On Two Techniques of Combining Branching and Treewidth
Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of...
Gespeichert in:
| Veröffentlicht in: | Algorithmica Jg. 54; H. 2; S. 181 - 207 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article Tagungsbericht |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer-Verlag
01.06.2009
Springer Springer Verlag |
| Schlagworte: | |
| ISSN: | 0178-4617, 1432-0541 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of
simple
algorithms based on combinations of these techniques. The idea behind these algorithms is very natural: If a parameter like the treewidth of a graph is small, algorithms based on dynamic programming perform well. On the other side, if the treewidth is large, then there must be vertices of high degree in the graph, which is good for branching algorithms. We give several examples of possible combinations of branching and programming which provide the fastest known algorithms for a number of NP hard problems. All our algorithms require non-trivial balancing of these two techniques.
In the first approach the algorithm either performs fast branching, or if there is an obstacle for fast branching, this obstacle is used for the construction of a path decomposition of small width for the original graph. Using this approach we give the fastest known algorithms for
Minimum Maximal Matching
and for counting all 3-colorings of a graph.
In the second approach the branching occurs until the algorithm reaches a subproblem with a small number of edges (and here the right choice of the size of subproblems is crucial) and then dynamic programming is applied on these subproblems of small width. We exemplify this approach by giving the fastest known algorithm to count all minimum weighted dominating sets of a graph.
We also discuss how similar techniques can be used to design faster parameterized algorithms. |
|---|---|
| AbstractList | Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of
simple
algorithms based on combinations of these techniques. The idea behind these algorithms is very natural: If a parameter like the treewidth of a graph is small, algorithms based on dynamic programming perform well. On the other side, if the treewidth is large, then there must be vertices of high degree in the graph, which is good for branching algorithms. We give several examples of possible combinations of branching and programming which provide the fastest known algorithms for a number of NP hard problems. All our algorithms require non-trivial balancing of these two techniques.
In the first approach the algorithm either performs fast branching, or if there is an obstacle for fast branching, this obstacle is used for the construction of a path decomposition of small width for the original graph. Using this approach we give the fastest known algorithms for
Minimum Maximal Matching
and for counting all 3-colorings of a graph.
In the second approach the branching occurs until the algorithm reaches a subproblem with a small number of edges (and here the right choice of the size of subproblems is crucial) and then dynamic programming is applied on these subproblems of small width. We exemplify this approach by giving the fastest known algorithm to count all minimum weighted dominating sets of a graph.
