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Everything about Longest common subsequence

Algorithmic problem on pairs of sequences

A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences. It differs from the longest common substring: unlike substrings, elements of subsequences are not required to occupy consecutive positions within the original sequences. The problem of computing longest common subsequences is a classic computer science problem. Because it is polynomial and has an efficient algorithm to solve it, it is employed to compare data and merge changes to files in programs such as the diff utility and revision control systems such as Git. It has similar applications in computational linguistics and bioinformatics. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Longest common subsequenceA 5-minute orientation
  2. Skim a recent paper: Time-series anomaly detection using dynamic programming based longest common subsequence on sensor dataInfluential work since 2022
  3. Pick up a classic book: Mathematical PuzzlesThe most-reprinted book on the subject
  4. Read the landmark paper: Algorithms for the Longest Common Subsequence ProblemCited 545 times
  5. Go sideways: Hirschberg's algorithmA closely related topic
  6. Go sideways: Shortest common supersequenceA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Complexity
  2. Solution for two sequences
  3. Relation to other problems
  4. Code for the dynamic programming solution
  5. Code optimization
  6. Behavior on random strings
  7. Computing the longest palindromic subsequence of a string

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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🔗 Related topics