| paper | d4-conf-aaai-2004-0178 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper presents computational procedures and experiments, but it contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. The opponent’s proposed continuous procurement model cannot overcome the failure of bit (a), which requires a qualifying result from the paper to anchor the mirror.
fails bit a — no named computational result to mirror
No qualifying named computational result is anchored; the paper’s constraint-generation procedures, arbitrary-weight methods, elicitation methods, and experiments remain unmirrored.
There is no qualifying anchor in this paper: it contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a complexity classification or algorithmic result. Its computational contributions are unnumbered procedures and empirical evaluations, including constraint generation for minimax regret. The NP-completeness of generic winner determination appears as cited background, not as a numbered result of this paper.
So there are zero anchors to mirror, and I can’t honestly provide the requested anchor-based continuous problems or predict their complexity classes.
The “zero anchors” claim reads “no numbered complexity theorem” as “no computational result.” The paper does lack a numbered theorem classifying a problem’s complexity, and the NP-completeness of generic winner determination is cited background. But it presents new computational methods as its main contribution: Section 4.1 gives an exact constraint-generation procedure for minimax regret with bounded weights; Section 4.2 develops methods for arbitrary weight constraints; and Section 5 studies comparison queries that refine the buyer’s preferences. Those are computational results even though they are not numbered theorems.
A credible mirror is a large, recurring procurement market with many interchangeable suppliers. A supplier type records its offered bundle, price, capacity, and relevant traits such as region or delivery reliability. Let \(\mu_t\) be the mass of suppliers of type \(t\), and let \(x_t\in[0,\mu_t]\) be the accepted mass. Coverage constraints require sufficient supply of each item; cost and non-price features are aggregate functions of \(x\). The bid taker still has an uncertain weight vector \(w\in W\), so the robust allocation problem is
\[ \min_{x\in F(\mu)}\ \max_{w\in W} \left[\max_{x'\in F(\mu)}u(x';w)-u(x;w)\right], \]
where \(F(\mu)\) is the feasible set of mass allocations. This keeps the paper’s central computational question—choosing an allocation under uncertain tradeoffs—while making the supplier population continuous. In repeated procurement of standardized lots, describing accepted capacity as a share of the supplier pool is a natural model. Per-capita supply and aggregate features are the corresponding co-modifications.
That gives a question tied directly to Section 4.1: how does exact minimax-regret computation scale with the number of items, supplier types, input bit length, and utility features when feasible allocations are masses? The constraints generated by the algorithm now range over a continuous allocation space, so the pricing or separation problem is part of the question. Section 4.2 yields another: can minimax regret and comparison-query elicitation be computed efficiently when the buyer’s feasible weight set is an arbitrary polytope and the alternatives are continuous allocations? These questions remain worth asking regardless of whether their answers turn out to be easy, hard, or unchanged from the discrete setting.
Identity-sensitive features narrow the range of suitable markets, but they do not rule out a mirror. A market focused on regional diversity, aggregate delivery quality, or the share of business by supplier type need not track particular named suppliers. A one-off auction with lumpy, supplier-specific bids is a poor fit; a large recurring market with many suppliers of the same types is a plausible one. So the paper has fewer formal complexity claims to mirror than the proponent’s wording suggests, but the absence of numbered theorems does not establish the absence of a worthwhile continuous question.
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.