Optimization via enumeration: A new algorithm for the Max Cut Problem

Mathematical Programming, Series B

Volumn 90, Issue 2, 2001, Pages 273-290

  Galluccio, Anna ^a   Loebl, Martin ^b   Vondrák, Jan ^b  

^a CNR   (Italy)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

Cut; Generating function; Modular arithmetics; Pfaffian orientation

Indexed keywords

EID: 0242372034     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011425     Document Type: Article

References (23)

1. Barahona, F. (1982): On the computational complexity of Ising spin glass models. J. Phys. A 15, 3241-3253
2. Barahona, F. (1983): Balancing signed toroidal graphs in polynomial time. Preprint University of Chile. Unpublished manuscript
3. Barahona, F., Grötschel, M., Jünger, M., Reinelt, G. (1988): An application of combinatorial optimization to statistical physics and circuit layout design. Operations Research 36, 493-513
4. De Simone, C., Diehl, M., Jünger, M., Mützel, P., Reinelt, G., Rinaldi, G. (1995): Exact ground states of Ising spin glasses: New experimental results with a branch and cut algorithm. Jour. of Stat. Physics 80, 487-496
5. De Simone, C., Diehl, M., Jünger, M., Mützel, P., Reinelt, G., Rinaldi, G. (1996): Exact ground states of 2d ± J Ising spin glasses. Jour. of Stat. Physics 84, 1363-1371
6. Delorme, C., Poljak, S. (1993): Laplacian eigenvalues and the maximum cut problem. Math. Prog. 62, 557-574
7. Fisher, M. (1966): On the dimer solution of planar Ising models. Journal of Mathematical Physics 7 10
8. Galluccio, A., Loebl, M. (1999): A theory of pfaffian orientations I: Perfect matchings and permanents. Electronic Jour. Combinatorics 6(1), http://www.combinatorics.org/Volume_6.
9. Galluccio, A., Loebl, M., Vondrák, J.V. (2000): A new algorithm for the Ising problem: partition function for finite lattice graphs. Physical Rev. Lett. 84(26), 5924-5927
10. Garey, M.R., Johnson, D.S. (1979): Computers and Intractability. W. H. Freeman and Company, New York
11. George, A. (1973): Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10, 345-363
12. Goemans, M.X., Williamson, D.P. (1995): Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. of ACM 42, 1115-1145
13. Junger, M., Reinelt, G., Rieger, H., Rinaldi, G. (1997): Algorithmic Techniques in Physics. Dagstuhl-Seminar-Report 197, Dagstuhl
14. Kac, M., Ward, J. (1952): A combinatorial solution of the two-dimensional Ising model. Physical Review 88, 1332-1337
15. Kardar, M., Saul, L. (1994): The 2D ± Ising spin glass: exact partition functions in polynomial time. Nuclear Physics B 432, 641-667
16. Kasteleyn, P.W. (1961): The statistics of dimers on a lattice. Physica 27, 1209-1225
17. Kasteleyn, P.W. (1963): Dimer statistics and phase transitions. Jour. Math. Physics 4, 287-293
18. Kasteleyn, P.W. (1967): Graph theory and crystal physics. In: Graph theory and theoretical physics, New York. Academic Press
19. Lipton, R., Rose, D., Tarjan, R.E. (1979): Generalized nested dissection. SIAM J. Numer. Anal. 16, 346-358
20. Poljak, S., Rendl, F. (1995): Solving the max-cut problem using eigenvalues. Discr. Appl. Math. 62, 249-278
21. Regge, T., Zecchina, R. (1996): Exact solution of the Ising model on group lattices of genus g > 1. J. Math. Physics 37(6), 2796-2814
22. van der Waerden, B. (1941): Die lange Reichweite der regelmässigen Atomanordnung in Mischkristallen. Z. Physik 118, 473
23. Vondrák, J. (1999):. Implementation and testing of a new algorithm for the MAX-CUT problem. Master's thesis, Charles University, Prague