Set covering approach for reconstruction of sibling relationships

Optimization Methods and Software

Volumn 22, Issue 1, 2007, Pages 11-24

  Chaovalitwongse, W A ^a,b   Berger Wolf, T Y ^b,c   Dasgupta, B ^c   Ashley, M V ^d  

^a DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c University of Illinois at Chicago   (United States)

^d UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

Combinatorial optimization; DNA markers; Linear assignment problems; Set covering problems; Sibling relationships

Indexed keywords

BIOMARKERS; COMPUTER SIMULATION; CONSTRAINT THEORY; DNA; GENETIC ENGINEERING; PROBLEM SOLVING;

COMBINATORIAL OPTIMIZATION; DNA MARKERS; LINEAR ASSIGNMENT PROBLEMS; SET COVERING PROBLEMS; SIBLING RELATIONSHIPS;

COMBINATORIAL MATHEMATICS;

EID: 33845307260     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780600881829     Document Type: Conference Paper

References (46)

1. Balas, E., 1983, A class of location, distribution and scheduling problems: Modeling and solution methods. In P. Gray and L. Yuanzhang, editors, Proceedings of the Chinese-US Symposium on Systems Analysis (New York: Wiley), pp. 36-65.
2. Ceria, S., Nobili, P. and Sassano, A., 1997, Set covering problem. In M. DellÁmico, F. Maffioli, and S. Martello (Eds), Annotated Bibliographies in Combinatorial Optimization (New York: Wiley), pp. 415-428.
3. Baker, E.K., Bodin, L.D., Finnegan, W.F. and Ponder, R.J., 1979, Efficient heuristic solutions to an airline crew scheduling problem. AIIE Transactions, 11, 79-85.
4. Bartholdi, J.J., 1981, A guaranteed-accuracy round-off algorithm for cyclic scheduling and set covering. Operations Research, 29, 501-510.
5. Caprara, A., Fischetti, M., Toth, P., Vigo, D., and Guida, P.L., 1997, Algorithms for railway crew management. Mathematical Programming, 79, 125-141.
6. Combs, T.E. and Moore, J.T., 2004, A hybrid tabu search/set partitioning approach to tanker crew scheduling. Military Operations Research Society Journal, 9, 43-57.
7. Rubin, J., 1973, A technique for the solution of massive set-covering problems with application to airline crew scheduling. Transportation Science, 7, 34-48.
8. Shepardson, F. and Marsten, R.E., 1980, A lagrangean relaxation algorithm for the two duly period scheduling problem. Management Science, 26, 274-281.
9. Toregas, C., Swain, R., Revelle, C. and Bergman, L., 1971, The location of emergency service facilities. Operations Research, 19, 1363-1373.
10. Walker, W., 1974, Using the set-covering problem on assign fire companies to fire houses. Operations Research, 22, 275-277.
11. Salveson, M.R., 1955, The assembly line balancing problem. Journal of Industrial Engineering, 6, 18-25.
12. Brauner, N., Dhaenens-Flipo, C., Espinouse, M.-L., Finke, F. and Gavranovic, H., 1999, Decomposition into parallel work phases with application to the sheet metal industry. Proceedings of International Conference on Industrial Engineering and Production Management, 1, 389-396.
13. Breuer, M.A., 1970, Simplification of the covering problem with aplication to Boolean expressions. Journal of the Association of Computing Machinery, 17, 166-181.
14. Garey, M.R. and Johnson, D.S., 1979, Computers and Intractability: A Guide to the. Theory of NP-Completeness (New York: W.H. Freeman and Co.).
15. Caprara, A., Fischetti, M. and Toth, P., 2000, Algorithms for the set covering problem. Annals of Operations Reseat, 98, 353-371.
16. Balas, E. and Carrera, M.C., 1996, A dynamic subgradient-based branch and bound procedure for set covering. Operations Research, 44, 875-890.
17. Balas, E. and Ho, A., 1980, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study. Mathematical Programming Study, 12, 37-60.
18. Balas, E. and Ng, S.M., 1989,On the set covering polytype: I all facets with coefficients in {0,1, 2}. Mathematical Programming, 43, 57-69.
19. Balas, E. and Ng, S.M., 1989, On the set covering polytype: Ii lifting the facets with coefficients in {0, 1,2}. Mathematical Programming, 43, 1-20.
