An improved bit parallel exact maximum clique algorithm
This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581, 2011 ), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring...
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| Published in: | Optimization letters Vol. 7; no. 3; pp. 467 - 479 |
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| Format: | Journal Article |
| Language: | English |
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01.03.2013
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| ISSN: | 1862-4472, 1862-4480 |
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| Abstract | This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581,
2011
), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring strategy in Tomita et al. (Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, pp 191–203,
2010
), which is now integrated in the bit string framework, as well as different optimization strategies for fast bit scanning. Reported results over DIMACS and random graphs show that the new variants improve over previous BB-MaxClique for a vast majority of cases. It is also established that recoloring is mainly useful for graphs with high densities. |
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| AbstractList | This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581,
2011
), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring strategy in Tomita et al. (Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, pp 191–203,
2010
), which is now integrated in the bit string framework, as well as different optimization strategies for fast bit scanning. Reported results over DIMACS and random graphs show that the new variants improve over previous BB-MaxClique for a vast majority of cases. It is also established that recoloring is mainly useful for graphs with high densities. |
| Author | Matia, Fernando San Segundo, Pablo Rodriguez-Losada, Diego Hernando, Miguel |
| Author_xml | – sequence: 1 givenname: Pablo surname: San Segundo fullname: San Segundo, Pablo email: pablo.sansegundo@upm.es organization: Center of Automatic Control and Robotics-CAR (UPM-CSIC) – sequence: 2 givenname: Fernando surname: Matia fullname: Matia, Fernando organization: Center of Automatic Control and Robotics-CAR (UPM-CSIC) – sequence: 3 givenname: Diego surname: Rodriguez-Losada fullname: Rodriguez-Losada, Diego organization: Center of Automatic Control and Robotics-CAR (UPM-CSIC) – sequence: 4 givenname: Miguel surname: Hernando fullname: Hernando, Miguel organization: Center of Automatic Control and Robotics-CAR (UPM-CSIC) |
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| Cites_doi | 10.1016/j.ejor.2005.05.026 10.1007/s10489-008-0147-6 10.1145/378239.379017 10.1007/978-1-4684-2001-2_9 10.1016/0167-6377(90)90057-C 10.1007/978-3-642-11440-3_18 10.1016/S0167-6377(97)00054-0 10.1016/S0166-218X(01)00284-0 10.1007/3-540-45066-1_22 10.1007/978-1-4757-3023-4_1 |
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| References | Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Chaff, S.M.: Engineering an efficient SAT solver. In: XXXVIII Proceedings of Design Automation Conference (DAC ’01), pp. 530–535. ACM, New York (2001) HottaK.TomitaE.TakahashiH.A view invariant human FACE detection method based on maximum cliquesTrans. IPSJ200344SIG14(TOM9)5770 BomzeI.M.BudinichM.PardalosP.M.PelilloM.HandBook of Combinatorial Optimization. Supplement A1999DordrechtKluwer Academic Publishers17410.1007/978-1-4757-3023-4_1 JohnsonD.S.TrickM.A.Cliques, coloring and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 261996ProvidenceAmerican Mathematical Society WoodD.R.An algorithm for finding a maximum clique in a graphOperat. Res. Lett.19772121121710.1016/S0167-6377(97)00054-0 San SegundoP.Rodriguez-LosadaD.JimenezA.An exact bit-parallel algorithm for the maximum clique problemComput. Oper. Resour.2011382571581 KoncJ.JanečičD.An improved branch and bound algorithm for the maximum clique problemMATCH Commun. Math. Comput. Chem.2007585695902353166 ButenkoS.WilhelmW.E.Clique-detection models in computational biochemistry and genomicsEur. J. Operat. Res.200617311722281071125.9202510.1016/j.ejor.2005.05.026 San SegundoP.Rodríguez-LosadaD.MatíaF.GalánR.Fast exact feature based data correspondence search with an efficient bit-parallel MCP solverAppl. Intel.201032331132910.1007/s10489-008-0147-6 Tomita, E., Sutani, Y., Higashi, T., Takahashi, S., Wakatsuki, M.: A simple and faster branch-and-bound algorithm for finding a maximum clique. In: Rahman MS, Fujita S. (eds.) Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol. 5942, pp. 191–203. Springer, Berlin (2010) ÖstergårdP.R.J.A fast algorithm for the maximum clique problemDiscrete Applied Mathematics2002120197207191286110.1016/S0166-218X(01)00290-6 Tomita, E., Seki, T.: An efficient branch and bound algorithm for finding a maximum clique. In: Calude, C., Dinneen, M., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. LNCS, vol. 2731, pp. 278–289, Springer, Berlin (2003) BahadurD.K.C.AkutsuT.TomitaE.SekiT.FujijamaA.Point matching under non-uniform distortions and protein side chain packing based on efficient maximum clique algorithmsGenome Inform.200613143152 Karp, R.M.: In: Miller, R.E., Thatcher, J.W. (eds.) Reducibility among Combinatorial Problems, pp. 85–103. Plenum, New York (1972) CarraghanR.PardalosP.M.An exact algorithm for the maximum clique problemOperat. Res. Lett.199093753820711.9008010.1016/0167-6377(90)90057-C (431_CR14) 1996 D.K.C. Bahadur (431_CR2) 2006; 13 D.R. Wood (431_CR7) 1977; 21 S. Butenko (431_CR3) 2006; 173 431_CR10 431_CR13 J. Konc (431_CR11) 2007; 58 431_CR12 431_CR15 P.R.J. Östergård (431_CR9) 2002; 120 K. Hotta (431_CR4) 2003; 44 R. Carraghan (431_CR8) 1990; 9 P. San Segundo (431_CR5) 2010; 32 431_CR1 I.M. Bomze (431_CR6) 1999 |
| References_xml | – reference: Karp, R.M.: In: Miller, R.E., Thatcher, J.W. (eds.) Reducibility among Combinatorial Problems, pp. 85–103. Plenum, New York (1972) – reference: ÖstergårdP.R.J.A fast algorithm for the maximum clique problemDiscrete Applied Mathematics2002120197207191286110.1016/S0166-218X(01)00290-6 – reference: Tomita, E., Sutani, Y., Higashi, T., Takahashi, S., Wakatsuki, M.: A simple and faster branch-and-bound algorithm for finding a maximum clique. In: Rahman MS, Fujita S. (eds.) Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol. 5942, pp. 191–203. Springer, Berlin (2010) – reference: San SegundoP.Rodríguez-LosadaD.MatíaF.GalánR.Fast exact feature based data correspondence search with an efficient bit-parallel MCP solverAppl. Intel.201032331132910.1007/s10489-008-0147-6 – reference: CarraghanR.PardalosP.M.An exact algorithm for the maximum clique problemOperat. Res. Lett.199093753820711.9008010.1016/0167-6377(90)90057-C – reference: BomzeI.M.BudinichM.PardalosP.M.PelilloM.HandBook of Combinatorial Optimization. Supplement A1999DordrechtKluwer Academic Publishers17410.1007/978-1-4757-3023-4_1 – reference: Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Chaff, S.M.: Engineering an efficient SAT solver. In: XXXVIII Proceedings of Design Automation Conference (DAC ’01), pp. 530–535. ACM, New York (2001) – reference: HottaK.TomitaE.TakahashiH.A view invariant human FACE detection method based on maximum cliquesTrans. IPSJ200344SIG14(TOM9)5770 – reference: ButenkoS.WilhelmW.E.Clique-detection models in computational biochemistry and genomicsEur. J. Operat. Res.200617311722281071125.9202510.1016/j.ejor.2005.05.026 – reference: WoodD.R.An algorithm for finding a maximum clique in a graphOperat. Res. Lett.19772121121710.1016/S0167-6377(97)00054-0 – reference: JohnsonD.S.TrickM.A.Cliques, coloring and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 261996ProvidenceAmerican Mathematical Society – reference: Tomita, E., Seki, T.: An efficient branch and bound algorithm for finding a maximum clique. In: Calude, C., Dinneen, M., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. LNCS, vol. 2731, pp. 278–289, Springer, Berlin (2003) – reference: KoncJ.JanečičD.An improved branch and bound algorithm for the maximum clique problemMATCH Commun. Math. Comput. Chem.2007585695902353166 – reference: San SegundoP.Rodriguez-LosadaD.JimenezA.An exact bit-parallel algorithm for the maximum clique problemComput. Oper. Resour.2011382571581 – reference: BahadurD.K.C.AkutsuT.TomitaE.SekiT.FujijamaA.Point matching under non-uniform distortions and protein side chain packing based on efficient maximum clique algorithmsGenome Inform.200613143152 – volume: 173 start-page: 1 year: 2006 ident: 431_CR3 publication-title: Eur. J. Operat. Res. doi: 10.1016/j.ejor.2005.05.026 – volume: 32 start-page: 311 issue: 3 year: 2010 ident: 431_CR5 publication-title: Appl. Intel. doi: 10.1007/s10489-008-0147-6 – volume: 13 start-page: 143 year: 2006 ident: 431_CR2 publication-title: Genome Inform. – ident: 431_CR15 doi: 10.1145/378239.379017 – ident: 431_CR13 – ident: 431_CR1 doi: 10.1007/978-1-4684-2001-2_9 – volume: 9 start-page: 375 year: 1990 ident: 431_CR8 publication-title: Operat. Res. Lett. doi: 10.1016/0167-6377(90)90057-C – ident: 431_CR12 doi: 10.1007/978-3-642-11440-3_18 – volume: 21 start-page: 211 year: 1977 ident: 431_CR7 publication-title: Operat. Res. Lett. doi: 10.1016/S0167-6377(97)00054-0 – volume: 58 start-page: 569 year: 2007 ident: 431_CR11 publication-title: MATCH Commun. Math. Comput. Chem. – volume: 120 start-page: 97 issue: 1 year: 2002 ident: 431_CR9 publication-title: Discrete Applied Mathematics doi: 10.1016/S0166-218X(01)00284-0 – volume-title: Cliques, coloring and Satisfiability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 26 year: 1996 ident: 431_CR14 – volume: 44 start-page: 57 issue: SIG14(TOM9) year: 2003 ident: 431_CR4 publication-title: Trans. IPSJ – ident: 431_CR10 doi: 10.1007/3-540-45066-1_22 – start-page: 1 volume-title: HandBook of Combinatorial Optimization. Supplement A year: 1999 ident: 431_CR6 doi: 10.1007/978-1-4757-3023-4_1 |
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