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22
A Structural View on Parameterizing Problems: Distance from Triviality
 In First International Workshop on Parameterized and Exact Computation, IWPEC 2004, LNCS Proceedings
, 2004
"... Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consider tractab ..."
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Cited by 22 (10 self)
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Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consider tractable special cases of generally hard problems and to introduce parameters that measure the distance from these special cases. In this paper we present several case studies of distance from triviality parameterizations (concerning Clique, Power Dominating Set, Set Cover, and Longest Common Subsequence) that exhibit the versatility of this approach to develop important new views for computational complexity analysis.
Computing the Similarity of Two Sequences with Nested Arc Annotations
 Theoretical Computer Science
, 2003
"... We present exact algorithms for the NPcomplete Longest Common Subsequence problem for sequences with nested arc annotations, a problem occurring in structure comparison of RNA. Given two sequences of length at most n and nested arc structure, one of our algorithms determines (if existent) in O(3.3 ..."
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Cited by 20 (2 self)
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We present exact algorithms for the NPcomplete Longest Common Subsequence problem for sequences with nested arc annotations, a problem occurring in structure comparison of RNA. Given two sequences of length at most n and nested arc structure, one of our algorithms determines (if existent) in O(3.31 time an arcpreserving subsequence of both sequences, which can be obtained by deleting (together with corresponding arcs) k 1 letters from the first and k 2 letters from the second sequence. A second algorithm shows that (in case of a four letter alphabet) we can find a length l arcannotated subsequence in O(12 n) time. This means that the problem is fixedparameter tractable when parameterized by the number of deletions as well as when parameterized by the subsequence length. Our findings complement known approximation results which give a quadratic time factor2approximation for the general and polynomial time approximation schemes for restricted versions of the problem. In addition, we obtain further fixedparameter tractability results for these restricted versions.
A.J.: Hybridization of memetic algorithms with branchandbound techniques
 IEEE Transactions on Systems, Man, and Cybernetics, Part B
, 2006
"... BranchandBound and memetic algorithms represent two very different approaches for tackling combinatorial optimization problems. These approaches are not incompatible however. In this paper, we consider a hybrid model that combines these two techniques. To be precise, it is based on the interleaved ..."
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Cited by 12 (4 self)
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BranchandBound and memetic algorithms represent two very different approaches for tackling combinatorial optimization problems. These approaches are not incompatible however. In this paper, we consider a hybrid model that combines these two techniques. To be precise, it is based on the interleaved execution of both approaches. Since the requirements of time and memory in branchandbound techniques are generally conflicting, we have opted for carrying out a truncated exact search, namely, beam search. The resulting hybrid algorithm has therefore a heuristic nature. The multidimensional 01 knapsack problem and the shortest common supersequence problem have been chosen as benchmarks. As will be shown, the hybrid algorithm can produce better results in both problems at the same computational cost, specially for large problem instances. I.
On the parameterized intractability of motif search problems
 Combinatorica
, 2006
"... We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n c) fo ..."
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Cited by 9 (3 self)
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We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k) · n c) for any function f of k and constant c independent of k. The problem can therefore be expected to be intractable, in any practical sense, for k ≥ 3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, although both problems are NPcomplete. We also prove W[1]hardness for other parameterizations in the case of unbounded alphabet size. Our W[1]hardness result for Closest Substring generalizes to Consensus Patterns, a problem of similar significance in computational biology. 1
The parameterized complexity of the unique coverage problem
 In Proceedings of the 18th International Symposium on Algorithms and Computation (ISAAC), number 4835 in Lecture Notes in Computer Science
, 2007
"... We consider the parameterized complexity of the Unique Coverage problem: given a family of sets and a parameter k, we ask whether there exists a subfamily that covers at least k elements exactly once. This NPcomplete problem has applications in wireless networks and radio broadcasting and is also a ..."
