Fast elimination of redundant linear equations and reconstruction of recombination-free mendelian inheritance on a pedigree

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 655-664

  Xiao, Jing ^a   Liu, Lan ^b   Xia, Lirong ^a   Jiang, Tao ^b  

^a TSINGHUA UNIVERSITY   (China)

^b University of California Riverside   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOINFORMATICS; TELECOMMUNICATION NETWORKS; TREES (MATHEMATICS);

COMPUTATIONAL BIOLOGY; COMPUTATIONAL INFERENCES; ELIMINATION METHOD; GAUSSIAN ELIMINATION; GRAPH STRUCTURES; LOW STRETCH SPANNING TREES; MENDELIAN LAW OF INHERITANCE; SYSTEM OF LINEAR EQUATIONS;

LINEAR EQUATIONS;

EID: 84969248518     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (38)

1. G. R. Abecasis, S. S. Cherny, W. O. Cookson and L. R. Cardon, Merlin-rapid analysis of dense genetic maps using sparse gene flow trees. Nat Genet, 30(1):97-101, 2002.
2. M. Y. Chan, W. Chan, F. Chin, S. Fung, and M. Kao Linear-Time Haplotype Inference on Pedigrees without Recombinations Proc. of the 6th Annual Workshop on Algorithms in Bioinformatics (WABI06), to appear, 2006.
3. F. Chin and Q. Zhang. Haplotype inference on tightly linked markers in pedigree data. Unpublished manuscript, 2005.
4. F. Chin, Q. Zhang, and H. Shen. k-Recombination Haplotype Inference in Pedigrees. Proc. of the International Workshop on Bioinformatics Research and Applications (ICCS), 985-993, 2005.
5. K. Doi, J. Li and T. Jiang. Minimum recombinant haplotype configuration on tree pedigrees. Proc. of the 3rd Annual Workshop on Algorithms in Bioinformatics (WABI03), 339-353, 2003.
6. M. J. Daly, J. D. Rioux, S. F. Schaffner, T. J. Hudson, and E. S. Lander. High-resolution haplotype structure in the human genome. Nat Genet, 29(2):229-32, 2001.
7. D. Coppersmith, and S. Winograd. Matrix multiplication via arithmetic programming. J. Symb. Comput. 9:251-280, 1990.
8. M. Elkin, Y. Emeky, D. A. Spielman, S. Teng. Lower-Stretch Spanning Trees Proc. 37th ACM Symposium on Theory of computing(STOC'05), 494-503, 2005.
9. E. Eskin, E. Halperin, and R. M. Karp. Large scale reconstruction of haplotypes from genotype data. In Proc. RECOMB'03, pages 104-113, 2003.
10. S. B. Gabriel, S. F. Schaffner, H. Nguyen, J. M. Moore, J. Roy, B. Blumenstiel, J. Higgins, M. De Felice, A. Lochner, M. Faggart, S. N. Liu-Cordero, C. Rotimi, A. Adeyemo, R. Cooper, R. Ward, E. S. Lander, M. J. Daly, and D. Altshuler. The structure of haplotype blocks in the human genome. Science, 296(5576):2225-9, 2002.
11. D. Gusfield. Haplotyping as perfect phylogeny: conceptual framework and efficient solutions. In Proc. RE-COMB'02, pages 166-175, 2002.
12. D. Gusfield. An overview of combinatorial methods for haplotype inference. Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference., 9-25, 2004.
13. D. F. Gudbjartsson, K. Jonasson, M. L. Frigge, and A. Kong. Allegro, a new computer program for multipoint linkage analysis. Nat Genet, 25(1):12-13, 2000.
14. M. Giesbrecht, A. Lobo, and B. Saunders. Certifying inconsistency of sparse linear systems. International Symposium on Symbolic and Algebraic Computation pp. 113-119, 1998.
15. G. H. Golub and C. F. Van Loan. Matrix Computations. John Hopins Univeristy Press, Baltimore, Maryland, third edition, 1996.
16. L. Helmuth. Genome research: Map of the human genome 3.0. Science, 293(5530):583-585, 2001.
