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About this paper
Hiroki Shibata
This research from Kyushu University disproves the long-standing greedy superstring conjecture by constructing a family of Shortest Common Superstring (SCS) instances where the greedy algorithm produces a superstring whose length is strictly greater than twice the optimal length. The findings demonstrate that the approximation ratio of the greedy algorithm for SCS is at least 9/4 (2.25), revising the theoretical lower bound.
Key insights
- The greedy superstring conjecture is false; the greedy algorithm does not guarantee a 2-approximation for all SCS instances.
- Specific instance structures can force the greedy algorithm to make choices that lead to significantly suboptimal superstring lengths.
- The worst-case approximation ratio of the greedy algorithm for SCS is shown to be at least 9/4 (2.25), which is derived as the limit of the calculated ratio for the constructed instances as parameters grow.
Summary by alphaXiv.
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