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Cited by 4 (1 self)
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We consider the parameterized complexity of the Unique Coverage problem: given a family of sets and a parameter k, we ask whether there exists a subfamily that covers at least k elements exactly once. This NPcomplete problem has applications in wireless networks and radio broadcasting and is also a natural generalization of the wellknown Max Cut problem. We show that this problem is fixedparameter tractable with respect to the parameter k. We also show a 4 k kernel for this problem. However a more general weighted version, with costs associated with each set and profits with each element, turns out to be much harder. The question here is whether there exists a subfamily with total cost at most a prespecified budget B such that the total profit of uniquely covered elements is at least k. In the most general setting, assuming real costs and profits, the problem is not fixedparameter tractable unless P = NP. Assuming integer costs and profits we show the problem to be W[1]hard with respect to B as parameter. However, under some reasonable restriction, the problem becomes fixedparameter tractable with respect to both B and k as parameters.
Solving the maximum agreement subtree and the maximum compatible tree problems on many bounded degree trees
 Proceedings of the 17th Annual Symposium on Combinatorial Pattern Matching (CPM’06
, 2006
"... Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as ..."
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Cited by 4 (0 self)
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Given a set of leaflabeled trees with identical leaf sets, the wellknown Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computational biology, where trees encountered have often small degrees. In this paper, we study the parameterized complexity of MAST and MCT with respect to the maximum degree, denoted by D, of the input trees. Although MAST is polynomial for bounded D [1, 6, 3], we show that the problem is W[1]hard with respect to parameter D. Moreover, relying on recent advances in parameterized complexity we obtain a tight lower bound: while MAST can be solved in O(N O(D)) time where N denotes the input length, we show that an O(N o(D) ) bound is not achievable, unless SNP ⊆ SE. We also show that MCT is W[1]hard with respect to D, and that MCT cannot be solved in O(N o(2D/2)) time, unless SNP ⊆ SE. 1
Parameterized complexity and approximability of the SLCS problem
 In preparation
"... Abstract. We introduce the Longest Compatible Sequence (Slcs) problem. This problem deals with psequences, which are strings on a given alphabet where each letter occurs at most once. The Slcs problem takes as input a collection of k psequences on a common alphabet L of size n, and seeks a pseque ..."
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Cited by 4 (2 self)
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Abstract. We introduce the Longest Compatible Sequence (Slcs) problem. This problem deals with psequences, which are strings on a given alphabet where each letter occurs at most once. The Slcs problem takes as input a collection of k psequences on a common alphabet L of size n, and seeks a psequence on L which respects the precedence constraints induced by each input sequence, and is of maximal length with this property. We investigate the parameterized complexity and the approximability of the problem. As a byproduct of our hardness results for Slcs, we derive new hardness results for the Longest Common Subsequence problem and other problems hard for the Whierarchy. 1
Parameterized Complexity and Biopolymer Sequence Comparison
, 2007
"... The paper surveys parameterized algorithms and complexities for computational tasks on biopolymer sequences, including the problems of longest common subsequence, shortest common supersequence, pairwise sequence alignment, multiple sequencing alignment, structure–sequence alignment and structure–str ..."
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Cited by 4 (0 self)
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The paper surveys parameterized algorithms and complexities for computational tasks on biopolymer sequences, including the problems of longest common subsequence, shortest common supersequence, pairwise sequence alignment, multiple sequencing alignment, structure–sequence alignment and structure–structure alignment. Algorithm techniques, built on the structuralunit level as well as on the residue level, are discussed.
Complexities of the centre and median string problems
 In Proceedings of the 14th Annual Symposium on Combinatorial Pattern Matching
, 2003
"... Abstract. Given a finite set of strings, the median string problem consists in finding a string that minimizes the sum of the distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarize ..."
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Cited by 4 (1 self)
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Abstract. Given a finite set of strings, the median string problem consists in finding a string that minimizes the sum of the distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarizes common information to the strings of the set. It is the case in Classification, in Speech and Pattern Recognition, and in Computational Biology. In the latter, median string is related to the key problem of Multiple Alignment. In the recent literature, one finds a theorem stating the NPcompleteness of the median string for unbounded alphabets. However, in the above mentioned areas, the alphabet is often finite. Thus, it remains a crucial question whether the median string problem is NPcomplete for finite and even binary alphabets. In this work, we provide an answer to this question and also give the complexity of the related centre string problem. Moreover, we study the parametrized complexity of both problems with respect to the number of input strings. 1