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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.26176 |
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| _version_ | 1866916063275384832 |
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| author | Yamano, Ryosuke Shibuya, Tetsuo |
| author_facet | Yamano, Ryosuke Shibuya, Tetsuo |
| contents | 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 $\frac{23}{8}$. In this paper, we present a new approximation algorithm achieving an improved ratio of $\frac{8}{3}$. 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 $\frac{333}{332}$. Notably, this hardness result holds even for the DNA alphabet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26176 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Approximation Algorithms and Hardness Results for Shortest Common Superstring with Reverse Complements Yamano, Ryosuke Shibuya, Tetsuo Data Structures and Algorithms 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 $\frac{23}{8}$. In this paper, we present a new approximation algorithm achieving an improved ratio of $\frac{8}{3}$. 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 $\frac{333}{332}$. Notably, this hardness result holds even for the DNA alphabet. |
| title | Improved Approximation Algorithms and Hardness Results for Shortest Common Superstring with Reverse Complements |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2603.26176 |