College of Engineering

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The College of Engineering at Montana State University will serve the State of Montana and the nation by fostering lifelong learning, integrating learning and discovery, developing and sharing technical expertise, and empowering students to be tomorrow's leaders.

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Author: search.filters.author.Zhu, Binhaisearch.filters.applied.f.department: search.filters.department.Computer Science

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    Permutation-constrained Common String Partitions with Applications
    (Springer Science and Business Media LLC, 2024-09) Lafond, Manuel; Zhu, Binhai
    We study a new combinatorial problem based on the famous Minimum Common String Partition (MCSP) problem, which we call Permutation-constrained Common String Partition (PCSP for short). In PCSP, we are given two sequences/genomes s and t with the same length and a permutation π on [`], the question is to decide whether it is possible to decompose s and t into ` blocks that can be matched according to some specified requirements, and that conform with the permutation π. Our main result is that PCSP is FPT in parameter ` + d, where d is the maximum number of occurrences that any symbol may have in s or t. We also study a variant where the input specifies whether each matched pair of block needs to be preserved as is, or reversed. With this result on PCSP, we show that a series of genome rearrangement problems are FPT k + d, where k is the rearrangement distance between two genomes of interest.
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    The longest letter-duplicated subsequence and related problems
    (Springer Science and Business Media LLC, 2024-07) Lai, Wenfeng; Liyanage, Adiesha; Zhu, Binhai; Zou, Peng
    Motivated by computing duplication patterns in sequences, a new problem called the longest letter-duplicated subsequence (LLDS) is proposed. Given a sequence S of length n, a letter- duplicated subsequence is a subsequence of S in the form of x d1 1 x d2 2 . . . x d k k with x i ∈ , x j = x j+1 and di ≥ 2 for all i in [k] and j in [k − 1]. A linear time algorithm for computing a longest letter-duplicated subsequence (LLDS) of S can be easily obtained. In this paper, we focus on two variants of this problem: (1) ‘all-appearance’ version, i.e., all letters in must appear in the solution, and (2) the weighted version. For the former, we obtain dichotomous results: We prove that, when each letter appears in S at least 4 times, the problem and a relaxed version on feasibility testing (FT) are both NP-hard. The reduction is from (3+, 1, 2−)- SAT, where all 3-clauses (i.e., containing 3 lals) are monotone (i.e., containing only positive literals) and all 2-clauses contain only negative literals. We then show that when each letter appears in S at most 3 times, then the problem admits an O(n) time algorithm. Finally, we consider the weighted version, where the weight of a block x di i (di ≥ 2) could be any positive function which might not grow with di . We give a non-trivial O(n2) time dynamic programming algorithm for this version, i.e., computing an LD-subsequence of S whose weight is maximized.
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