We also discuss how similar techniques can be used to design faster parameterized algorithms. Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of these techniques. The idea behind these algorithms is very natural: If a parameter like the treewidth of a graph is small, algorithms based on dynamic programming perform well. On the other side, if the treewidth is large, then there must be vertices of high degree in the graph, which is good for branching algorithms. We give several examples of possible combinations of branching and programming which provide the fastest known algorithms for a number of NP hard problems. All our algorithms require non-trivial balancing of these two techniques. In the first approach the algorithm either performs fast branching, or if there is an obstacle for fast branching, this obstacle is used for the construction of a path decomposition of small width for the original graph. Using this approach we give the fastest known algorithms for Minimum Maximal Matching and for counting all 3-colorings of a graph. In the second approach the branching occurs until the algorithm reaches a subproblem with a small number of edges (and here the right choice of the size of subproblems is crucial) and then dynamic programming is applied on these subproblems of small width. We exemplify this approach by giving the fastest known algorithm to count all minimum weighted dominating sets of a graph. We also discuss how similar techniques can be used to design faster parameterized algorithms. |
| Author | Stepanov, Alexey A. Fomin, Fedor V. Gaspers, Serge Saurabh, Saket |
| Author_xml | – sequence: 1 givenname: Fedor V. surname: Fomin fullname: Fomin, Fedor V. organization: Department of Informatics, University of Bergen – sequence: 2 givenname: Serge surname: Gaspers fullname: Gaspers, Serge email: serge@ii.uib.no organization: Department of Informatics, University of Bergen – sequence: 3 givenname: Saket surname: Saurabh fullname: Saurabh, Saket organization: Department of Informatics, University of Bergen, The Institute of Mathematical Sciences – sequence: 4 givenname: Alexey A. surname: Stepanov fullname: Stepanov, Alexey A. organization: Department of Informatics, University of Bergen |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21658239$$DView record in Pascal Francis https://hal-lirmm.ccsd.cnrs.fr/lirmm-00399668$$DView record in HAL |
| BookMark | eNp9kLFOwzAQhi1UJNrCA7BlYUKBs53YyVgqoEiVuoTZchy7cZU6xU6peHsSBXVg6HT_8H13p3-GJq51GqF7DE8YgD8HgCSlcR_jHFMa0ys0xQklMaQJnqApYJ7FCcP8Bs1C2AFgwnM2RWzjouLURoVWtbNfRx2i1kTLdl9aZ902evHSqXpI0lVR4bU-2aqrb9G1kU3Qd39zjj7fXovlKl5v3j-Wi3WsEgJdbPK0wrjkWVqlFUilc1JVpZTAccaNYpyk2GgmE2oIU3nJkpJwoBS0SXUiGZ2jx3FvLRtx8HYv_Y9opRWrxVo01u_3AoDmOWPZN-7ph5E-yKBkY4bfbTh7BLM0IzTvOTxyyrcheG3OCAYx1CnGOsUQhzoF7R3-z1G2k51tXeelbS6aZDRDf8VttRe79uhdX9sF6RfR5olZ |
| CitedBy_id | crossref_primary_10_1145_3170442 crossref_primary_10_1007_s00453_022_01034_7 crossref_primary_10_1016_j_tcs_2014_07_019 crossref_primary_10_1145_3341730 crossref_primary_10_1007_s00453_019_00600_w crossref_primary_10_1145_3506707 crossref_primary_10_1016_j_tcs_2011_09_001 crossref_primary_10_1016_j_disopt_2015_11_003 crossref_primary_10_1016_j_ic_2014_12_008 crossref_primary_10_1016_j_ipl_2012_01_010 crossref_primary_10_1145_3111499 crossref_primary_10_1007_s00224_017_9764_y crossref_primary_10_1007_s00453_010_9460_7 crossref_primary_10_1007_s00453_014_9883_7 crossref_primary_10_1007_s00453_021_00812_z crossref_primary_10_1016_j_ipl_2018_03_019 crossref_primary_10_1016_j_tcs_2012_06_022 crossref_primary_10_1587_transinf_2016FCP0005 crossref_primary_10_1016_j_tcs_2012_08_015 crossref_primary_10_1007_s00453_015_0095_6 crossref_primary_10_1145_3148227 crossref_primary_10_1587_transinf_E96_D_408 crossref_primary_10_1007_s00224_012_9410_7 crossref_primary_10_1016_j_tcs_2014_03_031 crossref_primary_10_1007_s00453_017_0349_6 crossref_primary_10_1137_15M1039584 crossref_primary_10_1186_s13673_020_00226_w crossref_primary_10_1002_net_21516 crossref_primary_10_1007_s00453_016_0216_x crossref_primary_10_1007_s00453_023_01197_x crossref_primary_10_1137_16M109017X crossref_primary_10_1007_s00224_014_9549_5 crossref_primary_10_1016_j_disc_2015_12_030 crossref_primary_10_1007_s00224_017_9751_3 crossref_primary_10_1007_s00453_013_9759_2 crossref_primary_10_1007_s00224_009_9185_7 crossref_primary_10_1007_s00453_011_9566_6 crossref_primary_10_1016_j_jcss_2017_05_003 crossref_primary_10_1007_s00453_011_9546_x |
