Expected Length of the Longest Common Subsequence for Large Alphabets

  • Marcos Kiwi
  • Martin Loebl
  • Jiří Matoušek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E[L]/n converges to a constant γ k . We prove a conjecture of Sankoff and Mainville from the early 80’s claiming that \(\gamma_{\kappa}\sqrt{k}\longrightarrow 2\) as \(K \longrightarrow \infty\).


Bipartite Graph Random Graph Young Tableau Color Classis Longe Common Subsequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Marcos Kiwi
    • 1
  • Martin Loebl
    • 2
  • Jiří Matoušek
    • 2
  1. 1.Dept. de Ing. Matemática and Ctr. de Modelamiento Matemático, UMR-UChile 2071University of ChileSantiagoChile
  2. 2.Dept. of Applied Mathematics and Institute of Theoretical Computer Science (ITI)Charles UniversityPraha 1Czech Republic

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