block edit models for approximate string matching in this paper we examine string block edit distance in which two strings a and b are compared by extracting collections of substrings and placing them into correspondence this model accounts for certain phenomena encountered in important real world applications including pen computing and molecular biology the basic problem admits a family of variations depending on whether the strings must be matched in their entireties and whether overlap is permitted we show that several variants are npcomplete and give polynomial time algorithms for solving the remainder

algorithms for approximate graph matching abstract labeled graphs are graphs in which each node and edge has a label the distance between two labeled graphs is considered to be the weighted sum of the costs of edit operations insert delete and relabel the nodes and edges to transform one graph to the other the paper considers two variants of the approximate graph matching problem agm given a pattern graph p and a data graph d 1 1 what is the distance between p and d 2 2 what is the minimum distance between p and d when subgraphs can be freely removed from d we first show that no efficient algorithm can solve either variant of the agm unless p np then we present several heuristic algorithms leading to approximate solutions the heuristics are based on probabilistic hill climbing and maximum flow techniques our experimental results involving the comparison of real and simulated data demonstrate the good performance of the algorithms presented

a four russians algorithm for regular expression pattern matching given a regular expression r of length p and a word a of length n the membership problem is to determine if a is in the language denoted by r an o pn lg n time algorithm is presented that is based on a lg n speedup of the standard o pn time simulation of r s nonderministic finite automaton on a using a combination of the node listing and four russians paradigms this result places a new worst case upper bound on regular expression pattern matching moreover in practice the method provides an implementation that is faster than existing software for small regular expressions

a fast bit vector algorithm for approximate string matching based on dynamic programming the approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with k or fewer differences simple and practical bit vector algorithms have been designed for this problem most notably the one used in agrep these algorithms compute a bit representation of the current state set of the k difference automaton for the query and asymptotically run in either o nm w or o nm log s w time where w is the word size of the machine e g 32 or 64 in practice and s is the size of the pattern alphabet here we present an algorithm of comparable simplicity that requires only o nm w time by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem thus the algorithm s performance is independent of k and it is found to be more efficient than the previous results for many choices of k and small m moreover because the algorithm is not dependent on k it can be used to rapidly compute blocks of the dynamic programming matrix as in the 4 russians algorithm of wu et al 1996 this gives rise to an o kn w expected time algorithm for the case where m may be arbitrarily large in practice this new algorithm that computes a region of the dynamic progr amming d p matrx w entries at a time using the basic algorithm as a subroutine is significantly faster than our previous 4 russians algorithm that computes the same region 4 or 5 entries at a time using table lookup this performance improvement yields a code that is either superior or competitive with all existing algorithms except for some filtration algorithms that are superior when k m is sufficiently small

algorithms for approximate string matching the edit distance between strings a 1 a m and b 1 b n is the minimum cost s of a sequence of editing steps insertions deletions changes that convert one string into the other a well known tabulating method computes s as well as the corresponding editing sequence in time and in space o mn in space o min m n if the editing sequence is not required starting from this method we develop an improved algorithm that works in time and in space o s min m n another improvement with time o s min m n and space o s min s m n is given for the special case where all editing steps have the same cost independently of the characters involved if the editing sequence that gives cost s is not required our algorithms can be implemented in space o min s m n since s o max m n the new methods are always asymptotically as good as the original tabulating method as a by product algorithms are obtained that given a threshold value t test in time o t min m n and in space o min t m n whether s t finally different generalized edit distances are analyzed and conditions are given under which our algorithms can be used in conjunction with extended edit operation sets including for example transposition of adjacent characters

analysis of two dimensional approximate pattern matching algorithms a k approximate occurrence of a pattern in a text is an occurrence which has hamming distance at most k with the pattern the problem of two dimensional approximate pattern matching is defined as follows given a pattern p of size m2 a text t of size n2 and an integer k find all k approximate occurrences of p in t

approximate all pairs suffix prefix overlaps finding approximate overlaps is the first phase of many sequence assembly methods given a set of strings of total length n and an error rate e the goal is to find for all pairs of strings their suffix prefix matches overlaps that are within edit distance email protected email protected email protected where is the length of the overlap we propose a new solution for this problem based on backward backtracking lam et al 2008 and suffix filters karkkainen and na 2008 our technique uses nh k o email protected rlogr bits of space where h k is the k th order entropy and s the alphabet size in practice it is more scalable in terms of space and comparable in terms of time than q gram filters rasmussen et al 2006 our method is also easy to parallelize and scales up to millions of dna reads

