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arXiv · 1511.08431

On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals

Gabriele Fici·Tomasz Kociumaka·Jakub Radoszewski·Wojciech Rytter·Tomasz Waleń
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Abstract

We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its reversal. We call this problem Shortest Common Superstring with Reversals (SCS-R). This problem has been introduced by Jiang et al., who designed a greedy-like algorithm with length approximation ratio $4$. In this paper, we show that a natural adaptation of the classical greedy algorithm for SCS has (optimal) compression ratio $\frac12$, i.e., the sum of the overlaps in the output string is at least half the sum of the overlaps in an optimal solution. We also provide a linear-time implementation of our algorithm.

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Gabriele Fici, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń. 2015-12-07. On the Greedy Algorithm for the Shortest Common Superstring Problem with Reversals. https://doi.org/10.1016/j.ipl.2015.11.015

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