Combinatorial Pattern Matching: 7th Annual Symposium, CPM 96 Laguna Beach, California, June 10–12, 1996 Proceedings

401 Pages·1996·6.271 MB·English

by  Ricardo Baeza-Yates, Gonzalo Navarro (auth.), Dan Hirschberg, Gene Myers (eds.)

Lecture Notes in Computer Science 1075
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: .W Brauer D. Gries J. Stoer
Dan Hirschberg Gene Myers (Eds.)
lairotanibmoC
nrettaP Matching
7th Annual Symposium, MPC 69
Laguna Beach, California, June 10-12, 1996
Proceedings
regnirpS
Series Editors
Gerhard Goos, Karlsruhe University, Germany
Juris Hartmanis, Cornell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Volume Editors
Dan Hirschberg
Information and Computer Science Department
University of California at Irvine
Irvine, CA 92717-3425, USA
Gene Myers
Department of Computer Science, University of Arizona
Tucson, AZ 85721, USA
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Combinatorial pattern matching (cid:12)9 7th annual symposium ;
proceedings / CPM 96, Laguna Beach, California, June 01 - 12,
1996. Dan Hirschberg ; Gene Myers (ed.). - Berlin ; Heidelberg
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Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1996
(Lecture notes in computer science ; Vol. )5701
ISBN 3-540-61258-0
NE: Hirschberg, Dan Hrsg.; CPM <7, 1996, <Laguna Beach, Calif.>;
GT
CR Subject Classification (1991): F.2.2, 1.5.4, 1.5.0, 1.7.3, H.3.3, E.4, G.2.1,
J.3
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Foreword
The papers contained in this volume were presented at the Seventh Annual
Symposium on Combinatorial Pattern Matching (CPM 96), held June 10-12,
1996, at the Aliso Creek Inn, a resort hotel located in Laguna Beach, California,
about 40 miles from Los Angeles. They were selected from 48 papers submit-
ted in response to a call for papers. In addition, invited lectures were given
by David Lipman (Computing Discoveries in Molecular Biology) and Richard
Arratia (Poisson Process Approximation for Repeats in One Sequence and Its
Application to Sequencing by Hybridization).
Combinatorial Pattern Matching addresses issues of searching and matching
strings and more complicated patterns such as trees, regular expressions, graphs,
point sets, and arrays. The goal is to derive non-trivial combinatorial proper-
ties for such structures and then to exploit these properties in order to achieve
improved performance for tile corresponding computationM problems.
In recent years, a steady flow of high-quality research on this subject has
changed a sparse set of isolated results into a full-fledged area of algorithmics
with important applications. This area is expected to grow even further due
to the increasing demand for speed and efficiency that comes especially from
molecular biology, but also from areas such as information retrieval, pattern
recognition, compiling, data compression, and program analysis. The objective
of annual CPM gatherings is to provide an international forum for research in
combinatorial pattern matching.
The general organization and orientation of CPM Conferences is coordinated
by a Steering Committee composed of A. Apostolico, M. Crochemore, Z. Galil,
and U. Manber.
The first six meetings were held in Paris (1990), London (1991), Tucson
(1992), Padova (1993), Pacific Grove (1994), and Helsinki (1995). After the first
meeting, a selection of the papers appeared as a special issue of Theoretical
Computer Science. Since the third meeting, the proceedings have appeared as
volumes 644, 684,807, and 937 of the present series.
CPM 96 s~aw organized by Dan Hirschberg of the Department of Information
and Computer Science at the University of California at Irvine. The conference
was supported in part by the University of California at Irvine Office of Research
and Graduate Studies, the Department of Information and Computer Science,
and the Irvine Research Unit on Computer Systems Design.