incremental string comparison the problem of comparing two sequences a and b to determine their longest common subsequence lcs or the edit distance between them has been much studied in this paper we consider the following incremental version of these problems given an appropriate encoding of a comparison between a and b can one incrementally compute the answer for a and bb and the answer for a and bb with equal efficiency where b is an additional symbol our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such adjacent problems given a threshold k on the number of differences to be permitted in an alignment the theorem leads directly to an o k algorithm for incrementally computing a new solution from an old one as contrasts the o k2 time required to compute a solution from scratch we further show with a series of applications that this algorithm is indeed more powerful than its nonincremental counterpart we show this by solving the applications with greater asymptotic efficiency than heretofore possible for example we obtain o nk algorithms for the longest prefix approximate match problem the approximate overlap problem and cyclic string comparison

on the construction of classes of suffix trees for square matrices we provide a uniform framework for the study of index data structures for a two dimensional matrixtext1 n 1 n whose entries are drawn from an ordered alphabet an index fortextcan be informally seen as the two dimensional analog of the suffix tree for a string it allows on line searches and statistics to be performed ontextby representing compactly the n3 square submatrices oftextin optimalo n2 space we identify 4n 1families of indices fortext each containing ni 1 2i 1 isomorphic data structures we also develop techniques leading to a single algorithm that efficiently builds any index in any family ino n2logn time ando n2 space such an algorithm improves in various respects the algorithms for the construction of the pat tree and the lsuffix tree the framework and the algorithm easily generalize tod 2 dimensions moreover as part of our algorithm we provide new algorithmic tools that yield a space efficient implementation of the naming scheme of r karpet al in proceedings fourth symposium on theory of computing pp 125 136 for strings and matrices

fast and compact regular expression matching we study 4 problems in string matching namely regular expression matching approximate regular expression matching string edit distance and subsequence indexing on a standard word ram model of computation that allows logarithmic sized words to be manipulated in constant time we show how to improve the space and or remove a dependency on the alphabet size for each problem using either an improved tabulation technique of an existing algorithm or by combining known algorithms in a new way

approximate boyer moore string matching the boyer moore idea applied in exact string matching is generalized to approximate string matching two versions of the problem are considered the k mismatches problem is to find all approximate occurrences of a pattern string length m in a text string length n with at most k mismatches the generalized boyer moore algorithm is shown under a mild independence assumption to solve the problem in expected time o kn 1 m k k c where c is the size of the alphabet a related algorithm is developed for the k differences problem where the task is to find all approximate occurrences of a pattern in a text with leqslant k differences insertions deletions changes experimental evaluation of the algorithms is reported showing that the new algorithms are often significantly faster than the old ones both algorithms are functionally equivalent with the horspool version of the boyer moore algorithm when k 0

a multisurface method for pattern classification abstract a method is presented to build a multisurface classifier for a two category set of samples the constructed classifier has some properties that make it a classifier of high quality and apparently a quasioptimal classifier the properties imposed on the classifier are based on a generalization of fisher s criterion function that is suitable for a non linear classifier the desired classifier is built in two stages in the first stage an initial classifier is built in the second stage the classifier is modified to obtain the desired properties modification is performed by use of the gradient descent procedure

fast text searching for regular expressions or automaton searching on tries we present algorithms for efficient searching of regular expressions on preprocessed text using a patricia tree as a logical model for the index we obtain searching algorithms that run in logarithmic expected time in the size of the text for a wide subclass of regular expressions and in sublinear expected time for any regular expression this is the first such algorithm to be found with this complexity

