WinC-MAPF: Complete Windowed MAPF

• WinC-MAPF is a framework for windowed multi-agent pathfinding that guarantees completeness by integrating real-time heuristic updates and agent grouping to overcome planning deadlocks.
• It combines heuristic learning from single-agent real-time search with independent agent planning to efficiently resolve conflicts without long-horizon computation.
• Empirical evaluations with its SS-CBS instantiation show near-instant planning and high success rates in dense environments with only a 2–8% increase in solution cost.

Searching arXiv for the core WinC-MAPF paper and closely related extensions/comparators. arXiv_search query: "^^^^^^^^2ti:\2 MAPF with Completeness Guarantees\"^^^^^^^^2 OR all:\2^^^^^^^^"WinC-MAPF\""

Windowed Complete Multi-Agent Path Finding (WinC-MAPF) is a framework for windowed MAPF that enables completeness by combining heuristic update insights from single-agent real-time heuristic search algorithms with agent independence ideas from MAPF algorithms. It was introduced to address a central tension in MAPF: traditional methods try to compute entire collision-free start-goal paths, but computing an entire path can take too long for systems in which agents must replan fast, whereas windowed methods plan only a short timestep horizon and therefore plan much faster at the cost of incompleteness. WinC-MAPF is formulated to retain the real-time speed associated with windowed planning while ensuring that all agents reach their goals if a solution exists in finite undirected spaces (&&&^^^^2ti:\2^^^^&&&).

^^^^2 OR all:\2^^^^. Motivation and planning model

Traditional MAPF computes entire collision-free paths for all agents. In practical systems such as large-scale robot fleets, this can be computationally expensive, with planning taking tens of seconds or even minutes for large numbers of agents. Windowed MAPF addresses this by planning only the first PRESERVED_PLACEHOLDER_^^^^2ti:\2^^^^ timesteps of a solution, guaranteeing collision-freedom only inside that window; agents execute their first step and then replan. In the standard windowed formulation, the remainder of each agent’s path is taken to be its optimal shortest solo path to the goal (&&&^^^^2ti:\2^^^^&&&).

This receding-horizon structure yields low-latency replanning, and windowed solvers such as ECBS, RHCR, and PIBT are therefore attractive in real-time settings. The cost is that short windows induce myopic decisions. The 2^^^^2ti:\22^^^^4 formulation of WinC-MAPF identifies deadlocks, in which agents block each other completely, and livelocks, in which agents repeat endless cycles without progress, as the characteristic failure modes of existing windowed approaches. Even with longer windows, completeness is not assured, and deadlocks and livelocks remain a widely observed practical problem (&&&^^^^2ti:\2^^^^&&&).

The framework is thus motivated by a specific question: whether the speed of windowed planning can be combined with a theoretical guarantee that all agents reach their goals if a solution exists. WinC-MAPF answers this in the affirmative by changing how the planner treats repeated configurations and by restricting heuristic learning to the agents that are actually coupled in the current obstruction pattern (&&&^^^^2ti:\2^^^^&&&).

2. Joint-state formulation and grouped heuristic learning

A core insight of WinC-MAPF is to view MAPF as a single-agent problem in the joint-state space, where a state is the composite configuration of all agent positions. In single-agent real-time search, heuristic learning avoids cycles by increasing the heuristic values of visited states. WinC-MAPF extends this idea to the multi-agent setting: when a joint configuration, or a relevant part of it, is revisited, the framework increases the heuristic cost for that configuration, thereby pushing future planning away from repeated cycles (&&&^^^^2ti:\2^^^^&&&).

Direct heuristic learning over the full joint-state space is impractical because that space is exponential in the number of agents. WinC-MAPF therefore exploits the observation that most deadlocks and livelocks involve only small subsets of agents. Rather than updating penalties for the entire global configuration, it updates heuristics only for the relevant group of coupled agents. Agents that are not currently involved in the blockage can ignore these penalties. This grouped heuristic mechanism is the framework’s principal device for combining real-time search ideas with agent independence ideas from MAPF (&&&^^^^2ti:\2^^^^&&&).

For a group PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^ of coupled agents at configuration $C_{Gr}$, the penalty is defined as

$$h_p(C_{Gr}) = c(C_{Gr}, C'_{Gr}) + h(C'_{Gr}) - h_{BD}(C_{Gr}),$$

where $h_{BD}(C_{Gr})$ is the sum of the individual backward Dijkstra heuristics for those agents. The full heuristic $h(C)$ is the sum of the static backward Dijkstra heuristic for each agent and any dynamic heuristic penalties for involved agent groups in their specific joint configuration. This yields a heuristic that is static where agents remain independent and dynamic where coupling produces repeated obstruction (&&&^^^^2ti:\2^^^^&&&).

