Ordinal ranking and intensity of preference: A linear programming approach
Management Science
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
On an instance of the inverse shortest paths problem
Mathematical Programming: Series A and B
On the use of an inverse shortest paths algorithm for recovering linearly correlated costs
Mathematical Programming: Series A and B
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Operations Research
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
Linear programming models for estimating weights in the analytic hierarchy process
Computers and Operations Research
Methodologies and Algorithms for Group-Rankings Decision
Management Science
Country credit-risk rating aggregation via the separation-deviation model
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Rating Customers According to Their Promptness to Adopt New Products
Operations Research
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The problem of rank aggregation has been studied in contexts varying from sports, to multi-criteria decision making, to machine learning, to academic citations, to ranking web pages, and to descriptive decision theory. Rank aggregation is the mapping of inputs that rank subsets of a set of objects into a consistent ranking that represents in some meaningful way the various inputs. In the ranking of sports competitors, or academic citations or ranking of web pages the inputs are in the form of pairwise comparisons. We present here a new paradigm using an optimization framework that addresses major shortcomings in current models of aggregate ranking. Ranking methods are often criticized for being subjective and ignoring some factors or emphasizing others. In the ranking scheme here subjective considerations can be easily incorporated while their contributions to the overall ranking are made explicit. The inverse equal paths problem is introduced here, and is shown to be tightly linked to the problem of aggregate ranking “optimally”. This framework is useful in making an optimization framework available and by introducing specific performance measures for the quality of the aggregate ranking as per its deviations from the input rankings provided. Presented as inverse equal paths problem we devise for the aggregate ranking problem polynomial time combinatorial algorithms for convex penalty functions of the deviations; and show the NP-hardness of some forms of nonlinear penalty functions. Interestingly, the algorithmic setup of the problem is that of a network flow problem. We compare the equal paths scheme here to the eigenvector method, Google PageRank for ranking web sites, and the academic citation method for ranking academic papers.