An exponential time 2-approximation algorithm for bandwidth
The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b. In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797...
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| Vydané v: | Theoretical computer science Ročník 511; s. 23 - 31 |
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Elsevier B.V
04.11.2013
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b.
In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797n)=O(30.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have O∗(3n) and O∗(2n) worst-case running time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident to vertices in the same bucket or to vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a divide-and-conquer strategy along with dynamic programming to achieve the improved time bound. |
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| AbstractList | The bandwidth of a graph G on n vertices is the minimum b such that the vertices of G can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b.
In this paper, we present a 2-approximation algorithm for the Bandwidth problem that takes worst-case O(1.9797n)=O(30.6217n) time and uses polynomial space. This improves both the previous best 2- and 3-approximation algorithms of Cygan et al. which have O∗(3n) and O∗(2n) worst-case running time bounds, respectively. Our algorithm is based on constructing bucket decompositions of the input graph. A bucket decomposition partitions the vertex set of a graph into ordered sets (called buckets) of (almost) equal sizes such that all edges are either incident to vertices in the same bucket or to vertices in two consecutive buckets. The idea is to find the smallest bucket size for which there exists a bucket decomposition. The algorithm uses a divide-and-conquer strategy along with dynamic programming to achieve the improved time bound. |
| Author | Kasiviswanathan, Shiva Prasad Fürer, Martin Gaspers, Serge |
| Author_xml | – sequence: 1 givenname: Martin surname: Fürer fullname: Fürer, Martin email: furer@cse.psu.edu organization: Computer Science and Engineering, Pennsylvania State University, University Park, PA, USA – sequence: 2 givenname: Serge surname: Gaspers fullname: Gaspers, Serge email: sergeg@cse.unsw.edu.au organization: The University of New South Wales and NICTA, Sydney, Australia – sequence: 3 givenname: Shiva Prasad surname: Kasiviswanathan fullname: Kasiviswanathan, Shiva Prasad email: kasivisw@gmail.com organization: General Electric Research, San Ramon, CA, USA |
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| Cites_doi | 10.1017/S0963548300000675 10.1016/S0166-218X(02)00404-3 10.1006/jcss.2000.1727 10.1007/11847250_10 10.1016/j.ipl.2009.05.003 10.1016/S0020-0190(98)00173-2 10.1006/jcss.1999.1682 10.1145/2071379.2071387 10.1007/BF02280884 10.1016/j.tcs.2009.02.007 10.1137/070683933 10.1007/s00453-007-9002-0 10.1145/1109557.1109558 10.1016/S0304-3975(99)00181-4 10.1137/0403033 10.1109/SFCS.1998.743431 10.1137/0602041 10.1016/j.dam.2011.07.009 10.1016/0890-5401(91)90045-4 10.1093/comjnl/bxm048 10.1016/j.ipl.2009.05.002 10.1007/978-3-642-11269-0_14 10.1006/jagm.1998.0997 10.1007/978-3-642-02927-1_8 10.1137/0607057 10.1137/0134037 10.1016/0196-6774(84)90006-3 10.1016/j.jda.2008.11.001 10.1145/1007352.1007391 10.1007/s00224-007-1334-2 10.1137/S0895480192232333 10.1007/s00453-008-9223-x 10.1145/195058.195229 10.1007/3-540-44985-X_2 10.1007/BF01940871 10.1016/j.tcs.2010.04.031 10.1016/j.dam.2011.10.032 10.1016/S0168-0072(01)00052-5 10.1007/978-3-642-22685-4_28 10.1016/j.tcs.2010.06.018 10.1007/3-540-44666-4_26 10.1007/s00454-009-9135-9 10.1007/11847250_11 |
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| Keywords | Graph bandwidth Bucket decomposition Approximation algorithm Exponential time algorithm |