20. Beasley, J.E. and Jornsten, K., 1992, Enhancing an algorithm for set covering problems. European Journal of Operations Research, 58, 293-300.
21. Mannino, C. and Sassano, A., 1995, Solving hard set covering problems. Operations Research Letters, 18, 1-5.
22. Chvatal, V., 1979, A greedy heuristic for the set covering problem. Mathematics of Operations Research, 3, 233-235.
23. Beasley, J.E., 1987, An algorithm for set covering problems. European Journal of Operations Research, 31, 85-93.
24. Fisher, M.L. and Kedia, P., 1990, Optimal solution of set covering/partitioning problems using dual heuristics. Management Science, 36, 674-688.
25. Beasley, J.E., 1990, A lagrangean heuristic for set-covering problems. Naval Research Logistics, 37, 151-164.
26. Jacobs, L.W. and Brusco, M.J., 1995, Note: A local-search heuristic for large set-covering problems. Naval Research Logistics, 42, 1129-1140.
27. Grossman, T. and Wool, A., 1997, Computational experience with approximation algorithms for the set covering problem. European Journal of Operations Research, 101, 81-92.
28. Beasley, J.E. and Chu, P.C., 1996, A genetic algorithm for the set covering problem. European Journal of Operations Research, 94, 392-404.
29. Eremeev, A.V., 1999, A genetic algorithm with a non-binary representation for the set covering problem. Proceedings of Symposium on Operations Research, Berlin, pp. 175-181.
30. Alexandrov, D. and Kochetov, Y., 2000, Behavior of the ant colony algorithm for the set covering problem. Proceedings of Symposium, on Operations Research, Dresden, Germany, pp. 255-260.
31. Papadimitriou, C.H. and Seiglitz, K., 1998, Combinatorial Optimization: Algorithms and Complexity (New York: Dover Publications).
32. Feige, U., 1998, A threshold of Inn for approximating set cover. Journal of the ACM, 45, 634-652.
33. Trevisan, L., 2001, Non-approximability reuslts for optimization problems on bounded degree instances. Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 453-461.
34. Maffioli, F. and Galbiati, G., 2000, Approximability of hard combinatorial optimization problems: an introduction. Annals of Operations Research, 96, 221-236.
35. Jones, A.G. and Ardren, W.R., 2003, Methods of parentage analysis in natural populations. Molecular Ecology, 12, 2511-2523.
36. Beyer, J. and May, B., 2003, A graph-theoretic approach to the partition of individuals into full-sib families. Molecular Ecology, 12, 2243-2250.
37. Blouin, M.S., 2003, DNA-based methods for pedigree reconstruction and kinship analysis in natural populations. TRENDS in Ecology and Evolution, 18, 503-511.
38. Blouin, M.S., Parsons, M., Lacaille, V. and Lotz, S., 1996, Use of microsatellite loci to classify individuals by relatedness. Molecular Ecology, 5, 393-401.
39. Thomas, S.C. and Hill, W.G., 2002, Sibship reconstruction in hierarchical population structures using markov chain monte carlo techniques. Genetic Research Cambridge, 79, 227-234.
40. Painter, I., 1997, Sibship reconstruction without parental information. Journal of Agricultural, Biological, and Environmental Statistics, 2, 212-229.
41. Smith, B.R., Herbinger, C.M. and Merry, H.R., 2001, Accurate partition of indivduals into full-sib families from genetic data without parental information. Genetics, 158, 1329-1338.
42. Wang, J., 2004, Sibship reconstruction from genetic data with typing errors. Genetics, 166, 1968-1979.
43. Almudevar, A. and Field, C., 1999, Estimation of single generation sibling relationships based on DNA markers. Journal of Agricultural, Biological, and Environmental Statistics, 4, 136-165.
44. Gusfleld, D., 2002, Partition-distance: a problem and class of perfect graphs arising in clustering. Information Processing Letters, 82, 159-164.
45. Cook. W., Cunningham, W., Pulleyblank, W. and Schrijver, A., 1998, Combinatorial Optimization (New York: Wiley-Interscience).
46. Lalwer, E.L., 1976, Combinatorial Optimization: Networks and Matroids (New York: Holt, Rinehart and Winston).