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Volumn 320, Issue 2-3, 2004, Pages 345-372

Heuristic average-case analysis of the backtrack resolution of random 3-satisfiability instances

Author keywords

Analysis of algorithms; Backtrack; Satisfiability

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; POLYNOMIALS; PROBABILITY; PROBLEM SOLVING; STATISTICAL METHODS; TREES (MATHEMATICS);

EID: 2442641940     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.02.034     Document Type: Article
Times cited : (12)

References (37)
  • 1
    • 0034892310 scopus 로고    scopus 로고
    • Lower bounds for random 3-SAT via differential equations
    • Achlioptas D. Lower bounds for random 3-SAT via differential equations. Theoret. Comput. Sci. 265:2001;159-185.
    • (2001) Theoret. Comput. Sci. , vol.265 , pp. 159-185
    • Achlioptas, D.1
  • 2
    • 0034826226 scopus 로고    scopus 로고
    • A sharp threshold in proof complexity
    • D. Achlioptas, P. Beame, M. Molloy, A sharp threshold in proof complexity, in: Proc. STOC 01, 2001, pp. 337-346.
    • (2001) Proc. STOC , vol.1 , pp. 337-346
    • Achlioptas, D.1    Beame, P.2    Molloy, M.3
  • 5
    • 0022809084 scopus 로고
    • Probabilistic analysis of two heuristics for the 3-satisfiability problem
    • Chao M.T., Franco J. Probabilistic analysis of two heuristics for the 3-satisfiability problem. SIAM J. Comput. 15:1986;1106-1118.
    • (1986) SIAM J. Comput. , vol.15 , pp. 1106-1118
    • Chao, M.T.1    Franco, J.2
  • 6
    • 0025471827 scopus 로고
    • Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k-satisfiability problem
    • Chao M.T., Franco J. Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k-satisfiability problem. Inform. Sci. 51:1990;289-314.
    • (1990) Inform. Sci. , vol.51 , pp. 289-314
    • Chao, M.T.1    Franco, J.2
  • 7
    • 0024090265 scopus 로고
    • Many hard examples for resolution
    • Chvàtal V., Szmeredi E. Many hard examples for resolution. J. ACM. 35:1988;759-768.
    • (1988) J. ACM , vol.35 , pp. 759-768
    • Chvàtal, V.1    Szmeredi, E.2
  • 8
  • 9
    • 0034825060 scopus 로고    scopus 로고
    • Trajectories in phase diagrams, growth processes and computational complexity: How search algorithms solve the 3-satisfiability problem
    • Cocco S., Monasson R. Trajectories in phase diagrams, growth processes and computational complexity. how search algorithms solve the 3-Satisfiability problem Phys. Rev. Lett. 86:2001;1654 Cocco S., Monasson R. Analysis of the computational complexity of solving random satisfiability problems using branch and bound search algorithms. Eur. Phys. J. B. 22:2001;505.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 1654
    • Cocco, S.1    Monasson, R.2
  • 10
    • 0000090412 scopus 로고    scopus 로고
    • Analysis of the computational complexity of solving random satisfiability problems using branch and bound search algorithms
    • Cocco S., Monasson R. Trajectories in phase diagrams, growth processes and computational complexity. how search algorithms solve the 3-Satisfiability problem Phys. Rev. Lett. 86:2001;1654 Cocco S., Monasson R. Analysis of the computational complexity of solving random satisfiability problems using branch and bound search algorithms. Eur. Phys. J. B. 22:2001;505.
    • (2001) Eur. Phys. J. B , vol.22 , pp. 505
    • Cocco, S.1    Monasson, R.2
  • 11
    • 37649027691 scopus 로고    scopus 로고
    • Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random satisfiability problem, and its application to stop-and-restart resolutions
    • Cocco S., Monasson R. Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random satisfiability problem, and its application to stop-and-restart resolutions. Phys. Rev. E. 66:2002;037101.
