Randomized greedy matching. II

Aronson, Jonathan; Dyer, Martin; Frieze, Alan; Suen, Stephen

doi:10.1002/rsa.3240060107

Cited by 48 publications

(94 citation statements)

References 3 publications

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“…All those who had previous aortic surgery and correction of congenital cardiac abnormality in childhood were excluded, as were those operated for infective endocarditis. Of 315 eligible redo patients, we found best matched pairs for 289 on the basis of age, gender, left ventricular systolic function and type of surgical procedure among patients who underwent primary cardiac operation, using the Greedy method [10]. Demographic information, clinical symptoms, comorbidities, operative and postoperative details were retrieved from the database and supplemented with chart review.…”

Section: Study Populationmentioning

confidence: 99%

The impact of symptom severity on cardiac reoperative risk: early referral and reoperation is warranted

Ngaage

Cowen

Griffin

et al. 2007

European Journal of Cardio-Thoracic Surgery

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Background: Operative mortality is comparatively higher for coronary artery bypass grafting (CABG) or valve reoperations. Studies of reoperative risk have focussed on surgical techniques. We sought to determine the risk and predictors of poor outcome in current practice, and the influence of preoperative symptoms. Method: For every redo patient (n = 289), we selected the best-matched pair of patients who underwent a primary operation (n = 578) between 1998 and 2006. Matching variables were age, gender, left ventricular ejection fraction (LVEF) and type of operation. Poor outcome was defined as operative mortality or major morbidity. Result: Median age was 68 (interquartile range 62-73) years and 28% were female for both groups. Severe symptoms and cardiac morbidity dominated the presentation of redo patients. CABG (53%), valve repair/ replacement (34%) and combined CABG and valve (12%) were performed with overall operative mortality of 6.6% (median additive EuroScore 7.0) for redo versus 1.6% (median additive EuroScore 4.0) for primary groups ( p < .0001). Whereas no significant difference was observed between primary (1.6%) and redo CABG (3.9%, p = .19), valve reoperations had higher operative mortality (9.6% vs 1.5%, p < .0001). Major complications occurred more frequently after redo valve compared to primary valve operations (28% vs 14%, p = .001). Reoperation (odds ratio [OR] 1.26, 95% confidence interval [CI] 0.66-2.42, p = .48) was not a predictor of major adverse event after CABG or valve surgery. Determinants of poor outcome after valve reoperations were New York Heart Association class III/IV (OR 6.86, 95% CI 2.29-12.11, p = .03), duration of extracorporeal circulation (OR 1.17, 95% CI 1.02-1.35, p = .03) and mitral valve replacement (OR 4.07, 95% CI 1.83-36.01, p = .04). The predictors of major adverse events after redo CABG were congestive heart failure (OR 1.85, 95% CI 1.04-8.98, p = .006) chronic obstructive pulmonary disease (OR 17.5, 95% CI 1.87-35.21, p = .05) and interval from prior surgery (OR 1.37, 95% CI 1.09-1.92, p = .01). Conclusion: In the current era, redo CABG is nearly as safe as the primary operation. A valve reoperation, on the contrary, is higher risk due, partly, to severe symptoms at presentation. Patients should be referred and operated on early before they develop severe symptoms. #

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Section: Study Populationmentioning

confidence: 99%

The impact of symptom severity on cardiac reoperative risk: early referral and reoperation is warranted

Ngaage

Cowen

Griffin

et al. 2007

European Journal of Cardio-Thoracic Surgery

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“…On the other hand, Aronson et al (1993) can show that (5.2) yields a 1 performance of at least --+ e with e>0.001, where the 2 lower bound is conjectured to be not best possible. Karp and Sipser (1981) have analyzed a greedy heuristic in the spirit of (5.1) that avoids the pitfalls of the worstcase example above: Select, if possible, a vertex with exactly one incident edge at random.…”

Section: Probabilistic Analysismentioning

confidence: 99%

“…Section 5 surveys some results on the probabilistic analysis of greedy algorithms for assignment problems. While most of these results refer to the estimation of the average-case performance, Aronson et al (1993) are able to show that randomization of the greedy algorithm for matching problems helps on concrete graphs. We consider on-line problems in Sect.…”

Section: Introductionmentioning

confidence: 99%

Some recent results in the analysis of greedy algorithms for assignment problems

Faigle

1994

OR Spektrum

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Abstract.We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems.

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“…This idea was first used by Aronson, Dyer, Frieze, and Suen in [2] where they gave the following randomized algorithm for the maximum matching problem -Pick a vertex at random and match it to one of its unmatched neighbors uniformly at random. They showed that this algorithm does marginally better than 0.5 and attains a factor of 0.50000025.…”

Section: Introductionmentioning

confidence: 99%

Matching with Our Eyes Closed

Goel

Tripathi

2012

2012 IEEE 53rd Annual Symposium on Foundations of Computer Science

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Abstract-Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of vertices to determine if they are adjacent. If the queried edge exists, we are committed to match the two endpoints. Our objective is to maximize the size of the matching.This restriction in the amount of information available to the algorithm constraints us to implement myopic, greedy-like algorithms. A simple deterministic greedy algorithm achieves a factor 1/2 which is tight for deterministic algorithms. An important open question in this direction is to give a randomized greedy algorithm that has a significantly better approximation factor. This question was first asked almost 20 years ago by Dyer and Frieze [9] where they showed that a natural randomized strategy of picking edges uniformly at random doesn't help and has an approximation factor of 1/2 + o(1). They left it as an open question to devise a better randomized greedy algorithm. In subsequent work, Aronson, Dyer, Frieze, and Suen [2] gave a different randomized greedy algorithm and showed that it attains a factor 0.5 + ǫ where ǫ is 0.0000025.In this paper we propose and analyze a new randomized greedy algorithm for finding a large matching in a general graph and use it to solve the query commit problem mentioned above. We show that our algorithm attains a factor of at least 0.56, a significant improvement over 0.50000025. We also show that no randomized algorithm can have an approximation factor better than 0.7916 for the query commit problem. For another large and interesting class of randomized algorithms that we call vertex-iterative algorithms, we show that no vertexiterative algorithm can have an approximation factor better than 0.75.

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Randomized greedy matching. II

Cited by 48 publications

References 3 publications

The impact of symptom severity on cardiac reoperative risk: early referral and reoperation is warranted

The impact of symptom severity on cardiac reoperative risk: early referral and reoperation is warranted

Some recent results in the analysis of greedy algorithms for assignment problems

Matching with Our Eyes Closed

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