| Cites_doi | 10.1007/978-3-540-31856-9_3 10.1016/j.ipl.2005.10.012 10.1007/11940128_4 10.1016/j.ipl.2004.10.003 10.1145/1198513.1198515 10.1007/3-540-36478-1_17 10.1007/11523468_16 10.1007/BF02760024 10.1007/11604686_34 10.1006/jagm.2001.1186 10.1016/j.tcs.2005.09.023 10.1016/S0196-6774(03)00005-1 10.1016/j.orl.2004.03.002 10.1016/S0304-3975(97)00228-4 10.1007/3-540-49116-3_53 10.1007/978-3-540-45193-8_6 10.1007/978-3-540-28639-4_25 10.1007/11602613_58 10.1016/j.jda.2005.03.002 10.1007/11847250_13 10.1016/0020-0190(88)90065-8 10.1007/978-1-4612-0515-9 10.1137/0138030 |
| ContentType | Journal Article Conference Proceeding |
| Copyright | Springer Science+Business Media, LLC 2007 2009 INIST-CNRS Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Springer Science+Business Media, LLC 2007 – notice: 2009 INIST-CNRS – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION IQODW 1XC |
| DOI | 10.1007/s00453-007-9133-3 |
| DatabaseName | CrossRef Pascal-Francis Hyper Article en Ligne (HAL) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science Applied Sciences Mathematics |
| EISSN | 1432-0541 |
| EndPage | 207 |
| ExternalDocumentID | oai:HAL:lirmm-00399668v1 21658239 10_1007_s00453_007_9133_3 |
| GroupedDBID | -4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION AABYN AAFGU AAPBV AAYFA ABFGW ABKAS ABPTK ACBMV ACBRV ACBYP ACIGE ACIPQ ACTTH ACVWB ACWMK ADGRI ADMDM ADOXG AEEQQ AEFTE AESTI AEVTX AEYWE AFNRJ AGGBP AIMYW AJDOV AKQUC G8K IQODW UNUBA Z7R Z8M 1XC |
| ID | FETCH-LOGICAL-c420t-f95d11b785d5d0ace92ddbaa07187fc67251fe6a43f26c9b64b270330ef5e4a63 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 76 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000265439600003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0178-4617 |
| IngestDate | Tue Oct 14 20:11:07 EDT 2025 Sun Oct 22 16:03:29 EDT 2023 Sat Nov 29 03:45:23 EST 2025 Tue Nov 18 21:28:19 EST 2025 Fri Feb 21 02:43:07 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Exact exponential time algorithms 3-Coloring Minimum maximal matching Weighted vertex cover Parameterized algorithms NP hard problems Minimum dominating set Treewidth Branching Dominating set Graph theory k-Weighted vertex cover Maximal Matching NP hard problem Graph degree Graph colouring Dynamic programming Graph covering Fast algorithm Counting Graph matching |
| Language | English |
| License | http://www.springer.com/tdm CC BY 4.0 Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MeetingName | 17th Annual International Symposium on Algorithms and Computation (ISAAC 2006) |
| MergedId | FETCHMERGED-LOGICAL-c420t-f95d11b785d5d0ace92ddbaa07187fc67251fe6a43f26c9b64b270330ef5e4a63 |
| ORCID | 0000-0001-7847-6402 0000-0003-1955-4612 |
| PageCount | 27 |
| ParticipantIDs | hal_primary_oai_HAL_lirmm_00399668v1 pascalfrancis_primary_21658239 crossref_primary_10_1007_s00453_007_9133_3 crossref_citationtrail_10_1007_s00453_007_9133_3 springer_journals_10_1007_s00453_007_9133_3 |
| PublicationCentury | 2000 |
| PublicationDate | 2009-06-01 |
| PublicationDateYYYYMMDD | 2009-06-01 |