some properties of the multisurface method for pattern classification abstract fisher 2 r a fisher the use of multiple measurements in taxonomic problems ann eugenics 7 part ii 179 188 1936 introduced a criterion function for classification of two categories of patterns by a hyperplane a i x i h 0 he then found the normal vector a i that maximizes this criterion function in the present paper we generalize fisher s criterion function making it suitable for a piecewise linear classifier we build the optimal piecewise linear classifier that maximizes the generalized fisher s criterion function the basis of the method is presented in reference 1 s spivak a multisurface method for pattern classification pattern recognition 22 587 591 1989 here we explore further the properties of the method which include extracting irrelevant planes from the desired classifier and removing ineffective features from each plane it is shown that the method can be easily generalized for separation of more than two categories of patterns

complexity of some problems from the theory of automata 1 1 given a finite alphabet l the regular events over x are those accepted by a finite state automaton by kleene s theorem a subset w of s is a regular event if and only if it can be constructed from the finiteword sets by boolean operations together with concatenation and operation in some sense the regular events are quite simple because they are accepted by a machine with no storage capacity nevertheless in recent years much attention has been paid to special subclasses of the class of regular events in this paper we shall be concerned with star free events events of dot depth one and piecewise testable events star free events are constructed like regular events from the finite word sets but with the restriction that the operation is not allowed events of dot depth one and piecewise testable events are star free of a very simple form and will be defined below star free events have been characterized in the work of schiitzenberger 1965 in terms of their syntactic monoid algebraic characterizations of the other two classes have been given simon 1975 knast 1983 from an algorithmic point of view these algebraic characterizations do not yield efficient procedures because computing the syntactic monoid of a regular event given e g by an automaton is obviously time consuming in this paper we investigate the complexity of three problems which we now describe in the style of garey and johnson 1979 we refer the reader to aho hopcroft and ullman 1983 garey and johnson 1979 for standard concepts of complexity theory

pitch strength of iterated rippled noise when the pitch is ambiguous two versions of a cascade of delay gain following delay and add circuits were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit the repetition pitch of irn is different when the delayed noise is subtracted gain 0 to the undelayed noise in the case of subtraction irn pitch is often ambiguous having two or more pitches listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli generated with different gains different network circuits and different number of iterations for most conditions the gain was less than one the data were described by a description based on an exponential function of the largest peak of the autocorrelation function of irn stimuli w a yost j acoust soc am 100 511 518 1996 processed such that the spectral dominance region is emphasized these results suggest that the strength of the pitch of irn stimuli can be described by temporal processing mechanisms as might be revealed by autocorrelation

suffix arrays a new method for on line string searches a new and conceptually simple data structure called a suffix array for on line string searches is introduced in this paper constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms the main advantage of suffix arrays over suffix trees is that in practice they use three to five times less space from a complexity standpoint suffix arrays permit on line string searches of the type is w a substring of a to be answered in time o p log n where p is the length of w and n is the length of a which is competitive with and in some cases slightly better than suffix trees the only drawback is that in those instances where the underlying alphabet is finite and small suffix trees can be constructed in o n time in the worst case versus o n log n time for suffix arrays however an augmented algorithm is given that regardless of the alphabet size constructs suffix arrays in o n expected time albeit with lesser space efficiency it is

pitch strength and pitch dominance of iterated rippled noises in hearing impaired listeners reports using a variety of psychophysical tasks indicate that pitch perception by hearing impaired listeners may be abnormal contributing to difficulties in understanding speech and enjoying music pitches of complex sounds may be weaker and more indistinct in the presence of cochlear damage especially when frequency regions are affected that form the strongest basis for pitch perception in normal hearing listeners in this study the strength of the complex pitch generated by iterated rippled noise was assessed in normal hearing and hearing impaired listeners pitch strength was measured for broadband noises with spectral ripples generated by iteratively delaying a copy of a given noise and adding it back into the original octave band pass versions of these noises also were evaluated to assess frequency dominance regions for rippled noise pitch hearing impaired listeners demonstrated consistently weaker pitches in response to the rippled noises relative to pitch strength in normal hearing listeners

a new filtration method and a hybrid strategy for approximate string matching in this paper we propose a new filtration algorithm as well as a hybrid filtration strategy to efficiently solve the approximate string matching problem also called k differences problem which aims to find all the positions i s in a given text such that there exists a substring of the text ending at position i whose edit distance from a given pattern is less than or equal to a given error bound k our experimental results on simulated datasets of dna sequences show that our filtration algorithm has better performance on the efficiency to filter out those positions of the text at which the pattern does not occur approximately moreover our hybrid filtration strategy further improves the performance efficiency of our filtration algorithm greatly when the ratio of the error bound and the pattern size is about 0 2

