Tight Cycle-Cover Inequalities and Improved Approximation for Shortest Common Superstring with Reverse Complements
Ryosuke Yamano, Tetsuo Shibuya
原文摘要
The Shortest Common Superstring (SCS) problem is a classical idealized model of genome assembly. However, SCS does not account for the double-stranded nature of DNA: sequencing reads may originate from either strand without a known orientation. This motivates a natural variant, Shortest Common Superstring with Reverse Complements (SCS-RC), which asks for a shortest string containing each input string or its reverse complement as a substring. For SCS, the MGREEDY algorithm constructs an optimal cycle cover of the overlap graph and concatenates the strings obtained by breaking each cycle at its minimum-overlap edge. This algorithm was recently shown to achieve a tight $3$-approximation. Its reverse-complement extension, MGREEDY-RC, also constructs an optimal cycle cover of the overlap graph augmented with reverse complements, but its best known approximation guarantee was $3.75$ (CPM 2026). We extend this cycle-cover inequality to SCS-RC and show that MGREEDY-RC achieves a $3$-approximation, which is tight even over the DNA alphabet. The $3$-approximation guarantee for MGREEDY-RC yields a $2.5$-approximation for TGREEDY-RC, which greedily merges the strings derived from the cycle cover. By replacing this greedy merging step with an algorithm based on a reduction to a maximum-weight Hamiltonian path problem constrained to contain a given perfect matching, we obtain a $(22/9+\varepsilon)$-approximation for every fixed $\varepsilon>0$. This improves upon the previous best ratio of $8/3$ (WABI 2026), establishing the best known polynomial-time approximation guarantee for SCS-RC.
cs.DS