| paper | d4-conf-aaai-2000-0175 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper’s NP-completeness statement is background attributed to earlier work, while its Casanova comparisons are empirical findings, not a numbered computational result with a stated guarantee. A high-multiplicity winner-determination model is a coherent possible research direction, but it is not anchored in an eligible computational result of this paper.
fails bit a — no named computational result to mirror
The opponent’s possible extension covers winner determination with bidder types and scaled supplies; it does not mirror a named result on Casanova’s empirical performance.
This paper has no numbered theorem, lemma, corollary, or proposition asserting a computational result, so it supplies no eligible anchor for the requested positive case. Its closest candidate is the unnumbered statement in §2.1 that optimal winner determination is equivalent to weighted set packing and is NP-complete; the paper cites that result from elsewhere ([16]) rather than proving it here. The Casanova comparisons are empirical table results, not named results of the required kind.
A continuous combinatorial-auction mirror could be proposed, but it would not be anchored in a qualifying result from this paper. There is therefore no per-anchor continuous problem to state under your criteria.
The appended case names no continuous mirror, so there is no proposed anchor to defeat. Its strongest point is that the paper contains no numbered theorem, lemma, or corollary giving a computational result. The NP-completeness of winner determination appears as background, attributed to earlier work. The paper’s own contribution is Casanova and its empirical comparison with CASS. Those experiments report performance on selected finite-instance distributions; they give no complexity or approximation result to carry over to a continuous society. On the paper-specific question, that is a strong reason to say there is no result here to mirror.
The best candidate for a new question would be a high-multiplicity auction: group bidders by complete valuation or bid type, scale supplies with the population, and optimize over how much mass of each type receives each feasible bundle. That can lead to a configuration LP and a pricing problem, so it is a plausible computational research direction. Repeated explicit bids for the same bundle are often redundant, but richer schematic or valuation types can make multiplicity matter.
That candidate also shows where the negative case is weak. The paper studies winner determination in combinatorial auctions, and a type-based, scaled-supply version could be recognized as a question about that problem. I cannot honestly rule out that it would be worthwhile. The narrower case is firmer: such a study would formulate and analyze a new high-multiplicity auction model; it would not mirror a computational theorem or complexity result established by this paper.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.