Solving VLSI design and DNA sequencing problems using bipartization of graphs

Computational Optimization and Applications

Volumn 51, Issue 2, 2012, Pages 749-781

  Fouilhoux, Pierre ^a   Mahjoub, A Ridha ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Bipartite induced subgraph problem; Branch and cut algorithm; Electronics; Genomics; Polyhedral approach

Indexed keywords

ASSEMBLY; DNA SEQUENCES; ELECTRONIC EQUIPMENT; ERROR CORRECTION; INTEGER PROGRAMMING; INTEGRATED CIRCUIT DESIGN; PRINTED CIRCUIT BOARDS; PRINTED CIRCUIT DESIGN; VLSI CIRCUITS;

ASSEMBLY PROBLEMS; BRANCH-AND-CUT ALGORITHMS; GENOMICS; INDUCED SUBGRAPHS; MINIMIZATION PROBLEMS; MINIMUM ERROR CORRECTION; PARTIAL CHARACTERIZATION; POLYHEDRAL APPROACH;

GENE ENCODING;

EID: 85027918104     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-010-9355-1     Document Type: Article

References (32)

1. Barahona, F.: On the complexity of max-cut. Rapport de recherche no. 186, IMAG, Université Scien-tifique et Médicale de Grenoble (1980)
2. Barahona, F., Mahjoub, A.R.: Facets of the balanced acyclic induced subgraph polytope. Math. Program. 45, 21-34 (1989)
3. Barahona, F., Mahjoub, A.R.: Composition of graphs and polyhedra I: Balanced induced subgraphs and acyclic subgraphs. SIAM J. Discrete Math. 7, 344-358 (1994)
4. Barahona, F., Grötschel, M., Mahjoub, A.R.: Facets of the bipartite subgraph polytope. Math. Oper. Res. 10, 340-358 (1985)
5. Barahona, F., Grötschel, M., Jünger, M., Reinelt, G.: An application of combinatorial optimization to statistical physics and circuit layout design. Oper. Res. 36, 493-513 (1988) (Pubitemid 18655113)
6. Bonizzoni, P., Vedova, G.D., Dondi, R., Li, J.: The haplotyping problem: An overview of computational models and solutions. J. Comput. Sci. Technol. 18, 675-688 (2003)
7. Chang, C.C., Cong, J.: An efficient approach to multi-layer layer assignment with application to via minimization. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 18, 608-620 (1999)
8. Cheng, E., Cunningham, W.: Wheel inequalities for stable set polytope. Math. Program. 77, 389-421 (1997) (Pubitemid 127403079)
9. Chen, R., Kajitani, Y., Chan, S.: A graph theoretic via minimization algorithm for two layer printed circuit boards. IEEE Trans. Circuits Syst. 30, 284-299 (1983) (Pubitemid 13540032)
10. Choi, H., Nakajima, K., Rim, C.: Graph bipartization and via minimization. SIAM J. Discrete Math. 2, 38-47 (1989)
11. Fonlupt, J., Mahjoub, A.R., Uhry, J.: Compositions in the bipartite subgraph polytope. Discrete Math. 105, 73-91 (1992)
12. er D.U. 1555, EDSPIC 314, Université Blaise Pascal, Clermont-Ferrand, France (2004)
13. Fouilhoux, P., Mahjoub, A.R.: An exact model for multi-layer constrained via minimization. Preprint (2006)
14. Fouilhoux, P., Mahjoub, A.R.: Polyhedral results for the bipartite induced subgraph problem. Discrete Appl. Math. 154, 2128-2149 (2006) (Pubitemid 44188929)
15. Fouilhoux, P., Mahjoub, A.R.: Cellular inequalities for the induced bipartite subgraph polytope (in preparation)
16. Froleyks, B., Korte, B., Prömel, H.J.: Routing in VLSI-layout. Acta Math. Appl. Sin. 7, 53-66 (1991)
17. Grötschel, M., Pulleyblank, W.: Weakly bipartite graphs and the max-cut problem, operations research. Oper. Res. 1, 23-27 (1981)
18. Grötschel, M., Lovasz, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin (1985)
19. Guenin, B.: A characterization of weakly bipartite graphs. J. Comb. Theory B 83, 112-168 (2001) (Pubitemid 33082421)
20. Hashimoto, A., Stevens, J.: Wire routing by optimizing channel assignment with large apertures. In: Proc. 8th Design Automation Workshop, pp. 155-169 (1971)
21. ISPD02: http://vlsicad.eecs.umich.edu/BK/ISPD02bench/ (2002)
22. Kajitani, Y.: On via hole minimization of routings on a 2-layer board. In: Proc. IEEE ICCC, pp. 295-298 (1980) (Pubitemid 11474486)
23. Lancia, G., Bafna, V., Istrail, S., Lippert, R., Schwartz, R.: SNPs problems, complexity, and algorithms. In: ESA, pp. 182-193 (2001) (Pubitemid 33328957)
24. Lengauer, T., Lügering, M.: Integer program formulations of global routing and placement problems. Reihe Informatik Nr. 95, Univ. Gesamthochschule-Paderborn (1991)
25. Lippert, R., Schwartz, R., Lancia, G., Istrail, S.: Algorithmic strategies for the single nucleotide polymorphism haplotype assembly problem. Brief. Bioinform 3, 23-31 (2002)
26. Möhring, R., Wagner, D., Wagner, F.: VLSI network design, a survey. TR No. 323, Univ. Berlin (1992)
27. Nemhauser, G., Sigismondi, G.: A strong cutting plane/branch-and-bound algorithm for node packing. J. Oper. Res. Soc. 43, 443-457 (1992)
28. Panconesi, A., Sozio, M.: Fast hare: a fast heuristic for single individual SNP haplotype reconstruction. In: Proc. WABI 2004, pp. 266-277 (2004) (Pubitemid 39750015)
29. Pinter, R.: Optimal layer assignment for interconnect. In: Proc. International Symposium on Circuits on Systems, pp. 398-401 (1982)
30. Sanger, F., Coulson, A., Hong, G., Hill, D., Petersen, G.: Nucleotide sequence of bacteriophage lambda DNA. J. Mol. Biol. 162, 729-773 (1982) (Pubitemid 13156840)
31. Schrijver, A.: Combinatorial Optimization-Polyhedra and Efficiency. Springer, Berlin (2003)
32. Venter, J.C., Adams, M.D., Myers, E.W., et al.: The sequence of the human genome. Science 291, 1304-1351 (2001) (Pubitemid 32173090)