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Improved Approximation Algorithms and Hardness Results for Shortest Common Superstring with Reverse Complements

Authors Ryosuke Yamano , Tetsuo Shibuya

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LIPIcs.WABI.2026.2.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Shortest Common Superstring
  • Approximation Algorithms
  • DNA Assembly

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Abstract

The Shortest Common Superstring (SCS) problem is a fundamental task in sequence analysis. In genome assembly, however, the double-stranded nature of DNA implies that each fragment may occur either in its original orientation or as its reverse complement. This motivates the Shortest Common Superstring with Reverse Complements (SCS-RC) problem, which asks for a shortest string that contains, for each input string, either the string itself or its reverse complement as a substring. The previously best-known approximation ratio for SCS-RC was 23/8. In this paper, we present a new approximation algorithm achieving an improved ratio of 8/3. Our approach computes an optimal constrained cycle cover by reducing the problem, via a novel gadget construction, to a maximum-weight perfect matching in a general graph. We also investigate the computational hardness of SCS-RC. While the decision version is known to be NP-complete, no explicit inapproximability results were previously established. We show that the hardness of SCS carries over to SCS-RC through a polynomial-time reduction, implying that it is NP-hard to approximate SCS-RC within a factor better than 333/332. Notably, this hardness result holds even for the DNA alphabet.

Cite As Get BibTex

Ryosuke Yamano and Tetsuo Shibuya. Improved Approximation Algorithms and Hardness Results for Shortest Common Superstring with Reverse Complements. In 26th International Conference on Algorithms for Bioinformatics (WABI 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 390, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WABI.2026.2

Author Details

Ryosuke Yamano
  • Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, Japan
  • Division of Medical Data Informatics, Human Genome Center, Institute of Medical Science, The University of Tokyo, Japan
Tetsuo Shibuya
  • Division of Medical Data Informatics, Human Genome Center, Institute of Medical Science, The University of Tokyo, Japan

Funding

This work was supported by MEXT KAKENHI Grant Number 23K28035.

References

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