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| References | Cai, Huang (br000050) 2010; 57 Jerrum, Vazirani (br000150) 1996; 16 Monien (br000185) 1986; 7 Blum, Konjevod, Ravi, Vempala (br000020) 2000; 235 Cygan, Pilipczuk (br000070) 2012; 160 Marx (br000180) 2008; 51 Y. Chen, M. Grohe, M. Grüber, On parameterized approximability, in: Proceedings of IWPEC 2006, 2006, pp. 109–120. Bourgeois, Escoffier, Paschos (br000030) 2011; 159 J. Chen, X. Huang, I.A. Kanj, G. Xia, Linear FPT reductions and computational lower bounds, in: Proceedings of STOC 2004, 2004, pp. 212–221. Kloks, Kratsch, Müller (br000165) 1999; 32 Cygan, Kowalik, Wykurz (br000065) 2009; 109 R.G. Downey, M.R. Fellows, C. McCartin, Parameterized approximation problems, in: Proceedings of IWPEC 2006, 2006, pp. 121–129. B. Monien, I.H. Sudborough, Bandwidth problems in graphs, in: Proceedings of Allerton Conference on Communication, Control, and Computing 1980, 1980, pp. 650–659. A.M.S. Shrestha, S. Tayu, S. Ueno, Bandwidth of convex bipartite graphs and related graph classes, in: Proceedings of COCOON 2011, 2011, pp. 307–318. W. Unger, The complexity of the approximation of the Bandwidth problem, in: Proceedings of FOCS 1998, 1998, pp. 82–91. V. Vassilevska, R. Williams, S.L.M. Woo, Confronting hardness using a hybrid approach, in: Proceedings of SODA 2006, 2006, pp. 1–10. Cygan, Pilipczuk (br000075) 2012; 8 Heggernes, Kratsch, Meister (br000135) 2009; 7 Lee (br000155) 2009; 41 Sprague (br000210) 1994; 7 Kloks, Kratsch, Müller (br000170) 1998; 68 Cygan, Pilipczuk (br000080) 2010; 411 U. Feige, Coping with the NP-hardness of the graph Bandwidth problem, in: Proceedings of SWAT 2000, 2000, pp. 10–19. Raman, Saurabh, Sikdar (br000200) 2007; 41 H.L. Bodlaender, M.R. Fellows, M.T. Hallett, Beyond NP-completeness for problems of bounded width: hardness for the W-hierarchy, in: Proceedings of STOC 1994, 1994, pp. 449–458. Mahesh, Rangan, Srinivasan (br000175) 1991; 95 Yan (br000225) 1997; 13 J. Dunagan, S. Vempala, On euclidean embeddings and bandwidth minimization, in: Proceedings of RANDOM-APPROX 2001, 2001, pp. 229–240. Feige, Talwar (br000115) 2009; 55 Garey, Graham, Johnson, Knuth (br000125) 1978; 34 Dyer, Frieze, Kannan, Kapoor, Perkovic, Vazirani (br000100) 1993; 2 Papadimitriou (br000195) 1976; 16 Hirsch (br000140) 2003; 130 Bourgeois, Escoffier, Paschos (br000040) 2009; 410 Feige (br000105) 2000; 60 Bourgeois, Lucarelli, Milis, Paschos (br000045) 2010; 411 M. Fürer, S. Gaspers, S.P. Kasiviswanathan, An exponential time 2-approximation algorithm for bandwidth, in: Proceedings of IWPEC 2009, 2009, pp. 173–184. Gurari, Sudborough (br000130) 1984; 5 Assmann, Peck, Sysło, Zak (br000010) 1981; 2 Dantsin, Gavrilovich, Hirsch, Konev (br000085) 2001; 113 Björklund, Husfeldt, Koivisto (br000015) 2009; 39 Impagliazzo, Paturi (br000145) 2001; 62 O. Amini, F.V. Fomin, S. Saurabh, Counting subgraphs via homomorphisms, in: Proceedings of ICALP 2009, 2009, pp. 71–82. Bourgeois, Escoffier, Paschos (br000035) 2009; 109 Kleitman, Vohra (br000160) 1990; 3 Dyer (10.1016/j.tcs.2013.03.024_br000100) 1993; 2 Garey (10.1016/j.tcs.2013.03.024_br000125) 1978; 34 Mahesh (10.1016/j.tcs.2013.03.024_br000175) 1991; 95 Impagliazzo (10.1016/j.tcs.2013.03.024_br000145) 2001; 62 Raman (10.1016/j.tcs.2013.03.024_br000200) 2007; 41 10.1016/j.tcs.2013.03.024_br000215 10.1016/j.tcs.2013.03.024_br000055 10.1016/j.tcs.2013.03.024_br000110 Papadimitriou (10.1016/j.tcs.2013.03.024_br000195) 1976; 16 Cygan (10.1016/j.tcs.2013.03.024_br000075) 2012; 8 10.1016/j.tcs.2013.03.024_br000095 10.1016/j.tcs.2013.03.024_br000060 Bourgeois (10.1016/j.tcs.2013.03.024_br000045) 2010; 411 Kleitman (10.1016/j.tcs.2013.03.024_br000160) 1990; 3 Lee (10.1016/j.tcs.2013.03.024_br000155) 2009; 41 Bourgeois (10.1016/j.tcs.2013.03.024_br000040) 2009; 410 Marx (10.1016/j.tcs.2013.03.024_br000180) 2008; 51 Assmann (10.1016/j.tcs.2013.03.024_br000010) 1981; 2 10.1016/j.tcs.2013.03.024_br000205 Blum (10.1016/j.tcs.2013.03.024_br000020) 2000; 235 Bourgeois (10.1016/j.tcs.2013.03.024_br000030) 2011; 