| PublicationDate_xml | – month: 06 year: 2009 text: 2009-06-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York – name: Heidelberg |
| PublicationTitle | Algorithmica |
| PublicationTitleAbbrev | Algorithmica |
| PublicationYear | 2009 |
| Publisher | Springer-Verlag Springer Springer Verlag |
| Publisher_xml | – name: Springer-Verlag – name: Springer – name: Springer Verlag |
| References | BodlaenderH.L.A tourist guide through treewidthActa Cybern.1993111210804.681011268488 FominF.V.KratschD.WoegingerG.J.Exact (exponential) algorithms for the dominating set problemProceedings of the 30th Workshop on Graph Theoretic Concepts in Computer Science (WG 2004)2005BerlinSpringer245256 GavrilF.YannakakisM.Edge dominating sets in graphsSIAM J. Appl. Math.1980383643720455.0504710.1137/0138030579424 Randerath, B., Schiermeyer, I.: Exact algorithms for MINIMUM DOMINATING SET. Technical Report zaik-469. Zentrum für Angewandte Informatik Köln, Germany (2004) WoegingerG.Exact algorithms for NP-hard problems: a surveyCombinatorial Optimization—Eureka, You Shrink!2003BerlinSpringer18520710.1007/3-540-36478-1_17 ByskovJ.M.Enumerating maximal independent sets with applications to graph colouringOper. Res. Lett.2004325475561052.0505510.1016/j.orl.2004.03.0022077457 FominF.V.GrandoniF.KratschD.Some new techniques in design and analysis of exact (exponential) algorithmsBull. EATCS20058747772192300 SchöningU.Algorithmics in exponential timeProceedings of the 22nd International Symposium on Theoretical Aspects of Computer Science (STACS 2005)2005BerlinSpringer3643 Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman (1979) FominF.V.GaspersS.SaurabhS.Branching and treewidth based exact algorithmsProceedings of the 17th International Symposium on Algorithms and Computation (ISAAC 2006)2006BerlinSpringer1625 MoonJ.W.MoserL.On cliques in graphsIsrael J. Math.1965323280144.2320510.1007/BF02760024182577 KneisJ.MölleD.RichterS.RossmanithP.Algorithms based in treewidth of sparse graphsProceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2005)2005BerlinSpringer38539610.1007/11604686_34 Scott, A.D., Sorkin, G.B.: Linear-programming design and analysis of fast algorithms for Max 2-Sat and Max 2-CSP, arXiv.org, cs/0604080, 2006 WoegingerG.Space and time complexity of exact algorithms: some open problemsProceedings of the 1st International Workshop on Parameterized and Exact Computation (IWPEC 2004)2004BerlinSpringer281290 NiedermeierR.RossmanithP.On efficient fixed-parameter algorithms for weighted vertex coverJ. Algorithms20034763771046.680581980328 Raman, V., Saurabh, S., Sikdar, S.: Efficient exact algorithms through enumerating maximal independent sets and other techniques. Theory Comput. Syst. (to appear) FominF.V.HøieK.Pathwidth of cubic graphs and exact algorithmsInf. Process. Lett.20069719119610.1016/j.ipl.2005.10.012 Angelsmark, O., Jonsson, P.: Improved algorithms for counting solutions in constraint satisfaction problems. In: Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming (CP 2003), pp. 81–95 (2003) FominF.V.GrandoniF.KratschD.Measure and conquer: domination—a case studyProceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005)2005BerlinSpringer191203 FominF.V.GrandoniF.PyatkinA.V.StepanovA.A.Bounding the number of minimal dominating sets: a measure and conquer approachProceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005)2005BerlinSpringer573582 GrandoniF.A note on the complexity of minimum dominating setJ. Discrete Algorithms200642092141127.0507010.1016/j.jda.2005.03.0022220296 IwamaK.Worst-case upper bounds for k-SATBull. EATCS20048261712132616 EppsteinD.Quasiconvex analysis