from cascade decompositions to bit vector algorithms a vector algorithm is an algorithm that applies a bounded number of vector operations to an input vcctor regardless of the length of the input in this paper we describe the links between the existence of vector algorithms and the cascade decompositions of counter free automata we show that any computation that can be carried out with a counter free automaton can be recast as a vector algorithm moreover we show that for a class of automata that is closely related to algorithms in bio computing the complexity of the resulting algorithms is linear in the number of transitions of the original automaton

an improved algorithm for approximate string matching given a text string a pattern string and an integer k a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented both its theoretical and practical variants improve upon the known algorithms

extending alignments with k mismatches and l gaps recently the problem of extending an alignment with k mismatches and a single gap for pairwise sequence alignment was introduced flouri et al 2011 the authors considered the problem of extending an alignment under the hamming distance model by also allowing the insertion of a single gap and presented a q email protected time algorithm to solve it where m is the length of the shortest sequence to be extended and b is the maximum allowed length of the single gap very recently it was shown flouri et al 2012 that this problem is strongly and directly motivated by the next generation re sequencing application aligning tens of millions of short dna sequences against a reference genome in this article we consider an extension of this problem extending an alignment with k mismatches and two gaps and present a q email protected time algorithm to solve it this extension is proved to be fundamental in the next generation re sequencing application alachiotis et al 2012 in addition we present a generalisation of our solution to solve the problem of extending an alignment with k mismatches and gaps in time q email protected the presented solutions work provided that all gaps in the alignment must occur in one of the two sequences

a note on the height of suffix trees consider a random word in which the individual symbols are drawn from a finite or infinite alphabet with symbol probabilities p i and let h n be the height of the suffix tree constructed from the first n suffixes of this word it is shown that h n is asymptotically close to 2 log n log 1 sum i p i 2 in many respects the difference is o log log n in probability and the ratio tends to one almost surely and in the mean

further evidence that fundamental frequency difference limens measure pitch discrimination difference limens for complex tones dlcs that differ in f0 are widely regarded as a measure of periodicity pitch discrimination however because f0 changes are inevitably accompanied by changes in the frequencies of the harmonics dlcs may actually reflect the discriminability of individual components to test this hypothesis dlcs were measured for complex tones the component frequencies of which were shifted coherently upward or downward by f 0 25 37 5 or 50 of the f0 yielding fully harmonic f 0 strongly inharmonic f 25 37 5 or odd harmonic f 50 tones if dlcs truly reflect periodicity pitch discriminability they should be larger worse for inharmonic tones than for harmonic and odd harmonic tones because inharmonic tones have a weaker pitch consistent with this prediction the results of two experiments showed a non monotonic dependence of dlcs on f with larger dlcs for f s of 25 or 37 5 than for f s of 0 or 50 of f0 these findings are consistent with

color image segmentation based on 3 d clustering morphological approach in this paper a new segmentation algorithm for color images based on mathematical morphology is presented color image segmentation is essentially a clustering process in 3 d color space but the characteristics of clusters vary severely according to the type of images and color coordinates hence the methodology employs the scheme of thresholding the difference of gaussian smoothed 3 d histogram to get the initial seeds for clustering and then uses a closing operation and adaptive dilation to extract the number of clusters and their representative values and to include the suppressed bins during gaussian smoothing without a priori knowledge on the image this procedure also implicitly takes into account the statistical properties such as the shape connectivity and distribution of clusters intensive computer simulation has been performed and the results are discussed in this paper the results of the simulation show that the proposed segmentation algorithm is independent of the choice of color coordinates the shape of clusters and the type of images the segmentation results using the k means technique are also presented for comparison purposes

discrimination of first and second order regular intervals from random intervals as a function of high pass filter cutoff frequency this study extends the work of kaernbach and demany j acoust soc am 104 2998 2306 1998 in which regular interval stimuli ris click trains with first order intervals could be discriminated from random interval click trains but ris with second order intervals could not kaernbach and demany concluded that their results cast doubt on autocorrelation as a method of analysis for such stimuli the present study investigated the same stimuli but for a variety of filter conditions the results suggest that while ris click trains with first order intervals are more easily discriminated from random interval stimuli than second order interval ris click trains discrimination based on second order intervals is possible except when the stimuli are high pass filtered above 8 khz i e above the spectral region of phase locking

