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Sharp Tractability Borderlines for Finding Connected Motifs in VertexColored Graphs
 34TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP 2007), WROCLAW: POLAND
, 2007
"... We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network an ..."
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Cited by 18 (8 self)
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We study the problem of finding occurrences of motifs in vertexcolored graphs, where a motif is a multiset of colors, and an occurrence of a motif is a subset of connected vertices with a bijection between its colors and the colors of the motif. This problem has applications in metabolic network analysis, an important area in bioinformatics. We give two positive results and three negative results that together draw sharp borderlines between tractable and intractable instances of the problem.
Average Parameterization and Partial Kernelization for Computing Medians
 PROC. 9TH LATIN
, 2010
"... We propose an effective polynomialtime preprocessing strategy for intractable median problems. Developing a new methodological framework, we show that if the input instances of generally intractable problems exhibit a sufficiently high degree of similarity between each other on average, then there ..."
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Cited by 14 (10 self)
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We propose an effective polynomialtime preprocessing strategy for intractable median problems. Developing a new methodological framework, we show that if the input instances of generally intractable problems exhibit a sufficiently high degree of similarity between each other on average, then there are efficient exact solving algorithms. In other words, we show that the median problems Swap Median Permutation, Consensus Clustering, Kemeny Score, and Kemeny Tie Score all are fixedparameter tractable with respect to the parameter “average distance between input objects”. To this end, we develop the new concept of “partial kernelization” and identify interesting polynomialtime solvable special cases for the considered problems.
Sorting by Transpositions is Difficult
"... Abstract. In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance ..."
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Cited by 12 (1 self)
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Abstract. In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the SORTING BY TRANSPOSITIONS problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this longstanding open question by proving that the SORTING BY TRANSPOSITIONS problem is NPhard. As a corollary of our result, we also prove that the following problem from [9] is NPhard: given a permutation π, is it possible to sort π using db(π)/3 permutations, where db(π) is the number of breakpoints of π?
Finding patterns in given intervals
 of Lecture Notes in Computer Science
, 2007
"... Abstract. In this paper, we study the pattern matching problem in given intervals. Depending on whether the intervals are given a priori for preprocessing, or during the query along with the pattern or, even in both cases, we develop solutions for different variants of this problem. In particular, ..."
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Cited by 9 (2 self)
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Abstract. In this paper, we study the pattern matching problem in given intervals. Depending on whether the intervals are given a priori for preprocessing, or during the query along with the pattern or, even in both cases, we develop solutions for different variants of this problem. In particular, we present efficient indexing schemes for each of the above variants of the problem. 1
Indexing Circular Patterns
"... Abstract. This paper deals with the Circular Pattern Matching Problem (CPM). In CPM, we are interested in pattern matching between the text T and the circular pattern C(P) of a given pattern P = P1... Pm. The circular pattern C(P) is formed by concatenating P1 to the right of Pm. We can view C(P) as ..."
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Abstract. This paper deals with the Circular Pattern Matching Problem (CPM). In CPM, we are interested in pattern matching between the text T and the circular pattern C(P) of a given pattern P = P1... Pm. The circular pattern C(P) is formed by concatenating P1 to the right of Pm. We can view C(P) as a set of m patterns starting at positions j ∈ [1..m] and wrapping around the end and if any of these patterns matches T, we find a match for C(P). In this paper, we present two efficient data structures to index circular patterns. This problem has applications in pattern matching in geometric and astronomical data as well as in computer graphics and bioinformatics. 1
Online Approximate Matching with Nonlocal Distances
"... Abstract. A black box method was recently given that solves the problem of online approximate matching for a class of problems whose distance functions can be classified as being local. A distance function is said to be local if for a pattern P of length m and any substring T [i, i+m−1] of a text T, ..."
