On Computational Complexity of Pickup-and-Delivery Problems with Precedence Constraints or Time Windows
Why this work is in the frame
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Bibliographic record
Abstract
Pickup-and-Delivery (PD) problems consider routing vehicles to achieve a set of tasks related to ``Pickup'', and to ``Delivery''. Meanwhile these tasks might subject to Precedence Constraints (PDPC) or Time Windows (PDTW). PD is a variant to Vehicle Routing Problems (VRP), which have been extensively studied for decades. In the recent years, PD demonstrates its closer relevance to AI. With an awareness that few work has been dedicated so far in addressing where the tractability boundary line can be drawn for PD problems, we identify in this paper a set of highly restricted PD problems and prove their NP-completeness. Many problems from a multitude of applications and industry domains are general versions of PDPC. Thus this new result of NP-hardness, of PDPC, not only clarifies the computational complexity of these problems, but also sets up a firm base for the requirement on use of approximation or heuristics, as opposed to looking for exact but intractable algorithms for solving them. We move on to perform an empirical study to locate sources of intractability in PD problems. That is, we propose a local-search formalism and algorithm for solving PDPC problems in particular. Experimental results support strongly effectiveness and efficiency of the local-search. Using the local-search as a solver for randomly generated PDPC problem instances, we obtained interesting and potentially useful insights regarding computational hardness of PDPC and PD.
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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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it