Exact Algorithms for L(2,1)-Labeling of Graphs

The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G =( V , E ) into an interval of integers {0,…, k } is an L (2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integer...

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Vydané v:	Algorithmica Ročník 59; číslo 2; s. 169 - 194
Hlavní autori:	Havet, Frédéric, Klazar, Martin, Kratochvíl, Jan, Kratsch, Dieter, Liedloff, Mathieu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer-Verlag 01.02.2011 Springer Springer Verlag
Predmet:	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Computer Systems Organization and Communication Networks Data Structures and Algorithms Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Mathematics of Computing Software Theoretical computing Theory of Computation (2,1)-labeling Graph Algorithm Moderately exponential time algorithm L(2, 1)-labeling Frequency allocation Graph colouring NP complete problem Vertex(graph) Dynamic programming Graph labelling
ISSN:	0178-4617, 1432-0541
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Abstract	The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G =( V , E ) into an interval of integers {0,…, k } is an L (2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed k ≥4, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive O * (( k +1) n ) algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of k =4, where the running time of our algorithm is O (1.3006 n ). Furthermore we show that dynamic programming can be used to establish an O (3.8730 n ) algorithm to compute an optimal L (2,1)-labeling.
AbstractList	The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G =( V , E ) into an interval of integers {0,…, k } is an L (2,1)-labeling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed k ≥4, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive O * (( k +1) n ) algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of k =4, where the running time of our algorithm is O (1.3006 n ). Furthermore we show that dynamic programming can be used to establish an O (3.8730 n ) algorithm to compute an optimal L (2,1)-labeling. The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph $G=(V,E)$ into an interval of integers $\{0, \dots ,k\}$ is an $L(2,1)$-labeling of $G$ of span $k$ if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbor are mapped onto distinct integers. It is known that for any fixed $k\ge 4$, deciding the existence of such a labeling is an NP-complete problem. We present exact exponential time algorithms that are faster than the naive $O^*((k+1)^n)$ algorithm that would try all possible mappings. The improvement is best seen in the first NP-complete case of $k=4$, where the running time of our algorithm is $O(1.3006^n)$. Furthermore we show that dynamic programming can be used to establish an $O(3.8730^n)$ algorithm to compute an optimal $L(2,1)$-labeling.
Author	Liedloff, Mathieu Kratochvíl, Jan Havet, Frédéric Klazar, Martin Kratsch, Dieter
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Keywords	(2,1)-labeling Graph Algorithm Moderately exponential time algorithm L(2, 1)-labeling Frequency allocation Graph colouring NP complete problem Vertex(graph) Dynamic programming Graph labelling
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References	ChangG.J.KuoD.The L(2,1)-labeling problem on graphsSIAM J. Discrete Math.199693093160860.0506410.1137/S08954801932453391386886 FominF.GrandoniF.KratschD.Measure and conquer: Domination—a case studyProceedings of ICALP 20052005BerlinSpringer192203 Hasunuma, T., Ishii, T., Ono, H., Uno, Y.: A linear time algorithm for L(2,1)-labeling of trees. arXiv:0810.0906v1 (2008) FominF.HeggernesP.KratschD.Exact algorithms for graph homomorphismsTheory Comput. Syst.2007413813931119.6813310.1007/s00224-007-2007-x2329330 FialaJ.GolovachP.KratochvílJ.Distance constrained labelings of graphs of bounded treewidthProceedings of ICALP 20052005BerlinSpringer360372 FialaJ.KloksT.KratochvílJ.Fixed-parameter complexity of λ-labelingsDiscrete Appl. Math.200111359720982.0508510.1016/S0166-218X(00)00387-51855514 Leese, R.A., Noble, S.D.: Cyclic labellings with constraints at two distances. Electron. J. Comb. 11 (2004) (Research paper 16) Roberts, F.S. Private communication to J. Griggs LiuD.ZhuX.Multilevel distance labelings for paths and cyclesSIAM J. Discrete