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A Scalable and Unified Framework to Weighted Rank Aggregation

Authors Amir Carmel , Debarati Das , Tien-Long Nguyen

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LIPIcs.ICALP.2026.49.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
  • Theory of computation → Facility location and clustering
Keywords
  • Rank aggregation
  • 1-median
  • Ulam distance
  • Spearman’s footrule
  • Kendall-tau
  • Hamming distance
  • weighted metrics
  • Massively Parallel Computation
  • Gromov product

Metrics

Abstract

The rank aggregation problem, seeks to combine multiple rank orderings of the same set of candidates into a single consensus ordering. Such problems arise in diverse domains, including web search, employment, college admissions, and voting. In this work we focus on the 1-median objective: given a set of m rankings over [n], the goal is to compute a ranking that minimizes the sum of its distances to all input rankings.
We study rank aggregation under several classical distance metrics: Ulam distance, Spearman’s footrule, Hamming distance, and Kendall-tau, as well as their weighted variants. Our contributions begin with a novel unified framework that identifies a key structural property: it suffices to focus on a small subset of rankings (of size three or five), where the corresponding local one-median provides a good approximation to the global median. This principle extends across these distance measures, yielding a general algorithmic framework for weighted rank aggregation.
Building on this, we present a new approximation algorithm for rank aggregation under the Ulam distance that scales in the Massively Parallel Computation (MPC) model. Our algorithm computes a (2-α)-approximation, for a constant α > 0, to the 1-median in a constant number of rounds, using local memory sublinear in n (the size of a ranking) and total memory near linear in n.
We further design new MPC approximation algorithms for Spearman’s footrule and for the element-weighted variants of Hamming and Kendall-tau distances. For each metric, we obtain a (2-ζ)-approximation, for a constant ζ > 0 (which may differ across metrics), to the 1-median in a constant number of rounds, using local memory sublinear in n and total memory linear or near-linear in n.
Moreover, for the Ulam distance, where computing the 1-median is NP-hard [Fischer et al., ESA, 2025], we simplify and strengthen the analysis of Chakraborty et al. [ITCS 2023], obtaining an improved 1.968-approximation that further extends to the weighted setting.

Cite As Get BibTex

Amir Carmel, Debarati Das, and Tien-Long Nguyen. A Scalable and Unified Framework to Weighted Rank Aggregation. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 49:1-49:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.49

Author Details

Amir Carmel
  • Weizmann Institute of Science, Rehovot, Israel
Debarati Das
  • Pennsylvania State University, University Park, PA, USA
Tien-Long Nguyen
  • Pennsylvania State University, University Park, PA, USA

Funding

  • Das, Debarati: This work is supported by NSF grant 2337832.

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