An investigation of representations of combinatorial auctions
Bibliographic record
Abstract
Combinatorial auctions (CAs) are an important mechanism for allocating multiple goods while allowing self-interested agents to specify preferences over bundles of items. Winner determination for a CA is known to be NP-complete. However, restricting the problem can allow us to solve winner determination in polynomial time. These restrictions sometimes apply to the CA's representation. There are two commonly studied, and structurally different graph representations of a CA: bid graphs and item graphs. We study the relationship between these two representations. We show that for a given combinatorial auction, if a graph with maximum cycle length three is a valid item graph for the auction, then its bid graph representation is a chordal graph. Next, we present a new technique for constructing item graphs using a novel definition of equivalence among combinatorial auctions. The solution to the WDP for a given CA can easily be translated to a solution on an equivalent CA. We use our technique to simplify item graphs, and show that if a CA's bid graph is chordal, then there exists an equivalent CA with a valid item graph of treewidth one, for which a solution to the WDP is known to be efficient. This result demonstrates how CA equivalence can simplify the structure of item graphs and lead to more efficient solutions to the WDP, which are also a solutions to the WDP for the original auctions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 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".