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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)

Abstract

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 \(K \longrightarrow \infty\).

Keywords

Bipartite Graph Random Graph Young Tableau Color Classis Longe Common Subsequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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