Abstract
Finding a longest increasing subsequence (LIS) of a given sequence is a classic problem in string matching, with applications mostly in computational biology.Recently,many variations of this problem have been introduced.We present new algorithms for two such problems: the longest increasing circular subsequence (LICS) and the slope-constrained longest increasing subsequence (SLIS). For LICS, our algorithm improves one of the most competitive techniques if the length of the output sequence is close to its expected value \(2\sqrt{n}+o(\sqrt{n})\). In the algorithm for SLIS, we show how to gain from modern successor search data structures, which is not trivial for this task.
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