of multivariate recurrence equations for backtracking algorithmsACM Trans. Algorithms2006249250910.1145/1198513.11985152284242 BodlaenderH.L.A partial k-arboretum of graphs with bounded treewidthTheor. Comput. Sci.19982091450912.6814810.1016/S0304-3975(97)00228-41647486 ChandranL.S.GrandoniF.Refined memorization for vertex coverInf. Process. Lett.20059312513110.1016/j.ipl.2004.10.0032108134 NiedermeierR.RossmanithP.Upper bounds for vertex cover further improvedProceedings of the 16th International Symposium on Theoretical Aspects of Computer Science (STACS 1999)1999BerlinSpringer561570 FernauH.Edge dominating set: efficient enumeration-based exact algorithmsProceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC 2006)2006BerlinSpringer14215310.1007/11847250_13 DowneyR.G.FellowsM.R.Parameterized Complexity1999New YorkSpringer ChenJ.KanjI.A.JiaW.Vertex cover: further observations and further improvementsJ. Algorithms2001412803011017.6808710.1006/jagm.2001.11861869253 JohnsonD.S.YannakakisM.PapadimitriouC.H.On generating all maximal independent setsInf. Process. Lett.1988271191230654.6808610.1016/0020-0190(88)90065-8933271 WilliamsR.A new algorithm for optimal 2-constraint satisfaction and its implicationsTheor. Comput. Sci.20053483573651081.6809510.1016/j.tcs.2005.09.023 Fürer, M., Kasiviswanathan, S.P.: Algorithms for counting 2-SAT solutions and colorings with applications. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 33 (2005) F.V. Fomin (9133_CR12) 2005 J.W. Moon (9133_CR23) 1965; 3 H.L. Bodlaender (9133_CR2) 1993; 11 G. Woeginger (9133_CR31) 2003 9133_CR29 H.L. Bodlaender (9133_CR3) 1998; 209 F. Grandoni (9133_CR19) 2006; 4 D. Eppstein (9133_CR8) 2006; 2 J. Kneis (9133_CR22) 2005 R. Niedermeier (9133_CR24) 1999 J.M. Byskov (9133_CR4) 2004; 32 9133_CR27 F.V. Fomin (9133_CR14) 2005 9133_CR26 F.V. Fomin (9133_CR11) 2005; 87 L.S. Chandran (9133_CR5) 2005; 93 U. Schöning (9133_CR28) 2005 R.G. Downey (9133_CR7) 1999 F.V. Fomin (9133_CR10) 2006; 97 F.V. Fomin (9133_CR13) 2005 R. Niedermeier (9133_CR25) 2003; 47 9133_CR17 9133_CR1 9133_CR16 R. Williams (9133_CR30) 2005; 348 J. Chen (9133_CR6) 2001; 41 D.S. Johnson (9133_CR21) 1988; 27 F.V. Fomin (9133_CR15) 2006 K. Iwama (9133_CR20) 2004; 82 H. Fernau (9133_CR9) 2006 G. Woeginger (9133_CR32) 2004 F. Gavril (9133_CR18) 1980; 38 |
| References_xml | – reference: Raman, V., Saurabh, S., Sikdar, S.: Efficient exact algorithms through enumerating maximal independent sets and other techniques. Theory Comput. Syst. (to appear) – reference: GrandoniF.A note on the complexity of minimum dominating setJ. Discrete Algorithms200642092141127.0507010.1016/j.jda.2005.03.0022220296 – reference: MoonJ.W.MoserL.On cliques in graphsIsrael J. Math.1965323280144.2320510.1007/BF02760024182577 – reference: ChenJ.KanjI.A.JiaW.Vertex cover: further observations and further improvementsJ. Algorithms2001412803011017.6808710.1006/jagm.2001.11861869253 – reference: FominF.V.HøieK.Pathwidth of cubic graphs and exact algorithmsInf. Process. Lett.20069719119610.1016/j.ipl.2005.10.012 – reference: Randerath, B., Schiermeyer, I.: Exact algorithms for MINIMUM DOMINATING SET. Technical Report zaik-469. Zentrum für Angewandte Informatik Köln, Germany (2004) – reference: FernauH.Edge dominating set: efficient enumeration-based exact algorithmsProceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC 2006)2006BerlinSpringer14215310.1007/11847250_13 – reference: NiedermeierR.RossmanithP.Upper bounds for vertex cover further improvedProceedings of the 16th International Symposium on Theoretical Aspects of Computer Science (STACS 