| paper | d4-conf-aaai-2008-0043 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Theorem 1 characterizes IDP's omitted splits, but gives no named guarantee for computing a coalition structure, complexity bound, or hardness result. The hybrid algorithm and its measured speedups are unnumbered, while the NP-completeness claim is attributed to prior work, so bit (a) fails.
fails bit a — no named computational result to mirror
No result is mirrored: Theorem 1 concerns omitted splits, the hybrid algorithm's optimality explanation and timing results are unnumbered, and the NP-completeness claim is prior work.
There is no anchor in this paper that meets the stated requirement for a named complexity result.
The only numbered theorem is Theorem 1, proved here. It says IDP does not evaluate splittings of coalitions whose sizes lie between \(\lfloor 2n/3\rfloor+1\) and \(n-1\). That is a structural fact about the algorithm, not a result classifying a problem as NP-hard, polynomial-time solvable, or similar. The paper’s claim that coalition structure generation is NP-complete appears in the introduction and is attributed to Sandholm et al. (1999); it is not a numbered result of this paper.
So I can’t give an anchor-grounded continuous problem under your rules. The hybrid algorithm’s reported performance is a contribution, but it does not supply the required named complexity anchor.
The proponent names no anchors, and that is the strongest point against treating this paper as a positive case. Theorem 1 says IDP skips certain coalition splittings; it does not classify the complexity of a computational problem. The NP-completeness claim in the introduction is attributed to Sandholm et al., and the \(O(3^n)\) and \(O(n^n)\) bounds describe earlier algorithms. The paper gives no worst-case complexity result for its own hybrid; it lists that analysis as future work. So there is no named complexity result here for a continuous mirror to anchor to.
The strongest possible mirror would be coalition structure generation for a high-multiplicity population: for example, many interchangeable sensors, with types describing capabilities and coalition values depending on type composition. One could ask how to partition type masses into coalitions to maximize total value. That is a recognizable computational question, and a configuration LP with a pricing problem is a plausible approach. I cannot honestly rule it out as worthwhile; the paper gives no evidence that it is already answered or that the continuous formulation would be trivial.
That exposes the limit of the negative case. Under the requested anchor standard, the proponent has established no positive mirror. But the stronger claim that *no scenario* yields a worthwhile one is not supported: the high-multiplicity CSG formulation is a credible candidate, even though it is a new question rather than a mirror of a complexity theorem proved in 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.