17. B. V. Halldórsson, V. Bafna, N. Edwards, R. Lippert, S. Yooseph and S. Istrail. A survey of computational methods for determining haplotypes. Lecture Notes in Computer Science (2983): Computational Methods for SNPs and Haplotype Inference., 26-47, 2004.
18. The international Hap Map Consortium. International Hap Map Project. Nature 426:789-796, 2003.
19. L. Helmuth. Genome research: Map of the human genome 3.0. Science, 293(5530):583-585, 2001.
20. L. Kruglyak, M. J. Daly, M. P. Reeve-Daly and E. S. Lander. Parametric and nonparametric linkage analysis: a unified multipoint approach. Am J Hum Genet, 58(6):1347-63, 1996.
21. J. Li and T. Jiang. Efficient rule-Based haplotyping algorithm for pedigree data. Proc. 7th Annual Conference on Research in Computational Molecular Biology (RECOMB'03), 197-206, 2003.
22. J. Li and T. Jiang. An exact solution for finding minimum recombinant haplotype configurations on pedigrees with missing data by integer linear programming. Proc. RECOMB'04, 20-29, 2004.
23. J. Li and T. Jiang. Computing the minimum recombinant haplotype configuration from incomplete genotype data on a pedigree by Integer Linear Programming. Journal of Computational Biology 12(6), 719-739, 2005.
24. S. Lin and T. P. Speed. An algorithm for haplotype analysis. J Comput Biol, 4(4):535-46, 1997.
25. X. Li, Y. Chen and J. Li. An efficient algorithm for the zero-recombinant haplotype cofiguration problem. Unpublished manuscript, 2006.
26. L. Liu, X. Chen, J. Xiao and T. Jiang. Complexity and approximation of the minimum recombination haplotype configuration problem. Proc. 16th International Symposium on Algorithms and Computation (ISAAC'05), 370-379, 2005.
27. B. La Macchia and A. Odlyzko. Solving large sparse linear systems over finite fields. Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology. Lecture Notes In Computer Science 537, pp. 109-133, 1990.
28. J. R. O'Connell. Zero-recombinant haplotyping: applications to fine mapping using SNPs. Genet Epidemiol, 19 Suppl 1:S64-70, 2000.
29. D. Qian and L. Beckmann. Minimum-recombinant haplotyping in pedigrees. Am J Hum Genet, 70(6):1434-1445, 2002.
30. H. Seltman, K. Roeder, and B.D. Devlin. Transmission/disequilibrium test meets measured haplotype analysis: family-based association analysis guided by evolution of haplotypes. Am J Hum Genet, 68(5):1250-1263, 2001.
31. E. Sobel, K. Lange, J. O'Connell, and D. Weeks. Haplotyping algorithms. T. Speed and M. Waterman, eds., Genetic Mapping and DNA Sequencing, IMA Vol in Math and its App, 81:89-110, 1996.
32. E. Sobel and K. Lange. Descent graphs in pedigree analysis: applications to haplotyping, location scores, and marker-sharing statistics. Am J Hum Genet, 58(6):1323-37, 1996.
33. V. Strassen. Gaussian Elimination is not Optimal Numer. Math. 13, pp. 354-356, 1969
34. P. Tapadar, S. Ghosh, and P. P. Majumder. Haplotyping in pedigrees via a genetic algorithm. Hum Hered, 50(1):43-56, 2000.
35. E. M. Wijsman. A deductive method of haplotype analysis in pedigrees. Am J Hum Genet, 41(3):356-73, 1987.
36. D. Wiedemann. Solving sparse linear euquations over finite fields. IEEE Trans. Inf. Theory, IT-32:52-62, 1986
37. S. Zhang et al. Transmission/Disequilibrium test based on haplotype sharing for tightly linked markers. Am J Hum Genet, 73(3):566-579, 2003.
38. Available at http://www.cs.ucr.edu/-lliu/paper/ZRHC.ps