Approximate Maximum Rank Aggregation: Beyond the Worst-Case

Authors Yan Hong Yao Alvin, Diptarka Chakraborty

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Yan Hong Yao Alvin
  • National University of Singapore, Singapore
Diptarka Chakraborty
  • National University of Singapore, Singapore

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Yan Hong Yao Alvin and Diptarka Chakraborty. Approximate Maximum Rank Aggregation: Beyond the Worst-Case. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The fundamental task of rank aggregation is to combine multiple rankings on a group of candidates into a single ranking to mitigate biases inherent in individual input rankings. This task has a myriad of applications, such as in social choice theory, collaborative filtering, web search, statistics, databases, sports, and admission systems. One popular version of this task, maximum rank aggregation (or the center ranking problem), aims to find a ranking (not necessarily from the input set) that minimizes the maximum distance to the input rankings. However, even for four input rankings, this problem is NP-hard (Dwork et al., WWW'01, and Biedl et al., Discrete Math.'09), and only a (folklore) polynomial-time 2-approximation algorithm is known for finding an optimal aggregate ranking under the commonly used Kendall-tau distance metric. Achieving a better approximation factor in polynomial time, ideally, a polynomial time approximation scheme (PTAS), is one of the major challenges. This paper presents significant progress in solving this problem by considering the Mallows model, a classical probabilistic model. Our proposed algorithm outputs an (1+ε)-approximate aggregate ranking for any ε > 0, with high probability, as long as the input rankings come from a Mallows model, even in a streaming fashion. Furthermore, the same approximation guarantee is achieved even in the presence of outliers, presumably a more challenging task.

Subject Classification

ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Facility location and clustering
  • Theory of computation → Theory and algorithms for application domains
  • Rank Aggregation
  • Center Problem
  • Mallows Model
  • Approximation Algorithms
  • Clustering with Outliers


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