Irvine and Tucson, March 1996 Dan Hirschberg
Gene Myers
Iv
Program Committee
Dan Hirschberg, co-chair Gene Myers, co-chair
Rob Irving Pavel Pevzner
Sampath Kannan Dennis Shasha
Rao Kosaraju Jim Storer
Gad Landau Andy Yao
Arthur Lesk Frances Yao
Additional Referees
David Eppstein Gesine Reinert
Martin Farach Martin Vingron
Table of Contents
A Faster Algorithm for Approximate String Matching ...................... 1
Ricardo Baeza-Yates, Gonzalo Navarro
Boyer-Moore Strategy to Efficient Approximate String Matching .......... 24
Nadia EI-Mabrouk, Maxime Crochemore
Randomized Efficient Algorithms for Compressed Strings:
The Finger-Print Approach ............................................... 39
Leszek Gqsieniec, Marek I(arpinski, Wojciech Plandowski, Wojciech Rytter
Filtration with q-Samples in Approximate String Matching ................ 50
Erkki Sutinen, Jorma Tarhio
Computing Discoveries in Molecular Biology (Abstract) ................... 64
David J. Lipman
Approximate Dictionary Queries .......................................... 65
Gerth Str Brodal, Leszek Gqsieniec
Approximate Multiple String Search ...................................... 75
Robert Muth, Udi Manber
A 2 ~-Approximation Algorithm for tile Shortest Superstring Problem .... 87
Chris Armen, Clifford Stein
Suffix Trees oll Words ................................................... 102
Arne Andersson, N. Jesper Larsson, I(urt Swanson
The Suffix Tree of a Tree and Minimizing Sequential Transducers ........ 116
Dany Breslauer
Perfect Hashing for Strings: Formalization and Algorithms ............... 130
Martin Faraeh, S. Muthukrishnan
Spliced Alignment: A New Approach to Gene Recognition ............... 141
Mikhail S. Gelfand, Andrey A. Mironov, Pavel A. Pevzner
Original Synteny ........................................................ 159
Vincent Fer~vtti, Joseph H. Nadeau, David Sankoff
Fast Sorting by Reversal ................................................. 168
Piotr Berman, Sridhar Hannenhalli
A Double Combinatorial Approach to Discovering
Patterns in Biological Sequences ......................................... 186
Marie-France Sagot, Alain Viari
Poisson Process Approximation for Repeats in One Sequence
and Its Application to Sequencing by Hybridization ...................... 209
Richard Arratia, Gesine Reinert
iiiv
Improved Approximation Algorithms for Tree Alignment ................. 220
Lusheng Wang, Dan dleisuG
The Asymmetric Median Tree -
A New Model for Building Consensus Trees .............................. 234
Cynthia A. Phillips, Tandy .J Warnow
Constructing Computer Virus Phylogenies ............................... 253
Leslie Ann ,grebdloG Paul .W ,grebdloG
Cynthia A. Phillips, Gregory B. Sorkin
Docking of Conformationally Flexible Proteins ........................... 271
Bilha Sandak, Ruth Nussinov, Haim .J Wolfson
Invariant Patterns in Crystal Lattices:
Implications for Protein Folding Algorithms .............................. 288
William E. Hart, Sorin Istrail
Graph Traversals, Genes, and Matroids:
An Efficient Case of the Travelling Salesman Problem .................... 304
Dan Gusfield, Richard I(arp, Lusheng Wang, Paul Stelling
Alphabet Independent and Dictionary Scaled Matching .................. 320
Amihood Amir, Gruia Calinescu
Analysis of Two-Dimensional Approximate
Pattern Matching Algorithms ............................................ 335
Kunsoo Park
Approximation Algorithms for Maximum
Two-DimensionM Pattern Matching ..................................... 348
Srinivasa R. Arikati, Anders Dessmark, Andrzej Lingas, Madhav Marathe
Efficient Parallel Algorithms for Tree Editing Problems .................. 361
I(aizhong Zhang
Approximate Pattern Matching in Directed Graphs ...................... 373
James J. uF
Finite-State Computability of Annotations of Strings and Trees .......... 384
Hans L. Bodlaender, Patricia A. Evans, Michael R. Fellows
Author Index ........................................................... 392
A Faster Algorithm for
Approximate String Matching *
Ricardo Baeza-Yates Gonzalo Navarro
Department of Computer Science
University of Chile
Blanco Encalada 2120 - Santiago - Chile
{rbaeza,gnavarro}~dcc.uchile.cl
Abstract. We present a new algorithm for on-line approximate string
matching. The algorithm is based on the simulation of a non-deterministic
finite automaton built from the pattern and using the text as input. This
simulation uses bit operations on a RAM machine with word length
O(log n), being n the maximum size of the text. The running time
achieved is O(n) for small patterns (i.e. of length m = O(v/1-d-~),
independently of the maximum number of errors allowed, k. This al-
gorithm is then used to design two general algorithms. One of them
partitions the problem into subproblems, while the other partitions the
automaton into sub-automata. These algorithms are combined to obtain
a hybrid algorithm which on average is O(n) for moderate k/m ratios,
O(v/mk / log n n) for medium ratios, and O((m - k)kn/log n) for large
ratios. We show experimentally that this hybrid algorithm is faster than
previous ones for moderate size of patterns and error ratios, which is the
case in text searching.
1 Introduction
Approximate string matching is one of the main problems in classical string
algorithms, with applications to text searching, computational biology, pattern
recognition, etc. Given a text of length n, a pattern of length m, and a maximal
number of errors allowed, k, we want to find all text positions where the pattern
matches the text up to k errors. Errors can be substituting, deleting or inserting
a character. The solutions to this problem differ if the algorithm has to be
on-line (that is, the text is not known in advance) or off-line (the text can be
preprocessed). In this paper we are interested in the first case, where the classical
dynamic programming solution is O(mn) running time 13, 14.
In the last years several algorithms have been presented that achieve O(kn)
comparisons in the worst-case 20, 9, 10, 11 or in the average case 21, 9, by
taking advantage of the properties of the dynamic programming matrix. In the
* This work has been supported in part by FONDECYT grant 1950622.
same trend is 6, with average time complexity O(kn/v~r- ) "o( is the alphabet
size). The algorithms which are O(kn) in the worst case tend to involve too much
overhead, and are not competitive in practice.
