An Approximation Algorithm for the Bipartite Traveling Tournament Problem
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Bibliographic record
Abstract
The bipartite traveling tournament problem (BTTP) is an NP-complete scheduling problem whose solution is a double round-robin inter-league tournament with minimum total travel distance. The 2n-team BTTP is a variant of the well-known traveling salesman problem (TSP), albeit much harder as it involves the simultaneous coordination of 2n teams playing a sequence of home and away games under fixed constraints, rather than a single entity passing through the locations corresponding to the teams' home venues. As the BTTP requires a distance-optimal schedule linking venues in close proximity, we provide an approximation algorithm for the BTTP based on an approximate solution to the corresponding TSP. We prove that our polynomial-time algorithm generates a 2n-team inter-league tournament schedule whose total distance is at most 1 + 2c/3 + (3 − c)/(3n) times the total distance of the optimal BTTP solution, where c is the approximation factor of the TSP. In practice, the actual approximation factor is far better; we provide a specific example by generating a nearly-optimal inter-league tournament for the 30-team National Basketball Association, with total travel distance just 1.06 times the trivial theoretical lower bound.
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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 | 0.011 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 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 it