159 Bourgeois (10.1016/j.tcs.2013.03.024_br000035) 2009; 109 10.1016/j.tcs.2013.03.024_br000005 Sprague (10.1016/j.tcs.2013.03.024_br000210) 1994; 7 Cai (10.1016/j.tcs.2013.03.024_br000050) 2010; 57 10.1016/j.tcs.2013.03.024_br000025 Kloks (10.1016/j.tcs.2013.03.024_br000170) 1998; 68 Gurari (10.1016/j.tcs.2013.03.024_br000130) 1984; 5 Jerrum (10.1016/j.tcs.2013.03.024_br000150) 1996; 16 Cygan (10.1016/j.tcs.2013.03.024_br000080) 2010; 411 10.1016/j.tcs.2013.03.024_br000220 10.1016/j.tcs.2013.03.024_br000120 Heggernes (10.1016/j.tcs.2013.03.024_br000135) 2009; 7 Yan (10.1016/j.tcs.2013.03.024_br000225) 1997; 13 10.1016/j.tcs.2013.03.024_br000190 Cygan (10.1016/j.tcs.2013.03.024_br000070) 2012; 160 10.1016/j.tcs.2013.03.024_br000090 Dantsin (10.1016/j.tcs.2013.03.024_br000085) 2001; 113 Cygan (10.1016/j.tcs.2013.03.024_br000065) 2009; 109 Kloks (10.1016/j.tcs.2013.03.024_br000165) 1999; 32 Feige (10.1016/j.tcs.2013.03.024_br000115) 2009; 55 Feige (10.1016/j.tcs.2013.03.024_br000105) 2000; 60 Monien (10.1016/j.tcs.2013.03.024_br000185) 1986; 7 Björklund (10.1016/j.tcs.2013.03.024_br000015) 2009; 39 Hirsch (10.1016/j.tcs.2013.03.024_br000140) 2003; 130 |
| References_xml | – volume: 410 start-page: 2184 year: 2009 end-page: 2195 ident: br000040 article-title: Efficient approximation of min set cover by moderately exponential algorithms publication-title: Theoret. Comput. Sci. – volume: 62 start-page: 367 year: 2001 end-page: 375 ident: br000145 article-title: On the complexity of publication-title: J. Comput. System Sci. – volume: 160 start-page: 494 year: 2012 end-page: 504 ident: br000070 article-title: Bandwidth and distortion revisited publication-title: Discrete Appl. Math. – volume: 95 start-page: 218 year: 1991 end-page: 224 ident: br000175 article-title: On finding the minimum bandwidth of interval graphs publication-title: Inf. Comput. – reference: W. Unger, The complexity of the approximation of the Bandwidth problem, in: Proceedings of FOCS 1998, 1998, pp. 82–91. – volume: 39 start-page: 546 year: 2009 end-page: 563 ident: br000015 article-title: Set partitioning via inclusion–exclusion publication-title: SIAM J. Comput. – volume: 57 start-page: 398 year: 2010 end-page: 412 ident: br000050 article-title: Fixed-parameter approximation: conceptual framework and approximability results publication-title: Algorithmica – volume: 130 start-page: 173 year: 2003 end-page: 184 ident: br000140 article-title: Worst-case study of local search for Max- publication-title: Discrete Appl. Math. – reference: O. Amini, F.V. Fomin, S. Saurabh, Counting subgraphs via homomorphisms, in: Proceedings of ICALP 2009, 2009, pp. 71–82. – reference: H.L. Bodlaender, M.R. Fellows, M.T. Hallett, Beyond NP-completeness for problems of bounded width: hardness for the W-hierarchy, in: Proceedings of STOC 1994, 1994, pp. 449–458. – volume: 51 start-page: 60 year: 2008 end-page: 78 ident: br000180 article-title: Parameterized complexity and approximation algorithms publication-title: Comput. J. – reference: M. Fürer, S. Gaspers, S.P. Kasiviswanathan, An exponential time 2-approximation algorithm for bandwidth, in: Proceedings of IWPEC 2009, 2009, pp. 173–184. – volume: 235 start-page: 25 year: 2000 end-page: 42 ident: br000020 article-title: Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems publication-title: Theoret. Comput. Sci. – volume: 2 start-page: 271 year: 1993 end-page: 284 ident: br000100 article-title: A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem publication-title: Combin. Probab. Comput. – volume: 159 start-page: 1954 year: 2011 end-page: 1970 ident: br000030 article-title: Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms publication-title: Discrete Appl. Math. – volume: 411 start-page: 3701 year: 2010 end-page: 3713 ident: br000080 article-title: Exact and approximate bandwidth publication-title: Theoret. Comput. Sci. – reference: J. Dunagan, S. Vempala, On euclidean