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Approximation Guarantees for Shortest Superstrings: Simpler and Better

Authors Matthias Englert , Nicolaos Matsakis , Pavel Veselý

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LIPIcs.ISAAC.2023.29.pdf
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Author Details

Matthias Englert
  • University of Warwick, Coventry, UK
Nicolaos Matsakis
  • Charles University, Prague, Czech Republic
Pavel Veselý
  • Charles University, Prague, Czech Republic

Funding

  • Matsakis, Nicolaos: Supported by GA ČR project 22-22997S.
  • Veselý, Pavel: Partially supported by GA ČR project 22-22997S and by Center for Foundations of Modern Computer Science (Charles University project UNCE/SCI/004).

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Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Approximation Guarantees for Shortest Superstrings: Simpler and Better. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.29

Abstract

The Shortest Superstring problem is an NP-hard problem, in which given as input a set of strings, we are looking for a string of minimum length that contains all input strings as substrings. The Greedy Conjecture (Tarhio and Ukkonen, 1988) states that the GREEDY algorithm, which repeatedly merges the two strings of maximum overlap, is 2-approximate. We have recently shown (STOC 2022) that the approximation guarantee of GREEDY is at most (13+√{57})/6 ≈ 3.425. Before that, the best established upper bound for this was 3.5 by Kaplan and Shafrir (IPL 2005), which improved upon the upper bound of 4 by Blum et al. (STOC 1991). To derive our previous result, we established two incomparable upper bounds on the overlap sum of all cycle-closing edges in an optimal cycle cover and utilized lemmas of Blum et al. We improve the more involved one of the two bounds and, at the same time, make its proof more straightforward. This results in an improved approximation guarantee of (√{67}+2)/3 ≈ 3.396 for GREEDY. Additionally, our result implies an algorithm for the Shortest Superstring problem having an approximation guarantee of (√{67}+14)/9 ≈ 2.466, improving slightly upon the previously best guarantee of (√{57}+37)/18 ≈ 2.475 (STOC 2022).

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Shortest Superstring problem
  • Approximation Algorithms

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