메뉴 건너뛰기




Volumn 8, Issue 1, 2013, Pages

Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; ASYMPTOMATIC PARAMETRIC EXACT 3 COLORING ALGORITHM; CONTROLLED STUDY; ERDOS RENYI CONNECTED RANDOM GRAPH; EXPERIMENTAL DESIGN; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PARAMETRIC TEST; PROBABILITY; PROBLEM SOLVING; PSEUDO RANDOM PLANAR GRAPH; RANDOM 4 REGULAR PLANAR GRAPH; STATISTICAL DISTRIBUTION;

EID: 84872341102     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0053437     Document Type: Article
Times cited : (5)

References (60)
  • 1
    • 84872307386 scopus 로고    scopus 로고
    • Arti_cial Intelligence: A Systems Approach
    • Jones & Bartlett Publishers, Incorporated
    • Jones M (2008) Arti_cial Intelligence: A Systems Approach. Computer Science. Jones & Bartlett Publishers, Incorporated.
    • (2008) Computer Science
    • Jones, M.1
  • 2
    • 0020829934 scopus 로고
    • Improving the performance guarantee for approximate graph coloring
    • Wigderson A, (1983) Improving the performance guarantee for approximate graph coloring. Journal of the ACM (JACM) 30: 729-735.
    • (1983) Journal of the ACM (JACM) , vol.30 , pp. 729-735
    • Wigderson, A.1
  • 5
    • 34848823114 scopus 로고    scopus 로고
    • Phase transitions in the coloring of random graphs
    • Zdeborová L, Krzakala F, (2007) Phase transitions in the coloring of random graphs. Physical Review E 76: 031131.
    • (2007) Physical Review E , vol.76 , pp. 031131
    • Zdeborová, L.1    Krzakala, F.2
  • 6
    • 84872350906 scopus 로고    scopus 로고
    • Ph.D. thesis, Universität Wien, Theoretical Biochemistry Group, Institute for Theoretical Chemistry website. Available
    • Abfalter I (2005) Nucleic acid sequence design as a graph colouring problem. Ph.D. thesis, Universität Wien, Theoretical Biochemistry Group, Institute for Theoretical Chemistry website. Available: http://www.tbi.univie.ac.at/papers/Abstracts/ingrid diss.pdf. Accessed 2012 Dec 02.
    • (2005) Nucleic acid sequence design as a graph colouring problem
    • Abfalter, I.1
  • 8
    • 78349308733 scopus 로고    scopus 로고
    • Heuristic algorithms in computational molecular biology
    • Karp R, (2011) Heuristic algorithms in computational molecular biology. Journal of Computer and System Sciences 77: 122-128.
    • (2011) Journal of Computer and System Sciences , vol.77 , pp. 122-128
    • Karp, R.1
  • 11
  • 13
    • 0000202647 scopus 로고
    • Universal sequential search problems
    • Levin L, (1973) Universal sequential search problems. Problemy Peredachi Informatsii 9: 115-116.
    • (1973) Problemy Peredachi Informatsii , vol.9 , pp. 115-116
    • Levin, L.1
  • 15
    • 0007134805 scopus 로고
    • The state of the three color problem
    • Steinberg R, (1993) The state of the three color problem. Annals of discrete mathematics 55: 211-248.
    • (1993) Annals of Discrete Mathematics , vol.55 , pp. 211-248
    • Steinberg, R.1
  • 19
    • 36249012990 scopus 로고    scopus 로고
    • Extremal optimization at the phase transition of the three-coloring problem
    • Boettcher S, Percus AG, (2004) Extremal optimization at the phase transition of the three-coloring problem. Physical Review E 69: 066703.
    • (2004) Physical Review E , vol.69 , pp. 066703
    • Boettcher, S.1    Percus, A.G.2
  • 20
    • 0004215178 scopus 로고
    • Publications of tke Matkemafical Insfifufe of the Hungarian Academy of Sciences 5
    • Erdo{double acute}s P, Rënyi A (1960) On the evolution of random graphs. Publications of tke Matkemafical Insfifufe of the Hungarian Academy of Sciences 5.
    • (1960) On the evolution of random graphs
    • Erdos, P.1    Rënyi, A.2
  • 22
    • 0030542968 scopus 로고    scopus 로고
    • Structural properties of plane graphs without adjacent triangles and an application to 3-colorings
    • Borodin OV, (1996) Structural properties of plane graphs without adjacent triangles and an application to 3-colorings. Journal of Graph Theory 21: 183-186.
    • (1996) Journal of Graph Theory , vol.21 , pp. 183-186
    • Borodin, O.V.1
  • 24
    • 35448955356 scopus 로고    scopus 로고
    • Planar graphs without 4,6,8-cycles are 3-colorable
    • Wang Wf, Chen M, (2007) Planar graphs without 4,6,8-cycles are 3-colorable. Science in China Series A: Mathematics 50: 1552-1562.
    • (2007) Science in China Series A: Mathematics , vol.50 , pp. 1552-1562
    • Wang, W.1    Chen, M.2
  • 26
    • 0000899024 scopus 로고
    • Gro{double acute}tzsch's 3-color theorem and its counterparts for the torus and the projective plane
    • Thomassen C, (1994) Gro{double acute}tzsch's 3-color theorem and its counterparts for the torus and the projective plane. Journal of Combinatorial Theory, Series B 62: 268-279.
    • (1994) Journal of Combinatorial Theory, Series B , vol.62 , pp. 268-279
    • Thomassen, C.1
  • 27
    • 0016349356 scopus 로고
    • Approximation algorithms for combinatorial problems
    • Johnson DS, (1974) Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9: 256-278.
    • (1974) Journal of Computer and System Sciences , vol.9 , pp. 256-278
