Intractability of Optimal Multi-Agent Pathfinding on Directed Graphs
Bibliographic record
Abstract
In Multi-Agent Pathfinding (MAPF) problems, multiple agents move simultaneously to reach their individual destinations without colliding with each other. The computational complexity of the problem has been extensively studied for undirected graphs over the past decades. However, plan existence for Directed MAPF (diMAPF) was only recently studied and was shown to be in PSPACE as well as NP-hard. In this paper, we study the optimization versions (on makespan and on travel distance of agents) of diMAPF problems and show that they remain NP-hard even when various important non-trivial restrictions are imposed (e.g., when considering the problem on directed, acyclic, and planar graphs where the vertex-degrees are bounded). We have also provide membership results, thus presenting the first set of NP-completeness results for various optimal diMAPF variants.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".