a linear classifier design approach abstract in this paper we discuss a linear classifier design approach based on an exhaustive search procedure the pattern classes are projected onto subspaces of the pattern space and bounded by hyperplanes with fixed orientation a set of such linear discriminators is then submitted to an optimization procedure which displaces the discriminators systematically the optimization procedure is characterized as a linear exhaustive search which performs an ordering of the set of all possible positions of the discriminators from this ordered sequence of solutions any particular solution can be chosen a cost minimization procedure in terms of classifier complexity is introduced the result of the minimization is the necessary and sufficient set of discriminators having the same discriminatory performance as the optimized solution for multimodal pattern sets we give a brief discussion of a simple set partition approach in two examples we show the results of this design approach on synthetic data

payphone coin validation using pattern recognition abstract in this paper we give a classifier design approach which yields classifiers of high computational efficiency and low memory requirements the method is based on subdivision of the pattern space by a minimum number of optimized linear inequalities i e the discriminators into regions containing the pattern classes the discrimination vectors are selected from the principal axes of each pattern class covariance matrix we present an optimization procedure for sets of discrete parameter bounds we briefly discuss the problem of multimodal pattern classes and the possibility of using suboptimum solutions the main objective is to design a group of optimum classifiers for payphone coin classification in two examples we compare our classifier performance with the classification performance derived from fitting normal probability densities to the pattern classes

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

undirected single source shortest paths with positive integer weights in linear time the single source shortest paths problem sssp is one of the classic problems in algorithmic graph theory given a positively weighted graph g with a source vertex s find the shortest path from s to all other vertices in the graph since 1959 all theoretical developments in sssp for general directed and undirected graphs have been based on dijkstra s algorithm visiting the vertices in order of increasing distance from s thus any implementation of dijkstra s algorithm sorts the vertices according to their distances from s however we do not know how to sort in linear time here a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights the algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure identifying vertex pairs that may be visited in any order

the role of the envelope in processing iterated rippled noise iterated rippled noise irn is generated by a cascade of delay and add the gain after the delay is 1 0 or delay and subtract the gain is 1 0 operations the delay and add subtract operations impart a spectral ripple and a temporal regularity to the noise the waveform fine structure is different in these two conditions but the envelope can be extremely similar four experiments were used to determine conditions in which the processing of irn stimuli might be mediated by the waveform fine structure or by the envelope in experiments 1 and 3 listeners discriminated among three stimuli in a single interval task irn stimuli generated with the delay and add operations g 1 0 irn stimuli generated using the delay and subtract operations g 1 0 and a flat spectrum noise stimulus in experiment 2 the listeners were presented two irn stimuli that differed in delay 4 vs 6 ms and a flat spectrum noise stimulus that was not an irn stimulus in experiments 1 and 2 both the envelope and waveform fine structure contained the spectral ripple and temporal regularity in experiment 3 only the envelope had this spectral and temporal structure in all experiments discrimination was determined as a function of high pass filtering the stimuli and listeners could discriminate between the two irn stimuli up to frequency regions as high as 4000 6000 hz listeners could discriminate the irn stimuli from the flat spectrum noise stimulus at even higher frequencies as high as 8000 hz but these discriminations did not appear to depend on the pitch of the irn stimuli a control experiment fourth experiment suggests that irn discriminations in high frequency regions are probably not due entirely to low frequency nonlinear distortion products the results of the paper imply that pitch processing of irn stimuli is based on the waveform fine structure

average complexity of exact and approximate multiple string matching we show that the average number of characters examined to search for r random patterns of length m in a text of length n over a uniformly distributed alphabet of size cannot be less than n log rm m when we permit up to k insertions deletions and or substitutions of characters in the occurrences of the patterns the lower bound becomes n k log rm m this generalizes previous single pattern lower bounds of yao for exact matching and of chang and marr for approximate matching and proves the optimality of several existing multipattern search algorithms