    • (2002) Phys. Rev. E , vol.66 , pp. 037101
    • Cocco, S.1    Monasson, R.2
  • 12
    • 0027708548 scopus 로고    scopus 로고
    • Experimental results on the cross-over point in satisfiability problems
    • The AAAI Press/MIT Press, Cambridge, MA
    • J. Crawford, L. Auton, Experimental results on the cross-over point in satisfiability problems, Proc. 11th National Conf. on Artificial Intelligence (AAAI-93), The AAAI Press/MIT Press, Cambridge, MA, 1993, pp. 21-27; Artif. Intell. 81 (1996).
    • (1993) Proc. 11th National Conf. on Artificial Intelligence (AAAI-93) , pp. 21-27
    • Crawford, J.1    Auton, L.2
  • 13
    • 0027708548 scopus 로고    scopus 로고
    • J. Crawford, L. Auton, Experimental results on the cross-over point in satisfiability problems, Proc. 11th National Conf. on Artificial Intelligence (AAAI-93), The AAAI Press/MIT Press, Cambridge, MA, 1993, pp. 21-27; Artif. Intell. 81 (1996).
    • (1996) Artif. Intell. , vol.81
  • 14
    • 84919401135 scopus 로고
    • A machine program for theorem proving
    • Davis M., Logemann G., Loveland D. A machine program for theorem proving. Commun. ACM. 5:1962;394-397.
    • (1962) Commun. ACM , vol.5 , pp. 394-397
    • Davis, M.1    Logemann, G.2    Loveland, D.3
  • 17
    • 0242594532 scopus 로고    scopus 로고
    • The dynamics of proving uncolorability of large random graphs
    • Ein-Dor L., Monasson R. The dynamics of proving uncolorability of large random graphs. J. Phys. A. 36:2003;11055.
    • (2003) J. Phys. A , vol.36 , pp. 11055
    • Ein-Dor, L.1    Monasson, R.2
  • 18
    • 0034882875 scopus 로고    scopus 로고
    • Results related to thresholds phenomena research in satisfiability: Lower bounds
    • Franco J. Results related to thresholds phenomena research in satisfiability. lower bounds Theoret. Comput. Sci. 265:2001;147-157.
    • (2001) Theoret. Comput. Sci. , vol.265 , pp. 147-157
    • Franco, J.1
  • 19
    • 0033458154 scopus 로고    scopus 로고
    • Sharp thresholds of graph properties, and the k-sat problem
    • Friedgut E. Sharp thresholds of graph properties, and the k-sat problem. J. Amer. Math. Soc. 12:1999;1017.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 1017
    • Friedgut, E.1
  • 20
    • 0030371894 scopus 로고    scopus 로고
    • Analysis of two simple heuristics on a random instance of k-SAT
    • Frieze A., Suen S. Analysis of two simple heuristics on a random instance of k-SAT. J. Algorithms. 20:1996;312-335.
    • (1996) J. Algorithms , vol.20 , pp. 312-335
    • Frieze, A.1    Suen, S.2
  • 22
    • 0028529155 scopus 로고
    • Easy problems are sometimes hard
    • Gent I.P., Walsh T. Easy problems are sometimes hard. Artif. Intell. 70:1994;335-345.
    • (1994) Artif. Intell. , vol.70 , pp. 335-345
    • Gent, I.P.1    Walsh, T.2
  • 25
    • 0034830080 scopus 로고    scopus 로고
    • Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs
    • Hartmann A., Weigt M. Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs. Phys. Rev. Lett. 86:2001;1658.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 1658
    • Hartmann, A.1    Weigt, M.2
  • 26
    • 0003072698 scopus 로고    scopus 로고
    • Frontiers in problem solving: Phase transitions and complexity
    • I and II, Elsevier Science, Essex, UK
    • T. Hogg, B.A. Huberman, C. Williams (Eds.), Frontiers in problem solving: phase transitions and complexity, Artificial Intelligence, Vols. 81, I and II, Elsevier Science, Essex, UK, 1996.
    • (1996) Artificial Intelligence , vol.81
    • Hogg, T.1    Huberman, B.A.2    Williams, C.3
  • 28
    • 84938084560 scopus 로고    scopus 로고
    • The probabilistic analysis of a greedy satisfiability algorithm