Math.2005196106211095.0503310.1137/S08954801024177682191283 FialaJ.KratochvílJ.Complexity of partial covers of graphsProceedings of ISAAC 20012001BerlinSpringer537549 Gonçalves, D.: On the L(p,1)-labelling of graphs. In: Discrete Mathematics and Theoretical Computer Science Proceedings, vol. AE, pp. 81–86 GriggsJ.R.YehR.K.Labelling graphs with a condition at distance 2SIAM J. Discrete Math.199255865950346.0511210.1137/04050481186826 Alon, N., Wormald, N.: High degree graphs contain large-star factors (submitted) Král’D.Channel assignment problem with variable weightsSIAM J. Discrete Math.2006206907040767.0508010.1137/0406196362272225 Koivisto, M.: An O(2n) algorithm for graph coloring and other partitioning problems via inclusion-exclusion. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science 2006, pp. 583–590 (2006) Havet, F., Reed, B., Sereni, J.-S.: L(2,1)-labellings of graphs. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms 2008, pp. 621–630 (2008) FialaJ.KratochvílJ.Partial covers of graphsDiscuss. Math. Graph Theory20022289991017.050941936227 HellP.NešetřilJ.On the complexity of H-colouringJ. Comb. Theory Ser. B199048921100639.0502310.1016/0095-8956(90)90132-J FialaJ.KratochvílJ.PórA.On the computational complexity of partial covers of theta graphsElectron. Notes Discrete Math.200519798510.1016/j.endm.2005.05.012 KratochvílJ.KratschD.LiedloffM.Exact algorithms for L(2,1)-labeling of graphsProceedings of MFCS 20072007BerlinSpringer513524 JohnsonD.S.YannakakisM.PapadimitriouC.H.On generating all maximal independent setsInf. Process. Lett.1988271191230654.6808610.1016/0020-0190(88)90065-8933271 LiuD.ZhuX.Circular distance two labelings and circular chromatic numbersArs Comb.2003691771831072.055702007650 Björklund, A., Husfeldt, T.: Inclusion-exclusion algorithms for counting set partitions. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science 2006, pp. 575–582 (2006) BodlaenderH.L.KloksT.TanR.B.van LeeuwenJ.Approximations for lambda-colorings of graphsComput. J.2004471932041039.6809010.1093/comjnl/47.2.193 F. Fomin (9302_CR11) 2007; 41 9302_CR21 9302_CR12 D. Král (9302_CR19) 2006; 20 9302_CR24 9302_CR14 9302_CR15 J. Fiala (9302_CR5) 2001 9302_CR1 H.L. Bodlaender (9302_CR3) 2004; 47 9302_CR18 D. Liu (9302_CR22) 2003; 69 F. Fomin (9302_CR10) 2005 J. Fiala (9302_CR8) 2005 D.S. Johnson (9302_CR17) 1988; 27 J. Fiala (9302_CR9) 2005; 19 D. Liu (9302_CR23) 2005; 19 J.R. Griggs (9302_CR13) 1992; 5 J. Kratochvíl (9302_CR20) 2007 9302_CR2 P. Hell (9302_CR16) 1990; 48 G.J. Chang (9302_CR4) 1996; 9 J. Fiala (9302_CR6) 2002; 22 J. Fiala (9302_CR7) 2001; 113
References_xml	– reference: HellP.NešetřilJ.On the complexity of H-colouringJ. Comb. Theory Ser. B199048921100639.0502310.1016/0095-8956(90)90132-J – reference: LiuD.ZhuX.Multilevel distance labelings for paths and cyclesSIAM J. Discrete Math.2005196106211095.0503310.1137/S08954801024177682191283 – reference: Alon, N., Wormald, N.: High degree graphs contain large-star factors (submitted) – reference: FialaJ.KratochvílJ.Partial covers of graphsDiscuss. Math. Graph Theory20022289991017.050941936227 – reference: FialaJ.GolovachP.KratochvílJ.Distance constrained labelings of graphs of bounded treewidthProceedings of ICALP 20052005BerlinSpringer360372 – reference: Gonçalves, D.: On the L(p,1)-labelling of graphs. In: Discrete Mathematics and Theoretical Computer Science Proceedings, vol. AE, pp. 81–86 – reference: BodlaenderH.L.KloksT.TanR.B.van LeeuwenJ.Approximations for lambda-colorings of graphsComput. J.2004471932041039.6809010.1093/comjnl/47.2.193 – reference: FominF.HeggernesP.KratschD.Exact algorithms for graph homomorphismsTheory Comput. Syst.2007413813931119.6813310.1007/s00224-007-2007-x2329330 – reference: Leese, R.A., Noble, S.D.: Cyclic labellings with constraints at two distances. Electron. J. Comb. 11 (2004) (Research paper 16) – reference: LiuD.ZhuX.Circular distance two labelings and circular chromatic numbersArs Comb.2003691771831072.055702007650 – reference: Havet, F., Reed, B., Sereni, J.-S.: L(2,1)-labellings of graphs. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms 2008, pp. 621–630 (2008) – reference: Björklund, A., Husfeldt, T.: Inclusion-exclusion algorithms for counting set partitions. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science 2006, pp. 575–582 (2006) – reference: FialaJ.KratochvílJ.PórA.On the computational complexity of partial covers of theta graphsElectron. Notes Discrete Math.200519798510.1016/j.endm.2005.05.012 – reference: JohnsonD.S.YannakakisM.PapadimitriouC.H.On generating all maximal independent setsInf. Process. Lett.1988271191230654.6808610.1016/0020-0190(88)90065-8933271 – reference: Koivisto, M.: An O(2n) algorithm for graph coloring and other partitioning problems via inclusion-exclusion. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science 2006, pp. 583–590 (2006) – reference: Král’D.Channel assignment problem with variable weightsSIAM J. Discrete Math.2006206907040767.0508010.1137/0406196362272225 – reference: GriggsJ.R.YehR.K.Labelling graphs with a condition at distance 2SIAM J. Discrete Math.199255865950346.0511210.1137/04050481186826 – reference: Roberts, F.S. Private communication to J. Griggs – reference: ChangG.J.KuoD.The L(2,1)-labeling problem on graphsSIAM J. Discrete Math.199693093160860.0506410.1137/S08954801932453391386886 – reference: Hasunuma, T., Ishii, T., Ono, H., Uno, Y.: A linear time algorithm for L(2,1)-labeling of trees. arXiv:0810.0906v1 (2008) – reference: FialaJ.KloksT.KratochvílJ.Fixed-parameter complexity of λ-labelingsDiscrete Appl. Math.200111359720982.0508510.1016/S0166-218X(00)00387-51855514 – reference: FominF.GrandoniF.KratschD.Measure and conquer: Domination—a case studyProceedings of ICALP 20052005BerlinSpringer192203 – reference: KratochvílJ.KratschD.LiedloffM.Exact algorithms for L(2,1)-labeling of graphsProceedings of MFCS 20072007BerlinSpringer513524 – reference: FialaJ.KratochvílJ.Complexity of partial covers of graphsProceedings of ISAAC 20012001BerlinSpringer537549 – volume: 41 start-page: 381 year: 2007 ident: 9302_CR11 publication-title: Theory Comput. Syst. doi: 10.1007/s00224-007-2007-x – volume: 69 start-page: 177 year: 2003 ident: 9302_CR22 publication-title: Ars Comb. – ident: 9302_CR1 – volume: 48 start-page: 92 year: 1990 ident: 9302_CR16 publication-title: J. Comb. Theory Ser. B doi: 10.1016/0095-8956(90)90132-J – volume: 9 start-page: 309 year: 1996 ident: 9302_CR4 publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480193245339 – ident: 9302_CR14 doi: 10.1007/978-3-642-04128-0_4 – ident: 9302_CR18 doi: 10.1109/FOCS.2006.11 – volume: 20 start-page: 690 year: 2006 ident: 9302_CR19 publication-title: SIAM J. Discrete Math. doi: 10.1137/040619636 – volume: 22 start-page: 89 year: 2002 ident: 9302_CR6 publication-title: Discuss. Math. Graph Theory doi: 10.7151/dmgt.1159 – ident: 9302_CR12 – ident: 9302_CR2 doi: 10.1109/FOCS.2006.41 – ident: 9302_CR15 – ident: 9302_CR21 doi: 10.37236/1769 – start-page: 360 volume-title: Proceedings of ICALP 2005 year: 2005 ident: 9302_CR8 – volume: 19 start-page: 79 year: 2005 ident: 9302_CR9 publication-title: Electron. Notes Discrete Math. doi: 10.1016/j.endm.2005.05.012 – volume: 47 start-page: 193 year: 2004 ident: 9302_CR3 publication-title: Comput. J. doi: 10.1093/comjnl/47.2.193 – start-page: 513 volume-title: Proceedings of MFCS 2007 year: 2007 ident: 9302_CR20 – start-page: 537 volume-title: Proceedings of ISAAC 2001 year: 2001 ident: 9302_CR5 – volume: 27 start-page: 119 year: 1988 ident: 9302_CR17 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(88)90065-8 – volume: 19 start-page: 610 year: 2005 ident: 9302_CR23 publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480102417768 – start-page: 192 volume-title: Proceedings of ICALP 2005 year: 2005 ident: 9302_CR10 – ident: 9302_CR24 – volume: 5 start-page: 586 year: 1992 ident: 9302_CR13 publication-title: SIAM J. Discrete Math. doi: 10.1137/0405048 – volume: 113 start-page: 59 year: 2001 ident: 9302_CR7 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(00)00387-5
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Snippet	The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph G... The notion of distance constrained graph labelings, motivated by the Frequency Assignment Problem, reads as follows: A mapping from the vertex set of a graph...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer systems and distributed systems. User interface Computer Systems Organization and Communication Networks Data Structures and Algorithms Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Mathematics of Computing Software Theoretical computing Theory of Computation
Title	Exact Algorithms for L(2,1)-Labeling of Graphs
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