Two Shortest Path Metrics on Well-Formed Parentheses Strings

We present an analysis of two transformations on well-formed parentheses strings. Using a lattice approach, the corresponding least-move distances are computable, the first in linear time and the second in quadratic time.

[1]  J. Barthelemy,et al.  On the use of ordered sets in problems of comparison and consensus of classifications , 1986 .

[2]  Rodica Simion,et al.  On the structure of the lattice of noncrossing partitions , 1991, Discret. Math..

[3]  Germain Kreweras,et al.  Sur les partitions non croisees d'un cycle , 1972, Discret. Math..

[4]  Jean Marcel Pallo,et al.  On the Rotation Distance in the Lattice of Binary Trees , 1987, Inf. Process. Lett..

[5]  Bernard Monjardet,et al.  Metrics on partially ordered sets - A survey , 1981, Discret. Math..

[6]  Jean Marcel Pallo,et al.  A Distance Metric on Binary Trees Using Lattice-Theoretic Measures , 1990, Inf. Process. Lett..

[7]  Jean Marcel Pallo,et al.  A note on generating binary trees in A-order and B-order , 1985 .

[8]  M. C. Er.  A Note on Generating Well-Formed Parenthesis Strings Lexicographically , 1983, Comput. J..

[9]  Robert E. Tarjan,et al.  Short Encodings of Evolving Structures , 1992, SIAM J. Discret. Math..

[10]  Nachum Dershowitz,et al.  Enumerations of ordered trees , 1980, Discret. Math..

[11]  Frank Ruskey,et al.  Generating Binary Trees by Transpositions , 1988, J. Algorithms.

[12]  Jean Marcel Pallo,et al.  A shortest path metric on unlabeled binary trees , 1992, Pattern Recognit. Lett..

[13]  Jean Marcel Pallo,et al.  The number of coverings in four catalan lattices , 1996, Int. J. Comput. Math..

[14]  Thomas M. Cover,et al.  Open Problems in Communication and Computation , 2011, Springer New York.