1999)1999BerlinSpringer561570 – reference: KneisJ.MölleD.RichterS.RossmanithP.Algorithms based in treewidth of sparse graphsProceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2005)2005BerlinSpringer38539610.1007/11604686_34 – reference: EppsteinD.Quasiconvex analysis of multivariate recurrence equations for backtracking algorithmsACM Trans. Algorithms2006249250910.1145/1198513.11985152284242 – reference: WilliamsR.A new algorithm for optimal 2-constraint satisfaction and its implicationsTheor. Comput. Sci.20053483573651081.6809510.1016/j.tcs.2005.09.023 – reference: WoegingerG.Space and time complexity of exact algorithms: some open problemsProceedings of the 1st International Workshop on Parameterized and Exact Computation (IWPEC 2004)2004BerlinSpringer281290 – reference: FominF.V.GrandoniF.KratschD.Measure and conquer: domination—a case studyProceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005)2005BerlinSpringer191203 – reference: JohnsonD.S.YannakakisM.PapadimitriouC.H.On generating all maximal independent setsInf. Process. Lett.1988271191230654.6808610.1016/0020-0190(88)90065-8933271 – reference: Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman (1979) – reference: DowneyR.G.FellowsM.R.Parameterized Complexity1999New YorkSpringer – reference: Fürer, M., Kasiviswanathan, S.P.: Algorithms for counting 2-SAT solutions and colorings with applications. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 33 (2005) – reference: NiedermeierR.RossmanithP.On efficient fixed-parameter algorithms for weighted vertex coverJ. Algorithms20034763771046.680581980328 – reference: SchöningU.Algorithmics in exponential timeProceedings of the 22nd International Symposium on Theoretical Aspects of Computer Science (STACS 2005)2005BerlinSpringer3643 – reference: Angelsmark, O., Jonsson, P.: Improved algorithms for counting solutions in constraint satisfaction problems. In: Proceedings of the 9th International Conference on Principles and Practice of Constraint Programming (CP 2003), pp. 81–95 (2003) – reference: Scott, A.D., Sorkin, G.B.: Linear-programming design and analysis of fast algorithms for Max 2-Sat and Max 2-CSP, arXiv.org, cs/0604080, 2006 – reference: ChandranL.S.GrandoniF.Refined memorization for vertex coverInf. Process. Lett.20059312513110.1016/j.ipl.2004.10.0032108134 – reference: FominF.V.GaspersS.SaurabhS.Branching and treewidth based exact algorithmsProceedings of the 17th International Symposium on Algorithms and Computation (ISAAC 2006)2006BerlinSpringer1625 – reference: WoegingerG.Exact algorithms for NP-hard problems: a surveyCombinatorial Optimization—Eureka, You Shrink!2003BerlinSpringer18520710.1007/3-540-36478-1_17 – reference: FominF.V.GrandoniF.KratschD.Some new techniques in design and analysis of exact (exponential) algorithmsBull. EATCS20058747772192300 – reference: GavrilF.YannakakisM.Edge dominating sets in graphsSIAM J. Appl. Math.1980383643720455.0504710.1137/0138030579424 – reference: BodlaenderH.L.A partial k-arboretum of graphs with bounded treewidthTheor. Comput. Sci.19982091450912.6814810.1016/S0304-3975(97)00228-41647486 – reference: BodlaenderH.L.A tourist guide through treewidthActa Cybern.1993111210804.681011268488 – reference: FominF.V.GrandoniF.PyatkinA.V.StepanovA.A.Bounding the number of minimal dominating sets: a measure and conquer approachProceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005)2005BerlinSpringer573582 – reference: IwamaK.Worst-case upper bounds for k-SATBull. EATCS20048261712132616 – reference: FominF.V.KratschD.WoegingerG.J.Exact (exponential) algorithms for the dominating set problemProceedings