Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
SIAM Journal on Computing
Extracting constrained 2-interval subsets in 2-interval sets
Theoretical Computer Science
Removing Noise and Ambiguities from Comparative Maps in Rearrangement Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximating the 2-interval pattern problem
Theoretical Computer Science
Improved Approximation Algorithms for Predicting RNA Secondary Structures with Arbitrary Pseudoknots
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
On Recovering Syntenic Blocks from Comparative Maps
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A PTAS for the weighted 2-interval pattern problem over the preceding-and-crossing model
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Algorithms for the extraction of synteny blocks from comparative maps
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
Parameterized Complexity
Approximability and Fixed-Parameter Tractability for the Exemplar Genomic Distance Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Inapproximability of Maximal Strip Recovery
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Maximal Strip Recovery Problem with Gaps: Hardness and Approximation Algorithms
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
On the parameterized complexity of some optimization problems related to multiple-interval graphs
Theoretical Computer Science
On the parameterized complexity of some optimization problems related to multiple-interval graphs
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Efficient exact and approximate algorithms for the complement of maximal strip recovery
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Inapproximability of maximal strip recovery: II
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Inapproximability of maximal strip recovery
Theoretical Computer Science
Tractability and approximability of maximal strip recovery
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Maximal strip recovery problem with gaps: Hardness and approximation algorithms
Journal of Discrete Algorithms
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Given two genomic maps G and H represented by a sequence of n gene markers, a strip (syntenic block) is a sequence of distinct markers of length at least two which appear as subsequences in the input maps, either directly or in reversed and negated form. The problem Maximal Strip Recovery (MSR) is to find two subsequences G *** and H *** of G and H , respectively, such that the total length of disjoint strips in G *** and H *** is maximized (or, conversely, the number of markers hence deleted, is minimized). Previously, besides some heuristic solutions, a factor-4 polynomial-time approximation is known for the MSR problem; moreover, several close variants of MSR, MSR-d (with d 2 input maps), MSR-DU (with marker duplications) and MSR-WT (with markers weighted) are all shown to be NP-complete. Before this work, the complexity of the original MSR problem was left open. In this paper, we solve the open problem by showing that MSR is NP-complete, using a polynomial time reduction from One-in-Three 3SAT. We also solve the MSR problem and its variants exactly with FPT algorithms, i.e., showing that MSR is fixed-parameter tractable. Let k be the minimum number of markers deleted in various versions of MSR, the running time of our algorithms are O (22.73k n + n 2) for MSR, O (22.73k dn + dn 2) for MSR-d , and O (25.46k n + n 2) for MSR-DU.