embeddings and bandwidth minimization, in: Proceedings of RANDOM-APPROX 2001, 2001, pp. 229–240. – volume: 5 start-page: 531 year: 1984 end-page: 546 ident: br000130 article-title: Improved dynamic programming algorithms for bandwidth minimization and the MinCut Linear Arrangement problem publication-title: J. Algorithms – volume: 7 start-page: 213 year: 1994 end-page: 220 ident: br000210 article-title: An publication-title: SIAM J. Discrete Math. – reference: A.M.S. Shrestha, S. Tayu, S. Ueno, Bandwidth of convex bipartite graphs and related graph classes, in: Proceedings of COCOON 2011, 2011, pp. 307–318. – volume: 34 start-page: 477 year: 1978 end-page: 495 ident: br000125 article-title: Complexity results for bandwidth minimization publication-title: SIAM J. Appl. Math. – volume: 41 start-page: 563 year: 2007 end-page: 587 ident: br000200 article-title: Efficient exact algorithms through enumerating maximal independent sets and other techniques publication-title: Theory Comput. Syst. – reference: V. Vassilevska, R. Williams, S.L.M. Woo, Confronting hardness using a hybrid approach, in: Proceedings of SODA 2006, 2006, pp. 1–10. – volume: 411 start-page: 3055 year: 2010 end-page: 3067 ident: br000045 article-title: Approximating the max-edge-coloring problem publication-title: Theoret. Comput. Sci. – volume: 113 start-page: 81 year: 2001 end-page: 94 ident: br000085 article-title: MAX SAT approximation beyond the limits of polynomial-time approximation publication-title: Ann. Pure Appl. Logic – reference: R.G. Downey, M.R. Fellows, C. McCartin, Parameterized approximation problems, in: Proceedings of IWPEC 2006, 2006, pp. 121–129. – volume: 3 start-page: 373 year: 1990 end-page: 375 ident: br000160 article-title: Computing the bandwidth of interval graphs publication-title: SIAM J. Discrete Math. – volume: 32 start-page: 41 year: 1999 end-page: 57 ident: br000165 article-title: Approximating the bandwidth for asteroidal triple-free graphs publication-title: J. Algorithms – volume: 13 start-page: 31 year: 1997 end-page: 36 ident: br000225 article-title: The Bandwidth problem in cographs publication-title: Tamsui Oxf. J. Math. Sci. – reference: U. Feige, Coping with the NP-hardness of the graph Bandwidth problem, in: Proceedings of SWAT 2000, 2000, pp. 10–19. – volume: 55 start-page: 190 year: 2009 end-page: 204 ident: br000115 article-title: Approximating the bandwidth of caterpillars publication-title: Algorithmica – reference: B. Monien, I.H. Sudborough, Bandwidth problems in graphs, in: Proceedings of Allerton Conference on Communication, Control, and Computing 1980, 1980, pp. 650–659. – volume: 109 start-page: 957 year: 2009 end-page: 961 ident: br000065 article-title: Exponential-time approximation of weighted set cover publication-title: Inform. Process. Lett. – volume: 41 start-page: 590 year: 2009 end-page: 615 ident: br000155 article-title: Volume distortion for subsets of euclidean spaces publication-title: Discrete Comput. Geom. – volume: 60 start-page: 510 year: 2000 end-page: 539 ident: br000105 article-title: Approximating the bandwidth via volume respecting embeddings publication-title: J. Comput. System Sci. – reference: Y. Chen, M. Grohe, M. Grüber, On parameterized approximability, in: Proceedings of IWPEC 2006, 2006, pp. 109–120. – volume: 7 start-page: 533 year: 2009 end-page: 544 ident: br000135 article-title: Bandwidth of bipartite permutation graphs in polynomial time publication-title: J. Discrete Algorithms – volume: 8 start-page: 8:1 year: 2012 end-page: 8:14 ident: br000075 article-title: Even faster exact bandwidth publication-title: ACM Trans. Algorithms – reference: J. Chen, X. Huang, I.A. Kanj, G. Xia, Linear FPT reductions and computational lower bounds, in: Proceedings of STOC 2004, 2004, pp. 212–221. – volume: 68 start-page: 313 year: 1998 end-page: 315 ident: br000170 article-title: Bandwidth of chain graphs publication-title: Inform. Process. Lett. – volume: 