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On the Parameterized Complexity of the fixed Alphabet Shortest Common Supersequence and Longest Common Subsequence Problems
, 2003
"... INTRODUCTION The Shortest Common Supersequence (SCS) and the Longest Common Subsequence (LCS) are classical problems in computer science. Shortest Common Supersequence (SCS) integer . is a supersequence Longest Common Subsequence (LCS) integer . is a subsequence The LCS and (not so m ..."
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Cited by 26 (0 self)
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INTRODUCTION The Shortest Common Supersequence (SCS) and the Longest Common Subsequence (LCS) are classical problems in computer science. Shortest Common Supersequence (SCS) integer . is a supersequence Longest Common Subsequence (LCS) integer . is a subsequence The LCS and (not so much) the SCS problems have been extensively studied over the last 30 years (see [7] and references). They are both known to be NPcomplete [8, 9]. In particular the case where the number of sequences is 2 has been studied in detail (see [7] and references). A string a is a supersequence of a string b if we can delete some characters in a such that the remaining string is equal to b, e.g. \1234" is a supersequence of \13". A string a is a subsequence of a string b if b is a supersequence of a, e.g. \13" is a subsequence of \1234". 1.1. Sequence Comparison in Bioinformatics With the recent availability of large amounts of molecular sequence data, the LCS and related problems received
Fixedparameter complexity of minimum profile problems
 In Proceedings IWPEC 2006
, 2006
"... The profile of a graph is an integervalued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NPhard problem, we consider parameterized versions of the problem. ..."
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Cited by 12 (7 self)
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The profile of a graph is an integervalued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NPhard problem, we consider parameterized versions of the problem. Namely, we study the problem of deciding whether the profile of a connected graph of order n is at most n − 1 + k, considering k as the parameter; this is a parameterization above guaranteed value, since n − 1 is a tight lower bound for the profile. We present two fixedparameter algorithms for this problem. The first algorithm is based on a forbidden subgraph characterization of interval graphs. The second algorithm is based on two simple kernelization rules which allow us to produce a kernel with linear number of vertices and edges. For showing the correctness of the second algorithm we need to establish structural properties of graphs with small profile which are of independent interest. 1
Parametric Complexity of Sequence Assembly: Theory and Applications to Next Generation Sequencing
"... In recent years a flurry of new DNA sequencing technologies have altered the landscape of genomics, providing a vast amount of sequence information at a fraction of the costs that were previously feasible. The task of assembling these sequences into a genome has, however, still remained an algorithm ..."
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Cited by 11 (1 self)
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In recent years a flurry of new DNA sequencing technologies have altered the landscape of genomics, providing a vast amount of sequence information at a fraction of the costs that were previously feasible. The task of assembling these sequences into a genome has, however, still remained an algorithmic challenge that is in practice answered by heuristic solutions. In order to design better assembly algorithms and exploit the characteristics of sequence data from new technologies we need an improved understanding of the parametric complexity of the assembly problem. In this work, we provide a first theoretical study in this direction, exploring the connections between repeat complexity, read lengths, overlap lengths and coverage in determining the “hard ” instances of the assembly problem. Our work suggests at least two ways in which existing assemblers can be extended in a rigorous fashion, in addition to delineating directions for future theoretical investigations. 1
Breakpoint Medians and Breakpoint Phylogenies: A FixedParameter Approach
, 2002
"... With breakpoint distance, the genome rearrangement field delivered one of the currently most popular measures in phylogenetic studies for related species. Here, BREAK POINT MEDIAN, which is NPcomplete already for three given species (whose genomes are represented as signed orderings), is the core ..."
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Cited by 4 (1 self)
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With breakpoint distance, the genome rearrangement field delivered one of the currently most popular measures in phylogenetic studies for related species. Here, BREAK POINT MEDIAN, which is NPcomplete already for three given species (whose genomes are represented as signed orderings), is the core basic problem. For the important special case of three species, approximation (ratio 7/6) and exact heuristic algorithms were developed. Here, we provide an exact, fixedparameter algorithm with provable performance bounds. For instance, a breakpoint median for three signed orderings over n elements that causes at most d breakpoints can be computed in time O((2.15) n). We show the algorithm's practical usefulness through experimental studies. In particular, we demonstrate that a simple implementation of our algorithm combined with a new tree construction heuristic allows for a new approach to breakpoint phylogeny, yielding evolutionary trees that are competitive in comparison with known results developed in a recent series of papers that use clever algorithm engineering methods.
The Hardness of Problems on Thin Colored Graphs
, 2000
"... In this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bou ..."
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In this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded treewidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in "yes"instances. For all of these problems with the exceptions of feasible register assignment and module allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W [t] for all t 2 Z + . We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NPComplete.
Problem and Motivation
"... ismatches between the sequences of s and the hybridizing substring of the same length in s 0 [10] (see [6] for further applications). 2 Previous Work When m = 2, the Closest substring problem is solvable in O(knm) time [5, Section 12.2.5]. The general version of the problem is known to NP hard ..."
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ismatches between the sequences of s and the hybridizing substring of the same length in s 0 [10] (see [6] for further applications). 2 Previous Work When m = 2, the Closest substring problem is solvable in O(knm) time [5, Section 12.2.5]. The general version of the problem is known to NP hard and has deterministic [6] and randomized [7] polynomial time approximation algorithms that nd solutionstrings that are within multiplicative factors of 2 and 2 2 2jj+1 mismatches of the optimal solution, respectively. Given the sensitivity of hybridization strength to the number of mismatches, this may not be acceptable in practice. A polynomial time approximation scheme has recently been derived [8] but its time complexity makes it unusable in practice. There are many primer design programs