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Maximizing Diversity in (Near-)Median String Selection

Authors Diptarka Chakraborty , Rudrayan Kundu, Nidhi Purohit, Aravinda Kanchana Ruwanpathirana

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ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Diversity maximization
  • Hamming median
  • diameter
  • dispersion
  • approximation algorithms

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Abstract

Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the underlying metric, this problem has extensive applications, ranging from bioinformatics to pattern recognition. However, modern applications often require the generation of multiple (near-)optimal yet diverse median strings to enhance flexibility and robustness in decision-making.
In this study, we address this need by focusing on two prominent diversity measures: sum dispersion and min dispersion. We first introduce an exact algorithm for the diameter variant of the problem, which identifies pairs of near-optimal medians that are maximally diverse. Subsequently, we propose a (1-ε)-approximation algorithm (for any ε > 0) for sum dispersion, as well as a bi-criteria approximation algorithm for the more challenging min dispersion case, allowing the generation of multiple (more than two) diverse near-optimal Hamming medians. Our approach primarily leverages structural insights into the Hamming median space and also draws on techniques from error-correcting code construction to establish these results.

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Diptarka Chakraborty, Rudrayan Kundu, Nidhi Purohit, and Aravinda Kanchana Ruwanpathirana. Maximizing Diversity in (Near-)Median String Selection. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.12

Author Details

Diptarka Chakraborty
  • National University of Singapore, Singapore
Rudrayan Kundu
  • Indian Statistical Institute Kolkata, India
Nidhi Purohit
  • Institute of Mathematical Sciences, Chennai, India
Aravinda Kanchana Ruwanpathirana
  • Nanyang Technological University, Singapore

Funding

This work was supported by an MoE AcRF Tier 1 grant (T1 251RES2303).

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