of the 30th Workshop on Graph Theoretic Concepts in Computer Science (WG 2004)2005BerlinSpringer245256 – reference: ByskovJ.M.Enumerating maximal independent sets with applications to graph colouringOper. Res. Lett.2004325475561052.0505510.1016/j.orl.2004.03.0022077457 – start-page: 36 volume-title: Proceedings of the 22nd International Symposium on Theoretical Aspects of Computer Science (STACS 2005) year: 2005 ident: 9133_CR28 doi: 10.1007/978-3-540-31856-9_3 – volume: 97 start-page: 191 year: 2006 ident: 9133_CR10 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2005.10.012 – start-page: 16 volume-title: Proceedings of the 17th International Symposium on Algorithms and Computation (ISAAC 2006) year: 2006 ident: 9133_CR15 doi: 10.1007/11940128_4 – volume: 87 start-page: 47 year: 2005 ident: 9133_CR11 publication-title: Bull. EATCS – volume: 93 start-page: 125 year: 2005 ident: 9133_CR5 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2004.10.003 – volume: 2 start-page: 492 year: 2006 ident: 9133_CR8 publication-title: ACM Trans. Algorithms doi: 10.1145/1198513.1198515 – ident: 9133_CR29 – ident: 9133_CR27 – start-page: 185 volume-title: Combinatorial Optimization—Eureka, You Shrink! year: 2003 ident: 9133_CR31 doi: 10.1007/3-540-36478-1_17 – start-page: 191 volume-title: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005) year: 2005 ident: 9133_CR12 doi: 10.1007/11523468_16 – volume: 82 start-page: 61 year: 2004 ident: 9133_CR20 publication-title: Bull. EATCS – volume: 11 start-page: 1 year: 1993 ident: 9133_CR2 publication-title: Acta Cybern. – volume: 3 start-page: 23 year: 1965 ident: 9133_CR23 publication-title: Israel J. Math. doi: 10.1007/BF02760024 – start-page: 385 volume-title: Proceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2005) year: 2005 ident: 9133_CR22 doi: 10.1007/11604686_34 – ident: 9133_CR17 – volume: 41 start-page: 280 year: 2001 ident: 9133_CR6 publication-title: J. Algorithms doi: 10.1006/jagm.2001.1186 – volume: 348 start-page: 357 year: 2005 ident: 9133_CR30 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2005.09.023 – volume: 47 start-page: 63 year: 2003 ident: 9133_CR25 publication-title: J. Algorithms doi: 10.1016/S0196-6774(03)00005-1 – volume: 32 start-page: 547 year: 2004 ident: 9133_CR4 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2004.03.002 – volume: 209 start-page: 1 year: 1998 ident: 9133_CR3 publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(97)00228-4 – start-page: 561 volume-title: Proceedings of the 16th International Symposium on Theoretical Aspects of Computer Science (STACS 1999) year: 1999 ident: 9133_CR24 doi: 10.1007/3-540-49116-3_53 – ident: 9133_CR1 doi: 10.1007/978-3-540-45193-8_6 – ident: 9133_CR26 – start-page: 281 volume-title: Proceedings of the 1st International Workshop on Parameterized and Exact Computation (IWPEC 2004) year: 2004 ident: 9133_CR32 doi: 10.1007/978-3-540-28639-4_25 – start-page: 573 volume-title: Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005) year: 2005 ident: 9133_CR13 doi: 10.1007/11602613_58 – volume: 4 start-page: 209 year: 2006 ident: 9133_CR19 publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2005.03.002 – start-page: 142 volume-title: Proceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC 2006) year: 2006 ident: 9133_CR9 doi: 10.1007/11847250_13 – start-page: 245 volume-title: Proceedings of the 30th Workshop on Graph Theoretic Concepts in Computer Science (WG 2004) year: 2005 ident: 9133_CR14 – volume: 27 start-page: 119 year: 1988 ident: 9133_CR21 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(88)90065-8 – ident: 9133_CR16 – volume-title: Parameterized Complexity year: 1999 ident: 9133_CR7 doi: 10.1007/978-1-4612-0515-9 – volume: 38 start-page: 364 year: 1980 ident: 9133_CR18 publication-title: SIAM J. Appl. Math. doi: 10.1137/0138030 |