Other approaches attempt to filter the text, reducing the area in which dynamic
programming needs to be used 18, 19, ,71 ,61 7, .8 These algorithms achieve
sublinear expected time in many cases (O(kn log a re~m) is a typical figure) for
moderate k/m ratios, but the filtration is not effective for larger ratios. A simple
and fast filtering technique is shown in 5, which yields an O(n) algorithm for
moderate k/rn ratios.
Yet other approaches use bit-parallelism ,2 52 in a RAM machine of word length
O(log n) to reduce the number of operations. 24 achieves O(kmn/log n) time,
which is competitive for patterns of length O(logn). 22 packs the cells differ-
ently to achieve O(mn log ~a log n) time complexity. 26 uses a Four Russians
approach and packs the table in machine words, achieving O(kn/log n) time on
average.
We present a new algorithm which combines the ideas of taking advantage of
the properties of the matrix, filtering the text and using bit-parallelism, being
faster than previous work for moderate size patterns and error ratios, as we are
interested in text searching.
We model the search with a non-deterministic finite automaton (NFA) built
from the pattern and using the text as input. This automaton is simulated
by an algorithm based on bit operations on a RAM machine of word length
O(logn). The algorithm achieves running time O(n), independently of k, for
small patterns (i.e. mk= O(log n)). This restricted algorithm is used to design
two general algorithms.
A first one partitions the problem into subproblems, and has average time
cost O(mn/logn) for small a = k/m (i.e. a < 1/logn), otherwise it is
O(v/rnk/logn n) (i.e. O(V~ n) for m = O(logn), else O(kn)). It involves al-
so a cost to verify potential matches, which is shown to be not significant for
a < al ~ 1 - mlllv/~'~/x/~. This algorithm is a generalization of an earlier
heuristic 23, 5, that reduces the problem to subproblems of exact matching
and is shown to be O(n) for a < a0 = 1/(3 log am).
The second one partitions the automaton in sub-automata, being O(k2n/(x/'~log
n)) on average. For a > 1 - 1/x/~ its worst case, O((m - k)kn/logn), domi-
nates. This algorithm is shown to be better than dynamic programming for
k < log(n)/(1 - a).
We analyze the optimal way to combine the algorithms. We show experimentally
that this hybrid algorithm is faster than previous ones, for moderate m and a.
Table 1 shows the combined complexity.
As a corollary of our analysis, we give tight bounds for the probability of finding
an occurrence of a pattern of length m with k errors starting at a fixed position
in random text. We also show that the heuristic of 21 works O(kn) time on
average, with a constant tighter than that of .6
li Condition Com~exity Method used
mk= O(log n) )n(O the simple algorithm
o(.) reducing to exact match
t~<~0

Oto < ot < trl 0 (~mk/log n n problem partitioning
a>alAk<logn/(1-ce) o((~ - k)k,,/log ,,) automaton partitioning
a > al A k > logn/(1 - a) )nm(O )lain dynamic programming
Table 1. Complexity of our hybrid algorithm.
2 Preliminaries
The problem of approximate string matching can be stated as follows: given
a (long) Text of length n, and a (short) pattern pat of length m, both being
sequences of characters from an alphabet Z, find all segments (called "occur-
rences" or "matches") of Text whose edit distance to pat is at most k, the number
of allowed errors. We use ~c = IzI.
The edit distance between two strings a and b is the minimum number of edit
operations needed to transform a into b. The allowed edit operations are deleting,
inserting and replacing a character. Therefore, the problem is non-trivial for
k<m.
Stated that way, we should report a number of segments that contain others.
Because of that, it is common to report only minimal or maximal segments. It
is also common to report not the matching segments but only their start or end
point. In this work we focus on returning end points of minimal segments (i.e.
those not containing others).
We use a C-like notation for the operations (e.g. ~:, l,--, ! =, A, >>). We use
text to denote the current character of Text and, unlike C, strj to denote the
j-th character of str. Except when otherwise indicated, the log function denotes
logarithm in base 2.
Consider the NFA for searching text with at most k --- 2 errors shown in Fig-
ure 1. Every row denotes the number of errors seen. The first one 0, the second
one 1, and so on. Every column represents matching the pattern up to a given
position. At each iteration, a new text character is considered and the automaton
changes its states. Horizontal arrows represent matching a character (they can
only be followed if the corresponding match occurs), vertical arrows represent
inserting a character in the pattern, solid diagonal arrows represent replacing a
character, and dashed diagonal arrows represent deleting a character of the pat-
tern (they are empty transitions, since we delete the character from the pattern
without advancing in the text). Finally, the empty transition at the initial state
allows to consider any character as a potential starting point of a match, and
the automaton accepts a character (as the end of a match) whenever a rightmost
state is active. If we do not care about the number of errors, we can consider