Efficient algorithms using subiterative convergence for Kemeny ranking problem
Badal, Prakash S
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Multidimensional ranking is useful to practitioners in political science, computer science, social science, medical science, and allied fields. The objective is to identify a consensus ranking of n objects that best fi ts independent rankings given by k different judges. The Kemeny distance is used as a metric to obtain consensus ranking. For large n, under present computing powers, it is not feasible to identify a consensus ranking. To address the problem, researchers have proposed several algorithms. These algorithms are able to handle datasets with n up to 200 in a reasonable amount of time. However, run-time increases very quickly as n increases. In the present paper, we propose two basic algorithms - Subiterative Convergence and Greedy Algorithm. Using these basic algorithms, two advanced algorithms - FUR and SIgFUR are developed. We show that our results are superior both in terms of Kemeny distance, as a performance measure, and run-time to existing algorithms. The proposed algorithms, even for large n, runs in few minutes.
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