3. Framework mechanics and completeness guarantee

WinC-MAPF is organized around an action generator (AG). Given the current configuration $\mathbf{C}^{cur}$ and a set of heuristic penalties $\mathcal{H}$, the AG proposes the next step or short windowed plan for all agents. The AG must select the new configuration $C'$ optimally with respect to immediate transition cost plus future heuristic, written in the framework as $C' = \arg\min_{C'} c(C,C') + h(C')$. The AG must also identify groups of coupled agents involved in the constraints or conflicts encountered during planning (&&&^^^^2ti:\2^^^^&&&).

After the AG returns a next configuration and coupled groups, WinC-MAPF performs a real-time heuristic update for each detected group using a Bellman-style update. In the description accompanying Algorithm ^^^^2 OR all:\2^^^^, this update takes the form

PRESERVED_PLACEHOLDER_^^^^2 OR all:\2ti:\2^^^^

and when the updated value exceeds the baseline heuristic, the excess is stored as a heuristic penalty for that group configuration. The system then advances to the selected next configuration and repeats until all goals are reached (&&&^^^^2ti:\2^^^^&&&).

The framework’s central theoretical statement is that if the AG always selects the optimal step considering current heuristic penalties, and correctly identifies coupled agent groups, then WinC-MAPF is theoretically complete in finite undirected spaces: all agents will reach their goals if a solution exists. The proof is described as paralleling classic LRTA* completeness. Intuitively, if a planner revisits a configuration involved in deadlock or livelock, the heuristic for that group configuration increases each time, until escaping the cycle becomes cheaper than remaining in it. Because the graph is finite and costs are bounded below, any cycle is eventually broken (&&&^^^^2ti:\2^^^^&&&).

This guarantee depends on both pieces of the framework. Heuristic learning alone is insufficient unless the action generator is optimal with respect to the current learned heuristic, and grouping is not merely an efficiency device but part of the completeness argument because the learned values are maintained over the configurations that actually encode the obstruction (&&&^^^^2ti:\2^^^^&&&).

4. Single-Step CBS (SS-CBS)

Single-Step CBS (SS-CBS) is the principal instantiation of WinC-MAPF. It is an optimal action generator with window PRESERVED_PLACEHOLDER_^^^^2 OR all:\2 OR all:\2^^^^: it computes the single best joint action for all agents while taking current heuristic penalties and agent groupings into account. The choice of PRESERVED_PLACEHOLDER_^^^^2 OR all:\22^^^^ is deliberate. The instantiation demonstrates that completeness does not require long-horizon windowed planning; in the framework, even single-step planning can escape the deadlocks and livelocks that defeat conventional short-window solvers (&&&^^^^2ti:\2^^^^&&&).

SS-CBS modifies standard Conflict-Based Search in several ways. A naive attempt to add heuristic penalties after planning paths would be unsound, because individual agents would plan greedily within their current constraints without anticipating which group-level penalties would arise under specific joint combinations. SS-CBS therefore introduces heuristic conflicts. When a joint configuration incurs a heuristic penalty for a group, CBS treats that penalty analogously to a conflict. At branching time, it creates one positive-constraint branch in which the agents must visit the penalized configuration and pay the penalty, and one negative constraint per agent in the group that forbids that agent from occupying the penalized location at the conflicting time. This recursive branching allows the search to discover joint deviations that avoid the penalty while preserving optimality under the learned heuristic (&&&^^^^2ti:\2^^^^&&&).

SS-CBS also extracts coupled groups from the CBS conflict structure. It maintains conflict pairs for every resolved conflict and merges all groups sharing any agent, for example via a union-find structure. The resulting groups are returned to the WinC-MAPF outer loop for heuristic updating. To avoid repeated cycles in symmetric situations, agent priorities can be used as a tie-breaker (&&&^^^^2ti:\2^^^^&&&).

The significance of SS-CBS is methodological as much as algorithmic. It shows that the framework’s requirements on the action generator are concrete: a windowed planner can be modified so that local collision resolution, group detection, and learned heuristic penalties are integrated into a single step-optimal search procedure (&&&^^^^2ti:\2^^^^&&&).

5. Empirical behavior and benchmark results

WinC-MAPF was evaluated through SS-CBS on established MAPF benchmark maps including random-32-32-2^^^^2ti:\2^^^^, ht_chantry, warehouse, and den52^^^^2ti:\2^^^^d. The comparisons included SS-CBS with PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^3, windowed ECBS with window sizes PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^4, and, for very hard small scenarios, full-horizon EECBS with all optimizations. Across these experiments, SS-CBS achieved higher success than any windowed method, especially as the number of agents grew, and the gap widened substantially in dense and congested settings. Its per-iteration runtimes were on par with shorter-window ECBS for PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^5, and below long-window ECBS for PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^6. In exchange for near-instant planning, overall solution cost was reported as only 2–8% higher than best windowed ECBS (&&&^^^^2ti:\2^^^^&&&).