    • Kaporis A.C., Kirousis L.M., Lalas E.G. The probabilistic analysis of a greedy satisfiability algorithm. ESA. 2002;574-585.
    • (2002) ESA , pp. 574-585
    • Kaporis, A.C.1    Kirousis, L.M.2    Lalas, E.G.3
  • 29
    • 0003316429 scopus 로고
    • The art of computer programming
    • Section 2.2.1, Addison-Wesley, New York
    • D.E. Knuth, The art of computer programming, Vol. 1: Fundamental Algorithms, Section 2.2.1, Addison-Wesley, New York, 1968.
    • (1968) Vol. 1: Fundamental Algorithms , vol.1
    • Knuth, D.E.1
  • 30
    • 0003672584 scopus 로고
    • Scale invariance, interfaces, and non-equilibrium dynamics
    • Plenum Press, New-York
    • A. McKane, M. Droz, J. Vannimenus, D. Wolf (Eds.), Scale invariance, interfaces, and non-equilibrium dynamics, NATO ASI Ser. B: Physics, Vol. 344, Plenum Press, New-York, 1995.
    • (1995) NATO ASI Ser. B: Physics , vol.344
    • McKane, A.1    Droz, M.2    Vannimenus, J.3    Wolf, D.4
  • 32
    • 2442675349 scopus 로고    scopus 로고
    • On the analysis of backtrack procedures for the coloring of random graphs
    • E. Ben-Naim, H. Frauenfelder, Z. Torczkai (Eds.), Springer, Berlin
    • R. Monasson, On the analysis of backtrack procedures for the coloring of random graphs, in: E. Ben-Naim, H. Frauenfelder, Z. Torczkai (Eds.), Complex Networks, Springer, Berlin, 2004.
    • (2004) Complex Networks
    • Monasson, R.1
  • 33
    • 0033536221 scopus 로고    scopus 로고
    • Determining computational complexity from characteristic 'phase transitions'
    • Monasson R., Zecchina R., Kirkpatrick S., Selman B., Troyansky L. Determining computational complexity from characteristic 'phase transitions'. Nature. 400:1999;133-137 Monasson R., Zecchina R., Kirkpatrick S., Selman B., Troyansky L. 2+p-SAT. relation of typical-case complexity to the nature of the phase transition Random Structure and Algorithms. 15:1999;414.
    • (1999) Nature , vol.400 , pp. 133-137
    • Monasson, R.1    Zecchina, R.2    Kirkpatrick, S.3    Selman, B.4    Troyansky, L.5
  • 34
    • 0033431975 scopus 로고    scopus 로고
    • 2+p-SAT: Relation of typical-case complexity to the nature of the phase transition
    • Monasson R., Zecchina R., Kirkpatrick S., Selman B., Troyansky L. Determining computational complexity from characteristic 'phase transitions'. Nature. 400:1999;133-137 Monasson R., Zecchina R., Kirkpatrick S., Selman B., Troyansky L. 2+p-SAT. relation of typical-case complexity to the nature of the phase transition, Random Structure and Algorithms. 15:1999;414.
    • (1999) Random Structure and Algorithms , vol.15 , pp. 414
    • Monasson, R.1    Zecchina, R.2    Kirkpatrick, S.3    Selman, B.4    Troyansky, L.5
  • 35
    • 0037193016 scopus 로고    scopus 로고
    • Optimizing searches via rare events
    • Montanari A., Zecchina R. Optimizing searches via rare events. Phys. Rev. Lett. 88:2002;178701.
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 178701
    • Montanari, A.1    Zecchina, R.2
  • 36
    • 0028434242 scopus 로고
    • Critical behavior in the satisfiability of random Boolean expressions
    • Selman B., Kirkpatrick S. Critical behavior in the satisfiability of random Boolean expressions. Science. 264:1994;1297-1301.
    • (1994) Science , vol.264 , pp. 1297-1301
    • Selman, B.1    Kirkpatrick, S.2
  • 37
    • 21344437483 scopus 로고
    • Differential equations for random processes and random graphs
    • Wormald N. Differential equations for random processes and random graphs. Ann. Appl. Probab. 5:1995;1217-1235.
    • (1995) Ann. Appl. Probab. , vol.5 , pp. 1217-1235
    • Wormald, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.