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Abstract. A black box method was recently given that solves the problem of online approximate matching for a class of problems whose distance functions can be classified as being local. A distance function is said to be local if for a pattern P of length m and any substring T [i, i+m−1] of a text T, the distance between P and T [i, i + m − 1] is equal to Σj∆(P [j], T [i + j − 1]), where ∆ is any distance function between individual characters. We extend this line of work by showing how to tackle online approximate matching when the distance function is nonlocal. We give solutions which are applicable to a wide variety of matching problems including function and parameterised matching, swap matching, swapmismatch, kdifference, kdifference with transpositions, overlap matching, edit distance/LCS, flipped bit, faulty bit and L1 and L2 rearrangement distances. The resulting unamortised online algorithms bound the worst case running time per input character to within a log factor of their comparable offline counterpart. 1
Practical block sequence alignment with moves
"... Abstract. In this paper we study a sequence alignment problem motivated by textual genetic criticism, a humanities discipline where the notion of edit distance with moves has been rediscovered by philologists. We present a formulation of the problem and show that the usual notion of edit distance wi ..."
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Abstract. In this paper we study a sequence alignment problem motivated by textual genetic criticism, a humanities discipline where the notion of edit distance with moves has been rediscovered by philologists. We present a formulation of the problem and show that the usual notion of edit distance with moves does not address it correctly because it is harder. We present a heuristic algorithm for this problem and compare it with a greedy algorithm which computes the edit distance with moves. We show that our algorithm is superior for this task of block sequence alignment with moves. 1
Matching with don’tcares and a small number of mismatches
"... In matching with don’tcares and k mismatches we are given a pattern of length m and a text of length n, both of which may contain don’tcares (a symbol that matches all symbols), and the goal is to find all locations in the text that match the pattern with at most k mismatches, where k is a paramet ..."
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In matching with don’tcares and k mismatches we are given a pattern of length m and a text of length n, both of which may contain don’tcares (a symbol that matches all symbols), and the goal is to find all locations in the text that match the pattern with at most k mismatches, where k is a parameter. We present new algorithms that solve this problem using a combination of convolutions and a dynamic programming procedure. We give randomized and deterministic solutions that run in time O(nk 2 log m) and O(nk 3 log m), respectively, and are faster than the most efficient extant methods for small values of k. Our deterministic algorithm is the first to obtain an O(poly(k) · n log m) running time.
Interchange Rearrangement: The ElementCost Model
"... Abstract. Given an input string S and a target string T when S is a permutation of T, the interchange rearrangement problem is to apply on S a sequence of interchanges, such that S is transformed into T. The interchange operation exchanges the position of the two elements on which it is applied. The ..."
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Abstract. Given an input string S and a target string T when S is a permutation of T, the interchange rearrangement problem is to apply on S a sequence of interchanges, such that S is transformed into T. The interchange operation exchanges the position of the two elements on which it is applied. The goal is to transform S into T at the minimum cost possible, referred to as the distance between S and T. The distance can be defined by several cost models that determine the cost of every operation. There are two known models: The Unitcost model and the Lengthcost model. In this paper, we suggest a natural cost model: The Elementcost model. In this model, the cost of an operation is determined by the elements that participate in it. Though this model has been studied in other fields, it has never been considered in the context of rearrangement problems. We consider both the special case where all elements in S and T are distinct, referred to as a permutation string, and the general case, referred to as a general string. An efficient optimal algorithm for the permutation string case and efficient approximation algorithms for the general string case, which is NPhard, are presented. The study is broadened to include the transposition rearrangement problem under the Elementcost model and under the other known models, in order to provide additional perspective on the new model.
Pattern matching in pseudo realtime
"... It has recently been shown how to construct online, nonamortised approximate pattern matching algorithms for a class of problems whose distance functions can be classified as being local. Informally, a distance function is said to be local if for a pattern P of length m and any substring T [i, i+m− ..."
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It has recently been shown how to construct online, nonamortised approximate pattern matching algorithms for a class of problems whose distance functions can be classified as being local. Informally, a distance function is said to be local if for a pattern P of length m and any substring T [i, i+m−1] of a text T, the distance between P and T [i, i + m − 1] can be expressed as Σj∆(P [j], T [i + j]), where ∆ is any distance function between individual characters. We show in this work how to tackle online approximate matching when the distance function is nonlocal. We give new solutions which are applicable to a wide variety of matching problems including function and parameterised matching, swap matching, swapmismatch, kdifference, kdifference with transpositions, overlap matching, edit distance/LCS and L1 and L2 rearrangement distances. The resulting online algorithms bound the worst case running time per input character to within a log factor of their comparable offline counterpart. 1.