A particularly diagnostic finding concerns repeated non-progress. When windowed ECBS fails because it repeats the same configuration ^^^^2 OR all:\2ti:\2ti:\2^^^^+ times, SS-CBS continues to make progress because heuristic penalties are updated after each step. This directly illustrates the mechanism by which WinC-MAPF converts repeated short-horizon failure into learned avoidance of that failure mode (&&&^^^^2ti:\2^^^^&&&).

The framework was also tested on extremely congested maps, including the “Tunnel”, “Loopchain”, and “Connector” scenarios from Okumura et al. 2^^^^2ti:\222^^^^. In these domains, all tested windowed ECBS variants failed completely due to deadlocks, and even full-horizon EECBS with all optimizations frequently failed or timed out. SS-CBS, despite planning only a single step at a time, solved almost all instances and did so faster (&&&^^^^2ti:\2^^^^&&&).

Method	Tunnel(4)	Loopchain(7)	Connector(6)
W-ECBS (PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^7)	fail	fail	fail
EECBS	^^^^2ti:\2^^^^%	^^^^2ti:\2^^^^%	^^^^2ti:\2^^^^%
SS-CBS	^^^^2 OR all:\2ti:\2ti:\2^^^^%	95%	^^^^2 OR all:\2ti:\2ti:\2^^^^%

These results support the framework’s claim that completeness is not merely a formal property detached from practice. In the reported settings, heuristic learning and grouped penalties materially alter empirical behavior in exactly those congested cases where myopic windowed planning is most brittle (&&&^^^^2ti:\2^^^^&&&).

6. Position in the windowed MAPF literature and later extensions

WinC-MAPF occupies a specific place within the broader windowed MAPF literature. Previous windowed MAPF methods are characterized in the framework as myopic and lacking a mechanism to escape or learn from deadlock; WinC-MAPF differs by combining a heuristic penalty mechanism from real-time search, grouped heuristics that target only the agents involved in blockages, and an optimal action generator per step. In that sense it was introduced as the first framework to guarantee completeness for windowed MAPF with practical, efficient planning (&&&^^^^2ti:\2^^^^&&&).

At the same time, “windowed MAPF” does not refer to a single guarantee regime. X* and the Windowed Anytime Multiagent Planning Framework (WAMPF) use window-based iterative local repairs in sparse domains, returning a valid collision-free solution after a single iteration and converging to the global joint optimal solution as windows grow and merge. That line emphasizes anytime refinement and sparsity-exploiting local repair rather than the specific heuristic-learning completeness mechanism of WinC-MAPF (&&&2^^^^2ti:\2^^^^&&&). Likewise, winPIBT extends PIBT with a configurable time window and proves that all agents reach their own destinations in finite time as long as the environment is a graph with adequate properties, for example biconnected. This suggests that guarantees in windowed planning depend strongly on the underlying planner model and graph assumptions (&&&2^^^^2 OR all:\2^^^^&&&).

A direct extension of WinC-MAPF is Dynamic Agent Grouping ECBS (DAG-ECBS), which addresses a limitation of the original framework: its requirement for an optimal windowed solver. DAG-ECBS shows how a bounded suboptimal solver can be used while maintaining completeness. It dynamically creates and plans agent groups, preserves group-wise bounded suboptimality, and proves that the resulting heuristics remain PRESERVED_PLACEHOLDER_^^^^2 OR all:\2^^^^8-admissible for each disjoint group, thereby extending the completeness logic of WinC-MAPF beyond SS-CBS (Zhang et al., 18 Sep 2025).

Subsequent work also shows the wider influence of windowed planning as a systems pattern, even when completeness is not the central concern. Real-Time MAPF has examined how planning budgets should be allocated across agents or neighborhoods in windowed versions of Prioritized Planning and MAPF-LNS2, arguing that distributed or conflict-proportional budget policies are more effective than a shared budget pool in over-constrained situations (Beck et al., 22 Jul 2025). In lifelong MAPF, LLLG uses a receding-horizon windowed planning framework with warm-started local guidance from the previous solution at each timestep (Arita et al., 16 May 2026). In execution, WinkTPG incrementally refines MAPF plans using a window-based mechanism that incorporates agent information during execution to reduce uncertainty (Yan et al., 2 Aug 2025). These developments do not replace the completeness theorem of WinC-MAPF, but they indicate that the framework helped establish windowed planning as a technically rich design space rather than merely a heuristic truncation of offline MAPF.