| SSID | ssj0012796 |
| Score | 2.2081203 |
| Snippet | Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately... |
| SourceID | hal pascalfrancis crossref springer |
| SourceType | Open Access Repository Index Database Enrichment Source Publisher |
| StartPage | 181 |
| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Combinatorics Combinatorics. Ordered structures Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Algorithms Data Structures and Information Theory Discrete Mathematics Exact sciences and technology Graph theory Information retrieval. Graph Mathematics Mathematics of Computing Sciences and techniques of general use Theoretical computing Theory of Computation |
| Title | On Two Techniques of Combining Branching and Treewidth |
| URI | https://link.springer.com/article/10.1007/s00453-007-9133-3 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00399668 |
| Volume | 54 |
| WOSCitedRecordID | wos000265439600003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB509SCIb3F9kYMnpZAmbdIcVRQPiwqu4q3kiQtud9mu69836bYF8QF662GSDjN5zGSS7wM4CbU_YSiOEqZ9gkJSEwmOZUR17BjOeKJM5ekev73Nnp_Fff2Ou2xuuzclyWqlbh-7heiDRuFoTfjEKqKLsJQGsJmQoj88taUDwitSrkA77xWIeVPK_K6LT5vR4ku4Crk6lqW3jpvTWnypj1bbzvX6vxTegLU6ykTn82GxCQu22IL1hsEB1RN6G9hdgfrvI9RvkFxLNHLIy6mKNwJdBP3CGRWShUH9ibXvAzN92YHH66v-5U1UMylEOiF4GjmRmjhWPEtNarDUVhBjlJQ-vsi404z7KMdZJhPqCNNCsUQRvxRQbF1qE8noLnSKUWH3AEmaYWdcLJRSCZEmE1wz6liCtXLGmi7gxqS5rmHGA9vFa94CJFd2ycNnsEtOu3DaNhnPMTZ-Ez7xfmrlAjr2zXkvfx1MhsMAdBryt2wWd-H4kyPbBiT2MRehogtnjdfyetqWP_91_0_SB7AyLzqFw5pD6Ewnb_YIlvVsOignx9Vw_QA2VeGw |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dSxwxEB-qLSiI2triqdU8-KQsZJNssnlUUa70ei10W3xb8skd6J7cnvrvm-ztLkhbob7twyQ7zORjJr9kfgDHEfuTluKEcRMSFJLZRAqsEmpSz3EumLaNp0diPM6vr-WP9h133d127yDJZqXuH7vF6IMm8WhNhsQqoSvwlkWWnZii__zdQwdENKRckXY-KJCKDsr8WxfPNqOVSbwKuXGn6mAdv6S1-AMfbbadq61XKbwNm22Uic6Ww-I9vHHVB9jqGBxQO6F3gH-vUPE4Q0VXybVGM4-CnG54I9B51C-eUSFVWVTMnXuc2sXkI_y6uiwuhknLpJAYRvAi8TKzaapFntnMYmWcJNZqpUJ8kQtvuAhRjndcMeoJN1JzpklYCih2PnNMcfoJVqtZ5XYBKZpjb30qtdaMKJtLYTj1nGGjvXV2ALgzaWnaMuOR7eKm7AskN3Yp42e0S0kHcNI3uVvW2HhJ-Dj4qZeL1bGHZ6PyZjq_vY2FTmP-lj-kAzh85si-AUlDzEWoHMBp57Wynbb1v_-691_SR7A2LL6NytGX8dd9WF8CUPHg5gBWF_N79xnemYfFtJ4fNkP3CdKu5JQ |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1La9wwEB6aNJRCaZo-6DaP6pBTi4ksyZJ1TJouCVk2Id2W3IyeZCHxLms3-fuV_ILQB5TcfBjZw4xkzWhG3wewH2t_0lKcMG5CgkIym0iBVUJN6jnOBdO28fRETKf51ZW86HhOq77bvS9JtncaIkpTWR8srT8YLr7FSIQm8ZhNhiQroWvwlIVEJvZ0XX77MZQRiGgIuiIFfVAmFX1Z80-veLAxrV3HtsgXS1UFS_mW4uK3WmmzBY03H638K3jZRZ_osJ0uW_DEla9hs2d2QN1CfwP8vESz-wWa9QivFVp4FOR0wyeBjqKu8ewKqdKi2cq5-7mtr9_C9_HX2ZeTpGNYSAwjuE68zGyaapFnNrNYGSeJtVqpEHfkwhsuQvTjHVeMesKN1JxpEn4RFDufOaY4fQfr5aJ07wEpmmNvfSq11owom0thOPWcYaO9dXYEuDdvYTr48ciCcVMMwMmNXYr4GO1S0BF8GoYsW-yNfwnvB58NchE1--RwUtzMV7e3EQA15nX5XTqCvQdOHQaQNMRihMoRfO49WHTLufr7Vz_8l_RHeHZxPC4mp9OzbXje1qXiec4OrNern24XNsxdPa9We80s_gXMoe14 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Algorithmica&rft.atitle=On+Two+Techniques+of+Combining+Branching+and+Treewidth&rft.au=FOMIN%2C+Fedor+V&rft.au=GASPERS%2C+Serge&rft.au=SAURABH%2C+Saket&rft.au=STEPANOV%2C+Alexey+A&rft.date=2009-06-01&rft.pub=Springer&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=54&rft.issue=2&rft.spage=181&rft.epage=207&rft_id=info:doi/10.1007%2Fs00453-007-9133-3&rft.externalDBID=n%2Fa&rft.externalDocID=21658239 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon |