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Volumn 26, Issue 8-10, 1997, Pages 1-11

Optimal cuts in graphs and statistical mechanics

Author keywords

Discrete optimisation; Ground state properties; Optimal cuts; Statistical mechanics

Indexed keywords

ALGORITHMS; FERROMAGNETIC MATERIALS; GRAPH THEORY; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING;

EID: 0031259119     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(97)00195-7     Document Type: Conference Paper
Times cited : (27)

References (42)
  • 1
    • 33947716431 scopus 로고
    • Beitrag zur theorie des ferromagnetismus
    • E. Ising, Beitrag zur Theorie des Ferromagnetismus, Z. Physik 31, 253-258 (1925).
    • (1925) Z. Physik , vol.31 , pp. 253-258
    • Ising, E.1
  • 2
    • 0042492825 scopus 로고
    • The potts model
    • F.Y. Wu, The Potts model, Rev. Mod. Phys. 54, 235-268 (1982).
    • (1982) Rev. Mod. Phys. , vol.54 , pp. 235-268
    • Wu, F.Y.1
  • 6
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • Edited by R.E. Miller and J.W. Thatcher, Plenum Press, New York
    • R.M. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations, (Edited by R.E. Miller and J.W. Thatcher), pp. 85-103, Plenum Press, New York, (1972).
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 9
    • 0000120312 scopus 로고
    • Finding a maximum cut of a planar graph in polynomial time
    • F. Hadlock, Finding a maximum cut of a planar graph in polynomial time, SIAM J. Computing 4, 221-225 (1975).
    • (1975) SIAM J. Computing , vol.4 , pp. 221-225
    • Hadlock, F.1
  • 10
    • 0002068485 scopus 로고
    • Finding the maximal cut in a graph
    • G.I. Orlova and Y.G. Dorfman, Finding the maximal cut in a graph, Engrg. Cybernetics 10, 502-504 (1972).
    • (1972) Engrg. Cybernetics , vol.10 , pp. 502-504
    • Orlova, G.I.1    Dorfman, Y.G.2
  • 15
    • 0002659735 scopus 로고
    • Computing edge-connectivity in multigraphs and capacited graphs
    • H. Nagamochi and T. Ibaraki, Computing edge-connectivity in multigraphs and capacited graphs, SIAM J. Disc. Math. 5, 54-66 (1992).
    • (1992) SIAM J. Disc. Math. , vol.5 , pp. 54-66
    • Nagamochi, H.1    Ibaraki, T.2
  • 18
    • 0002491487 scopus 로고
    • A polynomial algorithm for the k-cut problem for fixed k
    • O. Goldschmidt and D.S. Hochbaum, A polynomial algorithm for the k-cut problem for fixed k, Math. Operations Research 19, 24-37 (1994).
    • (1994) Math. Operations Research , vol.19 , pp. 24-37
    • Goldschmidt, O.1    Hochbaum, D.S.2
  • 20
    • 0001726160 scopus 로고
    • Theory of frustration effect in spin glasses: I
    • G. Toulouse, Theory of frustration effect in spin glasses: I, Comm. Phys. 2, 115-120 (1977).
    • (1977) Comm. Phys. , vol.2 , pp. 115-120
    • Toulouse, G.1
  • 21
    • 26444479778 scopus 로고
    • Optimization by simulated annealing
    • S. Kirkpatrick, C. Gelatt and M. Vecchi, Optimization by simulated annealing, Science 220, 671-680 (1983).
    • (1983) Science , vol.220 , pp. 671-680
    • Kirkpatrick, S.1    Gelatt, C.2    Vecchi, M.3
  • 23
    • 0000888388 scopus 로고
    • Integer optimization and zero-temperature fixed point in ising random-field systems
    • A. Ogielski, Integer optimization and zero-temperature fixed point in Ising random-field systems, Phys. Rev. Lett. 57, 1251-1254 (1986).
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 1251-1254
    • Ogielski, A.1
  • 24
    • 0031231677 scopus 로고    scopus 로고
    • The 3-d random field ising model at zero temperature
    • J.C. Anglès d'Auriac and N. Sourlas, The 3-d random field Ising model at zero temperature, Europhys. Lett. 39, 473-480 (1997).
    • (1997) Europhys. Lett. , vol.39 , pp. 473-480
    • Anglès d'Auriac, J.C.1    Sourlas, N.2
  • 25
    • 0002694122 scopus 로고
    • On the structure of all minimum cuts in a network and applications
    • J.-C. Picard and M. Queyranne, On the structure of all minimum cuts in a network and applications, Mathematical Programming Study 13, 8-16 (1980).
    • (1980) Mathematical Programming Study , vol.13 , pp. 8-16
    • Picard, J.-C.1    Queyranne, M.2
  • 26
    • 0023560289 scopus 로고
    • Counting almost minimum cutsets with reliability applications
    • A. Ramanathan and C.J. Colbourn, Counting almost minimum cutsets with reliability applications, Math. Prog. 39, 253-261 (1987).
    • (1987) Math. Prog. , vol.39 , pp. 253-261
    • Ramanathan, A.1    Colbourn, C.J.2
  • 27
    • 0022044535 scopus 로고
    • An algorithm to aid in the design of large scale networks
    • M.L. Gardner, An algorithm to aid in the design of large scale networks, Large Scale Systems 8, 147-156 (1985).
    • (1985) Large Scale Systems , vol.8 , pp. 147-156
    • Gardner, M.L.1
  • 28
    • 0020766597 scopus 로고
    • Calculating bounds on reachability and connectedness in stochastic networks
    • M.O. Ball and J.S. Provan, Calculating bounds on reachability and connectedness in stochastic networks, Networks 13, 253-278 (1983).
    • (1983) Networks , vol.13 , pp. 253-278
    • Ball, M.O.1    Provan, J.S.2
  • 30
    • 0001214263 scopus 로고
    • Maximum matching and a polyhedron with 0,1-vertices
    • J. Edmonds, Maximum matching and a polyhedron with 0,1-vertices, J. Res. Nat. Bur. Standards Sect. B 69, 125-130 (1965).
    • (1965) J. Res. Nat. Bur. Standards Sect. B , vol.69 , pp. 125-130
    • Edmonds, J.1
  • 31
    • 0021371475 scopus 로고
    • On the random antiphase state in the ±j spin glass model in two dimensions
    • J.C. Anglès d'Auriac and R. Maynard, On the random antiphase state in the ±J spin glass model in two dimensions, Solid State Communications 49, 785-790 (1984).
    • (1984) Solid State Communications , vol.49 , pp. 785-790
    • Anglès d'Auriac, J.C.1    Maynard, R.2
  • 32
    • 0001078074 scopus 로고
    • Morphology of ground states of two dimension frustration model
    • F. Barahona, R. Maynard, R. Rammal and J.P. Uhry, Morphology of ground states of two dimension frustration model, J. Phys. A 15, 673-699 (1982).
    • (1982) J. Phys. A , pp. 673-699
    • Barahona, F.1    Maynard, R.2    Rammal, R.3    Uhry, J.P.4
  • 33
    • 0001271312 scopus 로고
    • On the ground states of the frustration model of a spin glass by a matching method of graph theory
    • I. Bieche, R. Maynard, R. Rammal and J.P. Uhry, On the ground states of the frustration model of a spin glass by a matching method of graph theory, J. Phys. A13, 2553-2576 (1980).
    • (1980) J. Phys. , vol.A13 , pp. 2553-2576
    • Bieche, I.1    Maynard, R.2    Rammal, R.3    Uhry, J.P.4
  • 34
    • 12344318004 scopus 로고
    • Solvable spin systems with random interactions
    • D.C. Mattis, Solvable spin systems with random interactions, Physics Letters A56, 421-422 (1976).
    • (1976) Physics Letters , vol.A56 , pp. 421-422
    • Mattis, D.C.1
  • 35
    • 0020911881 scopus 로고
    • On some weakly bipartite graphs
    • F. Barahona, On some weakly bipartite graphs, Operations Research Letters 2, 239-242 (1983).
    • (1983) Operations Research Letters , vol.2 , pp. 239-242
    • Barahona, F.1
  • 36
    • 77957783608 scopus 로고
    • Methods of nonlinear 0-1 programming
    • P. Hansen, Methods of nonlinear 0-1 programming, Ann. Disc. Math. 5, 53-70 (1979).
    • (1979) Ann. Disc. Math. , vol.5 , pp. 53-70
    • Hansen, P.1
  • 37
    • 0001779898 scopus 로고
    • The random field ising model: Algorithmic complexity and phase transition
    • J.C. Anglès d'Auriac, M. Preissmann and R. Rammal, The Random Field Ising Model: Algorithmic complexity and phase transition, J. Physique Lett. 46, 173-180 (1985).
    • (1985) J. Physique Lett. , vol.46 , pp. 173-180
    • Anglès d'Auriac, J.C.1    Preissmann, M.2    Rammal, R.3
  • 38
    • 0001076503 scopus 로고    scopus 로고
    • Glassy behavior in the ferromagnetic Ising model on a Cayley tree
    • R. Melin, J.C. Anglès d'Auriac, B. Douçot and P. Chandra, Glassy behavior in the ferromagnetic Ising model on a Cayley tree, J. Phys. A: Math. Gen. 29, 573-582 (1996).
    • (1996) J. Phys. A: Math. Gen. , vol.29 , pp. 573-582
    • Melin, R.1    Anglès d'Auriac, J.C.2    Douçot, B.3
  • 39
    • 0001529639 scopus 로고
    • Aging without disorder on long time scales
    • W. Krauth and M. Mézard, Aging without disorder on long time scales, Z. Phys. B 97, 127-134 (1995).
    • (1995) Z. Phys. B , vol.97 , pp. 127-134
    • Krauth, W.1    Mézard, M.2
  • 40
    • 0037476529 scopus 로고
    • Labelings of graphs
    • F.R.K. Chung, Labelings of graphs, Graph Theory 3, 151-168 (1988).
    • (1988) Graph Theory , vol.3 , pp. 151-168
    • Chung, F.R.K.1
  • 42
    • 0004791043 scopus 로고
    • Upper and lower bounds on the complexity of the min-cut linear arrangement problem on trees
    • T. Lengauer, Upper and lower bounds on the complexity of the min-cut linear arrangement problem on trees, Siam J. Alg. Disc. Math. 3, 99-113 (1982).
    • (1982) Siam J. Alg. Disc. Math. , vol.3 , pp. 99-113
    • Lengauer, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.