SIAM Journal on Discrete Mathematics
On the complexity of approximating the independent set problem
Information and Computation
Computational Complexity
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
The budgeted maximum coverage problem
Information Processing Letters
Approximation algorithms
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
Packing triangles in bounded degree graphs
Information Processing Letters
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Vertex-Disjoint Triangles Problem
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Complexity of approximating bounded variants of optimization problems
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
On the complexity of approximating k-set packing
Computational Complexity
Reconstructing sibling relationships in wild populations
Bioinformatics
Set covering approach for reconstruction of sibling relationships
Optimization Methods & Software - Systems Analysis, Optimization and Data Mining in Biomedicine
A maximum profit coverage algorithm with application to small molecules cluster identification
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
On Approximating an Implicit Cover Problem in Biology
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
New Optimization Model and Algorithm for Sibling Reconstruction from Genetic Markers
INFORMS Journal on Computing
Discovering kinship through small subsets
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
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In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results in [A. Caprara, R. Rizzi, Packing triangles in bounded degree graphs, Inform. Process. Lett. 84 (4) (2002) 175-180; J. Chlebikova, M. Chlebik, Complexity of approximating bounded variants of optimization problems, Theoret. Comput. Sci. 354 (3) (2006) 320-338]; this is done by directly transforming the inapproximability gap of Hastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) [J. Hastad, Some optimal inapproximability results, in: Proc. of the 29th Annual ACM Symp. on Theory of Computing, 1997, pp. 1-10] and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. [T.Y. Berger-Wolf, B. DasGupta, W. Chaovalitwongse, M.V. Ashley, Combinatorial reconstruction of sibling relationships, in: Proc. of the 6th International Symposium on Computational Biology and Genome Informatics, 2005, pp. 1252-1255; T.Y. Berger-Wolf, S. Sheikh, B. DasGupta, M.V. Ashley, I. Caballero, W. Chaovalitwongse, S.L. Putrevu, Reconstructing sibling relationships in wild populations, Bioinformatics 23 (13) (2007) i49-i56] and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or [R. Hassin, E. Or, A maximum profit coverage algorithm with application to small molecules cluster identification, in: 5th International Workshop Experimental Algorithms, in: Lecture Notes in Comput. Sci., vol. 4007, Springer-Verlag, 2006, pp. 265-276].