Multi-Agent Path Finding via Finite-Horizon Hierarchical Factorization

Alessandro Zanardi; Gioele Zardini; Jiarui Li

REVIEW 3 major objections 7 minor 1 cited by

Multi-Agent Path Finding via Finite-Horizon Hierarchical Factorization

T0 review · 3 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A receding-horizon, hierarchically factored multi-agent path-finding planner lets large robot fleets start acting before any complete joint plan exists, cutting time-to-first-action by up to 60% on benchmark maps while keeping solution…

desk verdict A genuinely new online MAPF architecture with a meaningful latency result, but the evidence is thin (two maps, one baseline, no code) and the scalability claim rests on an unproven assumption about group sizes. read the letter →

arxiv 2505.07779 v1 pith:TGLKSCS4 submitted 2025-05-12 cs.RO

Jiarui Li , Alessandro Zanardi , Gioele Zardini This is my paper · ORCID

classification cs.RO

keywords multi-agentpathfindingfinite-horizonplanninghierarchicalfactorizationparallelconflictresolutiontime-to-first-actionwarehouseroboticsPIBT

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that multi-agent path finding can be solved online, one timestep at a time, without losing solution quality to offline planners. It proposes a finite-horizon hierarchical factorization: robots plan individually in parallel for the next $H$ steps, conflict-free robots are finalized as dynamic obstacles, and only robots that actually conflict are grouped and replanned together. This shifts most computation from a single exponential joint search to many small parallel subproblems. If the claim is right, large fleets can begin executing their first moves almost immediately, and later moves can be planned while robots are already acting. The reported experiments show up to a 60% reduction in time-to-first-action and lower sum-of-costs than the LaCAM* baseline on two benchmark maps.

What carries the argument

The load-bearing object is the two-level factorization controlled by the horizon parameter $H$. The first level uses spatial-hash conflict detection to split agents into finalized conflict-free robots and conflicted robots; the second level groups only the conflicted robots by reachability within $H$ and solves each group with the PIBT algorithm, enlarging groups through congestion resolution when replanning fails. This decomposition is what makes planning parallelizable: most robots stay conflict-free over short horizons, so the expensive joint search is confined to small groups, and executing only the first step keeps the plan adaptive.

What would settle it

On a dense grid where every robot conflicts within the next $H$ steps, run the method and measure whether all agents collapse into a single reachability group; if time-to-first-action then grows with fleet size roughly as fast as an offline planner, the claimed scalability fails. More directly, after executing the first-step plans, check whether any agent enters a vertex occupied by a finalized robot within the following $H$ timesteps, which would falsify the composability assumption.

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Extended reading notes

Core claim

On its own terms, the paper claims that the MAPF problem can be factored by a finite planning horizon $H$ into a fast individual layer and a targeted conflict-resolution layer. At each iteration every robot first computes a greedy plan; a spatial-hash conflict check over the next $H$ timesteps finalizes the conflict-free robots, which then serve as moving obstacles. The remaining robots are recursively grouped by horizon-limited reachability and replanned with the PIBT routine; when a group replan fails, a congestion-resolution module enlarges the group until it succeeds. Only the first move of the merged trajectory is executed, and the cycle repeats. The paper's experimental claim is that this pipeline, run with 12 threads, completes each planning step in under 30 ms even with 900 robots, reaches first action up to 60% faster than LaCAM*, and produces better sum-of-costs on the warehouse map and competitive or better results on the random map.

Load-bearing premise

The algorithm assumes that treating conflict-free robots as fixed moving obstacles and composing their one-step moves with separately replanned groups always produces an executable joint plan; the paper demonstrates this empirically on two maps but gives no formal feasibility proof.

Editorial extensions

If this is right

The first move of every robot is fixed and executable before any complete joint plan is computed, so fleets start acting immediately and planning continues while they move.
Because conflict-free robots are never replanned over the horizon, the joint-search bottleneck is confined to small conflict groups, keeping each planning step under 30 ms at the tested scales.
The online cycle naturally adapts to new conflicts or changes each timestep, since only the current first step is committed and later steps are recomputed from the new state.
On structured maps longer horizons improve solution quality by resolving conflicts earlier; on random maps an intermediate horizon balances coordination against the cost of drawing more robots into replanning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because only one step is committed per cycle, the same factorization should extend directly to lifelong MAPF with online task arrivals, although the paper only lists this as future work.
The non-monotonic horizon effect seen on the random map suggests an adaptive controller that tunes $H$ by local robot density could improve average solution quality; this is not tested in the paper.
A formal proof that finalized dynamic obstacles and group replans compose feasibly would turn the empirical claim into a guarantee; one testable route is verifying that every group replan avoids finalized robots exactly for the full $H$ steps, not just the first.
The 60% time-to-first-action reduction should be re-measured under different thread counts and denser maps, since the speedup rests on most robots staying conflict-free within the horizon; at high density that fraction shrinks.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The thing to know: this is not a rehash. The finite-horizon hierarchical factorization — parallel greedy individual planning, conflict detection over horizon H, finalizing conflict-free robots, grouping the rest by reachability, PIBT replanning, execute one step — is a new architecture. It directly targets time-to-first-action, a metric that matters in warehouses and one that offline planners structurally can't optimize. The 60% TNBE reduction over LaCAM* is plausible from the method, and letting LaCAM* keep refining until their own planner finishes makes the SOC comparison conservative in the baseline's favor. That's the right instinct.

The paper also does a few things honestly: it reports mean, std, and min-max; it shows the random map's non-monotonic behavior with H instead of hiding it; and the exposition is clear about the pipeline.

Now the soft spots. They are real but not disqualifying. Experiments are two maps and one baseline. LaCAM* is a strong anytime solver, but "outperforming state-of-the-art offline baselines across a range of problem sizes and planning horizons" is a claim that needs more baselines (CBS-family, MAPF-LNS2, other LaCAM variants) and more maps before it can be taken at face value. The comparison budget — TNBE measured while LaCAM* runs without a time cap — is fine for latency but makes the SOC comparison hard to interpret; they should report wall-clock time to a given suboptimality gap or similar.

The bigger gap is formal. The composition rule — finalized conflict-free agents treated as dynamic obstacles, conflicting agents group-replanned with PIBT, groups enlarged on failure — has no stated lemma that the one-step joint plan is always executable, nor that group size stays bounded. The stress-test worry that dense scenarios can produce groups of size O(N), collapsing the factorization, is a real unresolved question. The one-step execution buffer softens this, because the planner can recover next iteration, but the claim that the method "preserves feasibility" or scales better than centralized replanning needs a guarantee or at least a characterization of when the factorization succeeds. The paper gestures at future work on "tighter guarantees," which is fine, but the guarantees are load-bearing for the scalability claim, not a side detail.

Also, no code is released, and the video link is not a substitute. For a systems-style paper in robotics, code would materially raise confidence.

Bottom line: I'd send this to peer review. The core idea is worth evaluating, the latency metric is practically important, and the experiments, while thin, are honestly reported. A serious referee should ask for more baselines, a feasibility/complexity analysis of group enlargement, and code. I'd probably cite it if I worked on MAPF; I'd bring it to reading group as an example of receding-horizon factorization.

Recommendation: accept with major revision if the formal gap is addressed; otherwise this is a workshop-paper-to-strong-short-paper with the right idea.

Referee Report

3 major / 7 minor

Summary. The manuscript proposes Finite-Horizon Hierarchical Factorization (FHHF), an online MAPF method that plans one step at a time in a receding-horizon manner. At each iteration, robots compute individual paths in parallel; conflicts within a planning horizon H are detected; conflict-free robots are finalized and treated as dynamic obstacles, while conflicting robots are grouped by horizon-limited reachability and replanned with an adapted PIBT algorithm. If replanning fails, a congestion-resolution module enlarges the group. Only the first move of the merged plan is executed, and the process repeats. Experiments on two benchmark maps (warehouse-20-40-10-2-2 and random-64-64-10) with up to 900 robots compare the time-to-first-action (TNBE) and sum-of-costs (SOC) against the offline anytime planner LaCAM*. The authors report up to 60% reduction in TNBE and consistently lower SOC on the tested configurations, concluding that the method is a practical alternative for real-time multi-robot coordination.

Significance. If the empirical results are taken at face value, the method offers a useful engineering contribution: a parallelizable, online MAPF scheme with fast first-action latency and competitive solution quality on the tested benchmarks. The idea of limiting factorization to a finite horizon and grouping only conflicting agents by reachability is clearly presented and addresses a real gap in the MAPF literature. The paper also uses a reasonable anytime comparison protocol (giving LaCAM* a time budget equal to the total time of the proposed method) and reports standard deviation and min-max ranges, which is a positive sign for reproducibility. However, the manuscript is an extended abstract rather than a full paper: no formal guarantees are provided, no code is released, and the evaluation covers only two maps and one baseline. The central novelty—the hierarchical factorization—is not analyzed in terms of group-size growth, which is the key to its scalability. The contribution is therefore promising but not yet fully supported.

major comments (3)

[Section II, Algorithm composition] The paper never states a lemma or proof that the one-step joint plan produced by composing finalized individual trajectories with group PIBT replans is executable (i.e., free of vertex and edge conflicts). Since only the first move is executed, the framework can recover from many failures, but the claimed scalability relies on the assumption that most agents remain conflict-free within the horizon and that groups stay small. If the congestion resolution module keeps enlarging a group, the method degrades to centralized PIBT over O(N) agents, which reintroduces the scalability problem the abstract claims to solve. Please add a formal feasibility argument for the composition, a termination/bounded-group-size analysis of the congestion resolution, or at least an empirical study of group-size distributions on a variety of maps to support the scalability claim.
[Section III, Experimental setup and results] The experimental evaluation is limited to two maps (warehouse-20-40-10-2-2 and random-64-64-10) and a single baseline, LaCAM*. The abstract's claim that the method 'outperforms state-of-the-art offline baselines across a range of problem sizes and planning horizons' is not supported by this evidence: a range of problem sizes is shown (N=100, 500, 900) but only on these two maps, and no comparison is made to other scalable MAPF algorithms (e.g., PIBT, LaCAM, MAPF-LNS2, EECBS). Moreover, no absolute TNBE values are reported—only ratios—so the reader cannot judge the practical latency numbers. The paper also does not report success rates (i.e., whether all 200 runs completed within a time/memory limit) or the variance of group sizes. Please extend the benchmark set (at least one dense map and one maze-like map), add at least one additional baseline, and report absolute TNBE, total planning time, and success rates.
[Section III, Solution quality comparison] The SOC comparison protocol, in which LaCAM* is allowed to refine until the proposed method has completed all planning steps, is a legitimate anytime budget but must be described with absolute times. The claim in the text that the method 'consistently yields higher-quality solutions' is based on mean SOC values, yet the figures show overlapping standard-deviation and min-max ranges in several panels (e.g., random map with N=100 and warehouse with N=500 at short horizons). Please report the actual wall-clock time budgets, use paired statistical tests (e.g., Wilcoxon signed-rank) or report the fraction of runs in which the proposed method achieves lower SOC, and clarify whether the differences are practically significant.

minor comments (7)

[Section III, Experiment Setup] The phrase 'Each experiment was run 200 times' is ambiguous: what is randomized across runs (start-goal pairs, seeds, or identical instances)? If the same instances are used, explain what the variance represents.
[Section II, Figure 1] The figure caption and step numbering are informative, but a formal pseudocode block (Algorithm 1) would greatly improve reproducibility and precision.
[Abstract and Section I] The phrase 'state-of-the-art offline baselines' appears prematurely in the abstract and introduction; the only offline baseline evaluated is LaCAM*. Please soften to 'the offline anytime planner LaCAM*' or similar.
[Section III, Figures 2 and 3] The axes are labeled 'Horizon Parameter' but the text calls it 'planning horizon H'; be consistent. Also, the figures use ×10^4 on the SOC y-axis; consider normalizing SOC by the lower bound or the number of agents to make comparisons more interpretable.
[Section IV, Discussion and Conclusion] The sentence 'This yields solution quality competitive with leading offline methods' is stronger than what the experiments show; the method only outperforms LaCAM* on two maps. Please align the conclusion with the evidence.
[Section I, Related Work] Reference [14] is appropriate, but the paper would benefit from citing the current MAPF benchmark suite and the most recent LaCAM* variants more precisely (references [12] and [13] are both arXiv preprints).
[Section III, Time needed before execution] The sentence 'we observe a 60% reduction in TNBE' at N=900, H=20 should be accompanied by the exact absolute TNBE values for both methods, as a single ratio can be misleading if the baseline is very fast.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TNBE and solution-quality results are empirical measurements of an independently specified algorithm; self-citations are background only.

full rationale

The paper's central claims are experimental measurements: TNBE ratios and SOC values for its proposed online algorithm against LaCAM* on two MAPF benchmark maps. No quantity in the derivation chain is defined in terms of another measured quantity; the horizon H is a user-set parameter that is swept across experiments, and no parameter is fitted to force the reported 60% reduction. The algorithm itself (individual parallel planning, conflict detection over H, reachability-based grouping, PIBT group replanning, congestion-driven group enlargement, one-step execution) is specified independently of the reported outcomes, and the comparison protocol (LaCAM* given additional refinement time) is conservative rather than outcome-tuned. The references to the authors' prior factorization work (Zanardi et al., [17], [18]) appear in the introduction as background motivation and are not used to justify or derive the new algorithm's feasibility, completeness, or performance; hence they are not load-bearing. The absence of a formal feasibility/completeness proof for the hierarchical factorization is a correctness or robustness concern, not a circularity, because the performance claims are empirical and the procedure can fail without the claim being vacuously true.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The paper introduces no new theoretical entities; it combines existing MAPF concepts. Its main tunable parameter is the horizon H, which is not fit to data but user-specified.

free parameters (1)

planning horizon H = varied from 2 to 20
H is a user-chosen parameter in the receding-horizon loop; the paper sweeps it in experiments rather than fitting it, but the reported speedups depend on its value.

assumptions (2)

domain assumption Standard MAPF assumptions: discrete time, unit-cost moves, vertex and edge conflicts.
The benchmarks and algorithm operate on grid graphs with discrete time steps, as assumed in Section III.
domain assumption The PIBT-based replanning routine resolves conflicts within any group of agents within the finite horizon.
Used in step 4 of the algorithm; the paper does not prove completeness or failure bounds for the grouped replanning.

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Cite this review

Pith. "Pith review of Multi-Agent Path Finding via Finite-Horizon Hierarchical Factorization." pith.science (2026). https://pith.science/paper/TGLKSCS4

@misc{pith2026250507779,
  author       = {Pith},
  title        = {Pith review of: Multi-Agent Path Finding via Finite-Horizon Hierarchical Factorization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TGLKSCS4}},
  note         = {Machine review of arXiv:2505.07779}
}

read the original abstract

We present a novel algorithm for large-scale Multi-Agent Path Finding (MAPF) that enables fast, scalable planning in dynamic environments such as automated warehouses. Our approach introduces finite-horizon hierarchical factorization, a framework that plans one step at a time in a receding-horizon fashion. Robots first compute individual plans in parallel, and then dynamically group based on spatio-temporal conflicts and reachability. The framework accounts for conflict resolution, and for immediate execution and concurrent planning, significantly reducing response time compared to offline algorithms. Experimental results on benchmark maps demonstrate that our method achieves up to 60% reduction in time-to-first-action while consistently delivering high-quality solutions, outperforming state-of-the-art offline baselines across a range of problem sizes and planning horizons.

Figures

Figures reproduced from arXiv: 2505.07779 by the authors.

**Figure 2.** The ratio of the TNBE between our algorithm and offline baselines; [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Our algorithm consistently outperforms LaCAM* in solution [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

PRIMAL3: Pathfinding via Reinforcement and Imitation Multi-Agent Learning - Leveraging LaCAM3
cs.RO 2026-08 conditional novelty 6.0 of 10

A dual-graph, reinforcement-and-imitation learning framework for MAPF that scales to 100,000 agents, with results close to search-based solvers on random maps.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Coordinating hundreds of cooperative, autonomous vehi- cles in warehouses

Peter R Wurman, Raffaello D’Andrea, and Mick Mountz. Coordinating hundreds of cooperative, autonomous vehi- cles in warehouses. AI magazine, 29(1):9–9, 2008

work page 2008

[2] [2]

Finding optimal solutions to cooper- ative pathfinding problems

Trevor Standley. Finding optimal solutions to cooper- ative pathfinding problems. In Nat. Conf. on Artificial Intelligence (AAAI), volume 24, pages 173–178, 2010

work page 2010

[3] [3]

Cooperative pathfinding

David Silver. Cooperative pathfinding. Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment , 1(1):117–122, 2005

work page 2005

[4] [4]

Sturtevant, Ariel Felner, Sven Koenig, Hang Ma, Thayne T

Roni Stern, Nathan R. Sturtevant, Ariel Felner, Sven Koenig, Hang Ma, Thayne T. Walker, Jiaoyang Li, Dor Atzmon, Liron Cohen, T. K. Satish Kumar, Eli Boyarski, and Roman Bartak. Multi-agent pathfinding: Definitions, variants, and benchmarks. Symposium on Combinatorial Search (SoCS), pages 151–158, 2019

work page 2019

[5] [5]

Conflict-based search for optimal multi-agent pathfinding

Guni Sharon, Roni Stern, Ariel Felner, and Nathan R Sturtevant. Conflict-based search for optimal multi-agent pathfinding. Artificial Intelligence, 219:40–66, 2015

work page 2015

[6] [6]

Eecbs: A bounded-suboptimal search for multi-agent path find- ing

Jiaoyang Li, Wheeler Ruml, and Sven Koenig. Eecbs: A bounded-suboptimal search for multi-agent path find- ing. In Nat. Conf. on Artificial Intelligence (AAAI) , volume 35, pages 12353–12362, 2021

work page 2021

[7] [7]

Subdimensional expansion for multirobot path planning

Glenn Wagner and Howie Choset. Subdimensional expansion for multirobot path planning. Artificial Intel- ligence, 219:1–24, 2015

work page 2015

[8] [8]

Planning optimal paths for multiple robots on graphs

Jingjin Yu and Steven M LaValle. Planning optimal paths for multiple robots on graphs. In 2013 IEEE International Conference on Robotics and Automation , pages 3612–3617. IEEE, 2013

work page 2013