planning from execution-time conflict resolution enables scalable MAPF: Geometric Conflict Preemption plans agents sequentially with A* on the original graph while inflating costs to preempt vertex overlaps, after which a Decentralized Local Controller executes the paths using per-vertex FIFO queues to insert waits that avoid remaining conflicts, attaining 100 percent success rate and near-linear runtime scaling on standard maps with up to 1000 agents when the geometric feasibility assumption holds.

What carries the argument

The two-stage hybrid prioritized framework consisting of Geometric Conflict Preemption (GCP) for spatial path planning via cost-inflated A* and Decentralized Local Controller (DLC) for runtime conflict resolution via FIFO authorization queues.

If this is right

  • The method scales to 1000 agents while maintaining a 100 percent success rate on instances satisfying the geometric feasibility assumption.
  • Runtime exhibits a near-linear trend with increasing agent count instead of exponential growth from time-expanded models.
  • Prioritized sequential planning with cost inflation reduces vertex overlaps so that local wait insertion suffices for conflict resolution.
  • The approach eliminates the need for centralized conflict resolution at planning time by handling timing only at execution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • In environments with open space the geometric stage will frequently produce paths that the decentralized controller can execute without deadlock.
  • The decoupling may support incremental replanning when new agents are added or obstacles appear without restarting the entire search.
  • Real-world deployments in warehouses could reduce communication overhead since the execution stage operates locally per vertex.
  • Instances requiring tight time synchronization from the outset would expose the limits of purely spatial preemption.

Load-bearing premise

A set of spatially non-conflicting paths must exist and be discoverable by the inflated-cost A* stage without any need for time-dependent detours.

What would settle it

A benchmark instance with 1000 agents in a narrow corridor layout where the geometric stage produces valid spatial paths but the execution stage deadlocks because agents require simultaneous time coordination to pass.

Figures

Figures reproduced from arXiv: 2603.26684 by Cristian Mahulea, Eduardo Montijano, Fernando Salanova.

Figure 1
Figure 1. Figure 1: Success rate comparison against methods [5], [6], [12] [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Runtime comparison against methods [5], [6], [12] [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Cost comparison against methods [5], [6], [12] for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

Multi-Agent Path Finding (MAPF) requires collision-free trajectories for multiple agents on a shared graph, often with the objective of minimizing the sum-of-costs (SOC). Many optimal and bounded-suboptimal solvers rely on time-expanded models and centralized conflict resolution, which limits scalability in large or dense instances. We propose a hybrid prioritized framework that separates \emph{geometric planning} from \emph{execution-time conflict resolution}. In the first stage, \emph{Geometric Conflict Preemption (GCP)} plans agents sequentially with A* on the original graph while inflating costs for transitions entering vertices used by higher-priority paths, encouraging spatial detours without explicit time reasoning. In the second stage, a \emph{Decentralized Local Controller (DLC)} executes the geometric paths using per-vertex FIFO authorization queues and inserts wait actions to avoid vertex and edge-swap conflicts. Experiments on standard benchmark maps with up to 1000 agents show that the method scales with an near-linear runtime trend and attains a 100\% success rate on instances satisfying the geometric feasibility assumption. Page of the project: https://sites.google.com/unizar.es/multi-agent-path-finding/home

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a hybrid prioritized framework for Multi-Agent Path Finding that decouples geometric planning from execution. The Geometric Conflict Preemption (GCP) stage uses sequential inflated-cost A* on the original graph to produce spatially non-conflicting paths. The Decentralized Local Controller (DLC) stage then executes these paths via per-vertex FIFO authorization queues, inserting waits to resolve vertex and edge conflicts. Experiments on standard benchmarks with up to 1000 agents report near-linear runtime scaling and 100% success rate conditional on an unquantified geometric feasibility assumption.

Significance. If the geometric feasibility assumption holds for a substantial fraction of practical instances, the method offers a scalable alternative to centralized time-expanded solvers by avoiding explicit time reasoning in planning. The near-linear scaling trend on standard maps up to 1000 agents is a concrete strength that could support deployment in large-scale robotics applications, provided the assumption's coverage is clarified.

major comments (3)
  1. [Abstract] Abstract: the 100% success rate and near-linear scaling claims are conditioned on instances satisfying the 'geometric feasibility assumption,' yet no count of filtered versus total benchmark instances, no explicit definition of the assumption, and no verification procedure for spatial non-conflict are reported. This is load-bearing for the central scalability claim.
  2. [Method] DLC description (inferred from abstract and method): deadlock-freedom of the per-vertex FIFO queues is asserted for spatially disjoint paths, but no argument or counterexample analysis addresses potential cyclic waiting dependencies that could arise even without spatial overlap; this undermines the execution-stage guarantee.
  3. [Experiments] Experimental evaluation: the impact of the single free parameter (vertex cost inflation factor) on the fraction of instances satisfying geometric feasibility is not quantified, leaving open whether the reported metrics are robust or sensitive to this choice.
minor comments (2)
  1. [Abstract] Abstract: 'an near-linear' is a grammatical error and should read 'a near-linear'.
  2. [Abstract] The project page is referenced but no statement on code or benchmark instance availability is included, which would aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify key aspects of the geometric feasibility assumption and execution guarantees. We address each major comment below, indicating revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the 100% success rate and near-linear scaling claims are conditioned on instances satisfying the 'geometric feasibility assumption,' yet no count of filtered versus total benchmark instances, no explicit definition of the assumption, and no verification procedure for spatial non-conflict are reported. This is load-bearing for the central scalability claim.

    Authors: We agree that the geometric feasibility assumption requires an explicit definition and supporting statistics. In the revised manuscript we will define it precisely as the condition that GCP produces vertex- and edge-disjoint paths. We will also describe the post-planning verification procedure (pairwise overlap check) and report the exact counts of instances satisfying versus failing the assumption across all benchmark maps, thereby grounding the 100% success and scaling claims. revision: yes

  2. Referee: [Method] DLC description (inferred from abstract and method): deadlock-freedom of the per-vertex FIFO queues is asserted for spatially disjoint paths, but no argument or counterexample analysis addresses potential cyclic waiting dependencies that could arise even without spatial overlap; this undermines the execution-stage guarantee.

    Authors: We acknowledge that the deadlock-freedom claim was stated without sufficient justification. In the revised method section we will insert a short proof sketch showing that, because the paths are vertex-disjoint, each FIFO queue is accessed by only one agent at any vertex; consequently no inter-agent waiting cycle can form. We will also include a brief counterexample analysis confirming that cyclic dependencies are impossible under the disjoint-path precondition. revision: yes

  3. Referee: [Experiments] Experimental evaluation: the impact of the single free parameter (vertex cost inflation factor) on the fraction of instances satisfying geometric feasibility is not quantified, leaving open whether the reported metrics are robust or sensitive to this choice.

    Authors: We agree that sensitivity to the inflation factor should be quantified. The revised experiments section will add a table (or plot) showing, for several inflation values, the percentage of instances that satisfy the geometric feasibility assumption together with the corresponding runtime and success metrics. This will demonstrate that the reported near-linear scaling holds across a reasonable range of the parameter. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on external benchmarks and standard algorithms

full rationale

The paper presents a hybrid MAPF method using standard A* with inflated costs for geometric planning followed by FIFO-based decentralized execution. No equations, fitted parameters, or derivations appear that reduce the reported 100% success rate or near-linear runtime to self-defined quantities or self-citations. Evaluation occurs on standard external benchmark maps, with the geometric feasibility assumption serving as an explicit scope condition rather than a hidden tautology. The central results are therefore experimentally grounded and self-contained against outside data.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The method rests on standard graph-search assumptions and the existence of geometrically feasible paths; no new entities are postulated and the only tunable element is the inflation factor for vertex costs.

free parameters (1)
  • vertex cost inflation factor
    A scalar multiplier applied to transitions entering vertices used by higher-priority agents; its specific value is chosen to encourage spatial detours but is not derived from first principles.
axioms (2)
  • domain assumption The underlying graph is static and undirected with unit edge costs unless inflated.
    Invoked when A* is run on the original graph without time expansion.
  • domain assumption A set of spatially non-conflicting paths exists for the given start-goal pairs.
    Required for the 100% success guarantee; stated as the geometric feasibility assumption.

pith-pipeline@v0.9.0 · 5507 in / 1475 out tokens · 34197 ms · 2026-05-15T12:56:39.186102+00:00 · methodology

discussion (0)

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Reference graph

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