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Bounding the Expected Length of Longest Common Subsequences and Forests

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Abstract.

We present improvements to two techniques to find lower and upper bounds for the expected length of longest common subsequences and forests of two random sequences of the same length, over a fixed size, uniformly distributed alphabet. We emphasize the power of the methods used, which are Markov chains and Kolmogorov complexity. As a corollary, we obtain some new lower and upper bounds for the problems addressed as well as some new exact results for short sequences.

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Authors and Affiliations

  1. Department of Computer Science, University of Chile, Blanco Encalada 2120, Santiago, Chile rbaeza@dcc.uchile.cl, gnavarro@dcc.uchile.cl, rscheihi@dcc.uchile.cl , , , , , , CL

    R. A. Baeza-Yates, G. Navarro & R. Scheihing

  2. Department of LSI, Technical University of Catalunya, Jordi Girona Salgado 1—3, 08034 Barcelona, Spain gavalda@lsi.upc.es, , , , , , ES

    R. Gavaldà

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  1. R. A. Baeza-Yates
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  2. R. Gavaldà
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  3. G. Navarro
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  4. R. Scheihing
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Received November 1996, and in final form October 1998.

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Baeza-Yates, R., Gavaldà, R., Navarro, G. et al. Bounding the Expected Length of Longest Common Subsequences and Forests . Theory Comput. Systems 32, 435–452 (1999). https://doi.org/10.1007/s002240000125

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  • DOI: https://doi.org/10.1007/s002240000125

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