Problem
LCBS asks for a longest common subsequence of two ordered sequences that increases up to a single peak and then decreases, with either phase allowed to be empty.
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arXiv ยท revised January 2026
The Longest Common Bitonic Subsequence: A Match-Sensitive Dynamic Programming Approach
A preprint by Md. Tanzeem Rahat and Md. Manzurul Hasan on exact algorithms for longest common bitonic subsequences.
Why It Matters
Bitonic patterns model rise-fall structure in signals, finance, biological sequences, and ordered data. Exact computation becomes difficult when dense dynamic programming scales poorly.
Core Idea
The work combines increasing and decreasing common subsequence structure around common peaks, then develops an instance-sensitive view based on matching pairs.
Main Result
The paper gives a dense exact baseline and a match-sensitive algorithm using dominance dynamic programming, improving when the number of matches is much smaller than the dense grid.
What Was Difficult
The key challenge is coordinating the increasing and decreasing halves around peaks while keeping the algorithm sensitive to the actual match structure of the input.
Resources
Open Directions
- Can LCBS be solved faster for broader sparse or structured instances?
- Which range-query structures give the best practical implementation?
- Can the bitonic framework extend to richer rise-fall pattern families?