The Position Heap of a Trie

The position heap is a text indexing structure for a single text string, recently proposed by Ehrenfeucht et al. [Position heaps: A simple and dynamic text indexing data structure, Journal of Discrete Algorithms, 9(1):100-121, 2011]. In this paper we introduce the position heap for a set of strings, and propose an efficient algorithm to construct the position heap for a set of strings which is given as a trie. For a fixed alphabet our algorithm runs in time linear in the size of the trie. We also show that the position heap can be efficiently updated after addition/removal of a leaf of the input trie.

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

[2]  Uzi Vishkin,et al.  Finding Level-Ancestors in Trees , 1994, J. Comput. Syst. Sci..

[3]  David Haussler,et al.  Complete inverted files for efficient text retrieval and analysis , 1987, JACM.

[4]  Peter Sanders,et al.  Linear work suffix array construction , 2006, JACM.

[5]  Michael A. Bender,et al.  The Level Ancestor Problem Simplified , 2002, LATIN.

[6]  S. Rao Kosaraju,et al.  Efficient tree pattern matching , 1989, 30th Annual Symposium on Foundations of Computer Science.

[7]  Edward G. Coffman,et al.  File structures using hashing functions , 1970, CACM.

[8]  Andrzej Ehrenfeucht,et al.  Position heaps: A simple and dynamic text indexing data structure , 2011, J. Discrete Algorithms.

[9]  Alejandro A. Schäffer,et al.  Improved dynamic dictionary matching , 1995, SODA '93.

[10]  Mikkel Thorup,et al.  Maintaining information in fully dynamic trees with top trees , 2003, TALG.

[11]  Gregory Kucherov,et al.  On-line construction of position heaps , 2011, J. Discrete Algorithms.

[12]  Eugene W. Myers,et al.  Suffix arrays: a new method for on-line string searches , 1993, SODA '90.

[13]  Wojciech Rytter,et al.  Extracting Powers and Periods in a String from Its Runs Structure , 2010, SPIRE.

[14]  Dany Breslauer.  The suffix Tree of a Tree and Minimizing Sequential Transducers , 1996, CPM.

[15]  Giancarlo Mauri,et al.  On-Line Construction of Compact Directed Acyclic Word Graphs , 2005, CPM.

[16]  Jeffery R. Westbrook.  Fast Incremental Planarity Testing , 1992, ICALP.

[17]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[18]  Tetsuo Shibuya.  Constructing the Suffix Tree of a Tree with a Large Alphabet , 1999, ISAAC.

[19]  David Haussler,et al.  The Smallest Automaton Recognizing the Subwords of a Text , 1985, Theor. Comput. Sci..

[20]  M. Crochemore,et al.  On-line construction of suffix trees , 2002 .