Optimal Lower Bounds for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.United States-Israel Binational Science FoundationIsrael. Ministry of ScienceGoogle Inter-University Center for Electronic Markets and Auction

Coronary artery endothelial dysfunction is positively correlated with low density lipoprotein and inversely correlated with high density lipoprotein subclass particles measured by nuclear magnetic resonance spectroscopy.

OBJECTIVE: The association between cholesterol and endothelial dysfunction remains controversial. We tested the hypothesis that lipoprotein subclasses are associated with coronary endothelial dysfunction. METHODS AND RESULTS: Coronary endothelial function was assessed in 490 patients between November 1993 and February 2007. Fasting lipids and nuclear magnetic resonance (NMR) lipoprotein particle subclasses were measured. There were 325 females and 165 males with a mean age of 49.8+/-11.6 years. Coronary endothelial dysfunction (epicardial constriction>20% or increase in coronary blood flow<50% in response to intracoronary acetylcholine) was diagnosed in 273 patients, the majority of whom (64.5%) had microvascular dysfunction. Total cholesterol and LDL-C (low density lipoprotein cholesterol) were not associated with endothelial dysfunction. One-way analysis and multivariate methods adjusting for age, gender, diabetes, hypertension and lipid-lowering agent use were used to determine the correlation between lipoprotein subclasses and coronary endothelial dysfunction. Epicardial endothelial dysfunction was significantly correlated with total (p=0.03) and small LDLp (LDL particles) (p<0.01) and inversely correlated with total and large HDLp (high density lipoprotein particles) (p<0.01). CONCLUSIONS: Epicardial, but not microvascular, coronary endothelial dysfunction was associated directly with LDL particles and inversely with HDL particles, suggesting location-dependent impact of lipoprotein particles on the coronary circulation

Complete revascularization with multivessel PCI for myocardial infarction

BACKGROUND In patients with ST-segment elevation myocardial infarction (STEMI), percutaneous coronary intervention (PCI) of the culprit lesion reduces the risk of cardiovascular death or myocardial infarction. Whether PCI of nonculprit lesions further reduces the risk of such events is unclear. METHODS We randomly assigned patients with STEMI and multivessel coronary artery disease who had undergone successful culprit-lesion PCI to a strategy of either complete revascularization with PCI of angiographically significant nonculprit lesions or no further revascularization. Randomization was stratified according to the intended timing of nonculprit-lesion PCI (either during or after the index hospitalization). The first coprimary outcome was the composite of cardiovascular death or myocardial infarction; the second coprimary outcome was the composite of cardiovascular death, myocardial infarction, or ischemia-driven revascularization. RESULTS At a median follow-up of 3 years, the first coprimary outcome had occurred in 158 of the 2016 patients (7.8%) in the complete-revascularization group as compared with 213 of the 2025 patients (10.5%) in the culprit-lesion-only PCI group (hazard ratio, 0.74; 95% confidence interval [CI], 0.60 to 0.91; P=0.004). The second coprimary outcome had occurred in 179 patients (8.9%) in the complete-revascularization group as compared with 339 patients (16.7%) in the culprit-lesion-only PCI group (hazard ratio, 0.51; 95% CI, 0.43 to 0.61; P<0.001). For both coprimary outcomes, the benefit of complete revascularization was consistently observed regardless of the intended timing of nonculprit-lesion PCI (P=0.62 and P=0.27 for interaction for the first and second coprimary outcomes, respectively). CONCLUSIONS Among patients with STEMI and multivessel coronary artery disease, complete revascularization was superior to culprit-lesion-only PCI in reducing the risk of cardiovascular death or myocardial infarction, as well as the risk of cardiovascular death, myocardial infarction, or ischemia-driven revascularization. (Funded by the Canadian Institutes of Health Research and others; COMPLETE ClinicalTrials.gov number, NCT01740479. opens in new tab.

An Optimal Lower Bound for Anonymous Scheduling Mechanisms

We consider the problem of designing truthful mechanisms to minimize the makespan on m unrelated machines. In their seminal paper, Nisan and Ronen [14] showed a lower bound of 2, and an upper bound of m, thus leaving a large gap. They conjectured that their upper bound is tight, but were unable to prove it. Despite many attempts that yield positive results for several special cases, the conjecture is far from being solved: the lower bound was only recently slightly increased to 2.61 [5, 10], while the best upper bound remained unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. This is the first concrete evidence to the correctness of the Nisan-Ronen conjecture, especially given that the classic scheduling algorithms are anonymous, and all state-of-the-art mechanisms for special cases of the problem are anonymous as well

Multi-unit auctions with budget limits. In

Abstract We study multi-unit auctions where the bidders have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there are no incentive-compatible auctions that always produce a Pareto-optimal allocation. We also obtain some surprising positive results for certain special cases. JEL Classification Numbers: C70, D44, D82 Keywords: Multi-Unit Auctions, Budget Constraints, Pareto Optimality. * A preliminary version appeared in FOCS&apos;08. We thank Peerapong Dhangwatnotai for pointing out an error in a previous version

Multi-unit auctions with budget limits

We study multi-unit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentive-compatible auctions that always produce a Pareto-optimal allocation. We also obtain some surprising positive results for certain special cases.