Abstract
We consider ranking and clustering problems related to the aggregation of inconsistent information. Ailon, Charikar, and Newman [1] proposed randomized constant factor approximation algorithms for these problems. Together with Hegde and Jain, we recently proposed deterministic versions of some of these randomized algorithms [2]. With one exception, these algorithms required the solution of a linear programming relaxation. In this paper, we introduce a purely combinatorial deterministic pivoting algorithm for weighted ranking problems with weights that satisfy the triangle inequality; our analysis is quite simple. We then shown how to use this algorithm to get the first deterministic combinatorial approximation algorithm for the partial rank aggregation problem with performance guarantee better than 2. In addition, we extend our approach to the linear programming based algorithms in Ailon et al. [1] and Ailon [3]. Finally, we show that constrained rank aggregation is not harder than unconstrained rank aggregation.
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References
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van Zuylen, A., Williamson, D.P. (2008). Deterministic Algorithms for Rank Aggregation and Other Ranking and Clustering Problems. In: Kaklamanis, C., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2007. Lecture Notes in Computer Science, vol 4927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77918-6_21
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DOI: https://doi.org/10.1007/978-3-540-77918-6_21
Publisher Name: Springer, Berlin, Heidelberg
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