Parallel construction of a suffix tree with applications

Many string manipulations can be performed efficiently on suffix trees. In this paper a CRCW parallel RAM algorithm is presented that constructs the suffix tree associated with a string ofn symbols inO(logn) time withn processors. The algorithm requires Θ(n2) space. However, the space needed can be reduced toO(n1+ɛ) for any 0< ɛ ≤1, with a corresponding slow-down proportional to 1/ɛ. Efficient parallel procedures are also given for some string problems that can be solved with suffix trees.

[1]  Leslie G. Valiant,et al.  Parallelism in Comparison Problems , 1975, SIAM J. Comput..

[2]  Zvi Galil,et al.  Open Problems in Stringology , 1985 .

[3]  Dorit S. Hochbaum,et al.  Database Location in Computer Networks , 1980, JACM.

[4]  Clyde P. Kruskal,et al.  Searching, Merging, and Sorting in Parallel Computation , 1983, IEEE Transactions on Computers.

[5]  Richard Cole,et al.  Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking , 2018, Inf. Control..

[6]  Gad M. Landau,et al.  Introducing efficient parallelism into approximate string matching and a new serial algorithm , 1986, STOC '86.

[7]  Raffaele Giancarlo,et al.  The Boyer-Moore-Galil String Searching Strategies Revisited , 1986, SIAM J. Comput..

[8]  Arnold L. Rosenberg,et al.  Rapid identification of repeated patterns in strings, trees and arrays , 1972, STOC.

[9]  Franco P. Preparata,et al.  Structural Properties of the String Statistics Problem , 1985, J. Comput. Syst. Sci..

[10]  Uzi Vishkin,et al.  Randomized speed-ups in parallel computation , 2015, STOC '84.

[11]  Peter Weiner,et al.  Linear Pattern Matching Algorithms , 1973, SWAT.

[12]  Franco P. Preparata,et al.  Optimal Off-Line Detection of Repetitions in a String , 1983, Theor. Comput. Sci..

[13]  Edward M. McCreight,et al.  A Space-Economical Suffix Tree Construction Algorithm , 1976, JACM.

[14]  Gad M. Landau,et al.  Parallel Construction of a Suffix Tree (Extended Abstract) , 1987, ICALP.

[15]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[16]  Alberto Apostolico,et al.  The Myriad Virtues of Subword Trees , 1985 .

[17]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..

[18]  Richard Cole,et al.  Approximate and exact parallel scheduling with applications to list, tree and graph problems , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[19]  Franco P. Preparata,et al.  Data structures and algorithms for the string statistics problem , 1996, Algorithmica.

[20]  Alberto Apostolico,et al.  On Context Constrained Squares and Repetitions in a String , 1984, RAIRO Theor. Informatics Appl..

[21]  Sanjeev Saxena,et al.  On Parallel Prefix Computation , 1994, Parallel Process. Lett..

[22]  Costas S. Iliopoulos,et al.  Parallel Log-time Construction of Suffix Trees , 1986 .

[23]  Xerox Polo,et al.  A Space-Economical Suffix Tree Construction Algorithm , 1976 .

[24]  Uzi Vishkin,et al.  Finding the maximum, merging and sorting in a parallel computation model , 1981, CONPAR.