    • Johnson, D.S.1
  • 29
  • 30
    • 0041931546 scopus 로고
    • A better performance guarantee for approximate graph coloring
    • Berger B, Rompel J, (1990) A better performance guarantee for approximate graph coloring. Algorithmica 5: 459-466.
    • (1990) Algorithmica , vol.5 , pp. 459-466
    • Berger, B.1    Rompel, J.2
  • 31
    • 0027201216 scopus 로고
    • A still better performance guarantee for approximate graph coloring
    • Halldórsson M, (1993) A still better performance guarantee for approximate graph coloring. Information Processing Letters 45: 19-23.
    • (1993) Information Processing Letters , vol.45 , pp. 19-23
    • Halldórsson, M.1
  • 32
    • 0028425392 scopus 로고
    • New approximation algorithms for graph coloring
    • Blum A, (1994) New approximation algorithms for graph coloring. Journal of the ACM (JACM) 41: 516.
    • (1994) Journal of the ACM (JACM) , vol.41 , pp. 516
    • Blum, A.1
  • 34
    • 0032028848 scopus 로고    scopus 로고
    • Approximate graph coloring by semidefinite programming
    • Karger D, Motwani R, Sudan M, (1998) Approximate graph coloring by semidefinite programming. Journal of the ACM (JACM) 45: 246-265.
    • (1998) Journal of the ACM (JACM) , vol.45 , pp. 246-265
    • Karger, D.1    Motwani, R.2    Sudan, M.3
  • 35
    • 0039550370 scopus 로고    scopus 로고
    • On the hardness of approximating the chromatic number
    • Khanna S, Linial N, Safra S, (2000) On the hardness of approximating the chromatic number. Combinatorica 20: 393-415.
    • (2000) Combinatorica , vol.20 , pp. 393-415
    • Khanna, S.1    Linial, N.2    Safra, S.3
  • 39
    • 0024057387 scopus 로고
    • Are there interactive proofs for co-NP languages?
    • Fortnow L, Sipser M, (1988) Are there interactive proofs for co-NP languages? Information Processing Letters 28: 249-251.
    • (1988) Information Processing Letters , vol.28 , pp. 249-251
    • Fortnow, L.1    Sipser, M.2
  • 43
    • 0042668159 scopus 로고
    • Generating all planer graphs regular of degree four
    • Manca P, (1979) Generating all planer graphs regular of degree four. Journal of graph theory 3: 357-364.
    • (1979) Journal of Graph Theory , vol.3 , pp. 357-364
    • Manca, P.1
  • 44
    • 84988972033 scopus 로고
    • Generating all 4-regular planar graphs from the graph of the octahedron
    • Lehel J, (1981) Generating all 4-regular planar graphs from the graph of the octahedron. Journal of graph theory 5: 423-426.
    • (1981) Journal of Graph Theory , vol.5 , pp. 423-426
    • Lehel, J.1
  • 45
    • 84987467100 scopus 로고
    • Generating all 3-connected 4-regular planar graphs from the octahedron graph
    • Broersma H, Duijvestijn A, Go{double acute}bel F, (1993) Generating all 3-connected 4-regular planar graphs from the octahedron graph. Journal of graph theory 17: 613-620.
    • (1993) Journal of Graph Theory , vol.17 , pp. 613-620
    • Broersma, H.1    Duijvestijn, A.2    Gobel, F.3
  • 48
    • 0012588345 scopus 로고
    • Planar 3-colorability is polynomial complete
    • Stockmeyer L, (1973) Planar 3-colorability is polynomial complete. SIGACT News 5: 19-25.
    • (1973) SIGACT News , vol.5 , pp. 19-25
    • Stockmeyer, L.1
  • 49
    • 84872359251 scopus 로고    scopus 로고
    • Minimal non-extensible precolorings and implicit-relations
    • abs/1104.0510
    • Martin H JA (2011) Minimal non-extensible precolorings and implicit-relations. CoRR - Computing Research Repository abs/1104.0510.
    • (2011) CoRR - Computing Research Repository
    • Martin, H.J.A.1
  • 53
    • 37049022364 scopus 로고    scopus 로고
    • Constructive generation of very hard 3-colorability instances
    • Mizuno K, Nishihara S, (2008) Constructive generation of very hard 3-colorability instances. Discrete Applied Mathematics 156: 218-229.
    • (2008) Discrete Applied Mathematics , vol.156 , pp. 218-229
    • Mizuno, K.1    Nishihara, S.2
  • 54
    • 84972498411 scopus 로고
    • Every planar map is four colorable. Part I: Discharging
    • Appel K, Haken W, Koch J, (1977) Every planar map is four colorable. Part I: Discharging. Illinois Journal of Mathematics 21: 429-490.
    • (1977) Illinois Journal of Mathematics , vol.21 , pp. 429-490
    • Appel, K.1    Haken, W.2    Koch, J.3
  • 55
    • 84972500815 scopus 로고
    • Every planar map is four colorable. Part II: Reducibility
    • Appel K, Haken W, Koch J, (1977) Every planar map is four colorable. Part II: Reducibility. Illinois Journal of Mathematics 21: 491-567.
    • (1977) Illinois Journal of Mathematics , vol.21 , pp. 491-567
    • Appel, K.1    Haken, W.2    Koch, J.3
  • 56
    • 0344351687 scopus 로고
    • Uniqueness of colorability and colorability of planar 4-regular graphs are npcomplete
    • Dailey DP, (1980) Uniqueness of colorability and colorability of planar 4-regular graphs are npcomplete. Discrete Mathematics 30: 289-293.
    • (1980) Discrete Mathematics , vol.30 , pp. 289-293
    • Dailey, D.P.1
  • 59


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.