16 start-page: 392 year: 1996 end-page: 401 ident: br000150 article-title: A mildly exponential approximation algorithm for the permanent publication-title: Algorithmica – volume: 2 start-page: 387 year: 1981 end-page: 393 ident: br000010 article-title: The bandwidth of caterpillars with hairs of length 1 and 2 publication-title: SIAM J. Algebr. Discrete – volume: 109 start-page: 950 year: 2009 end-page: 954 ident: br000035 article-title: Approximation of min coloring by moderately exponential algorithms publication-title: Inform. Process. Lett. – volume: 7 start-page: 505 year: 1986 end-page: 512 ident: br000185 article-title: The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete publication-title: SIAM J. Algebr. Discrete – volume: 16 start-page: 263 year: 1976 end-page: 270 ident: br000195 article-title: The NP-completeness of the bandwidth minimization problem publication-title: Computing – volume: 2 start-page: 271 year: 1993 ident: 10.1016/j.tcs.2013.03.024_br000100 article-title: A mildly exponential time algorithm for approximating the number of solutions to a multidimensional knapsack problem publication-title: Combin. Probab. Comput. doi: 10.1017/S0963548300000675 – volume: 130 start-page: 173 issue: 2 year: 2003 ident: 10.1016/j.tcs.2013.03.024_br000140 article-title: Worst-case study of local search for Max-k-SAT publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(02)00404-3 – volume: 62 start-page: 367 issue: 2 year: 2001 ident: 10.1016/j.tcs.2013.03.024_br000145 article-title: On the complexity of k-SAT publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2000.1727 – ident: 10.1016/j.tcs.2013.03.024_br000055 doi: 10.1007/11847250_10 – volume: 109 start-page: 957 issue: 16 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000065 article-title: Exponential-time approximation of weighted set cover publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2009.05.003 – volume: 68 start-page: 313 year: 1998 ident: 10.1016/j.tcs.2013.03.024_br000170 article-title: Bandwidth of chain graphs publication-title: Inform. Process. Lett. doi: 10.1016/S0020-0190(98)00173-2 – volume: 60 start-page: 510 issue: 3 year: 2000 ident: 10.1016/j.tcs.2013.03.024_br000105 article-title: Approximating the bandwidth via volume respecting embeddings publication-title: J. Comput. System Sci. doi: 10.1006/jcss.1999.1682 – volume: 8 start-page: 8:1 issue: 1 year: 2012 ident: 10.1016/j.tcs.2013.03.024_br000075 article-title: Even faster exact bandwidth publication-title: ACM Trans. Algorithms doi: 10.1145/2071379.2071387 – volume: 16 start-page: 263 year: 1976 ident: 10.1016/j.tcs.2013.03.024_br000195 article-title: The NP-completeness of the bandwidth minimization problem publication-title: Computing doi: 10.1007/BF02280884 – volume: 410 start-page: 2184 issue: 21–23 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000040 article-title: Efficient approximation of min set cover by moderately exponential algorithms publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2009.02.007 – volume: 39 start-page: 546 issue: 2 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000015 article-title: Set partitioning via inclusion–exclusion publication-title: SIAM J. Comput. doi: 10.1137/070683933 – volume: 55 start-page: 190 issue: 1 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000115 article-title: Approximating the bandwidth of caterpillars publication-title: Algorithmica doi: 10.1007/s00453-007-9002-0 – ident: 10.1016/j.tcs.2013.03.024_br000220 doi: 10.1145/1109557.1109558 – volume: 235 start-page: 25 issue: 1 year: 2000 ident: 10.1016/j.tcs.2013.03.024_br000020 article-title: Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems publication-title: Theoret. Comput. Sci. doi: 10.1016/S0304-3975(99)00181-4 – volume: 3 start-page: 373 year: 1990 ident: 10.1016/j.tcs.2013.03.024_br000160 article-title: Computing the bandwidth of interval graphs publication-title: SIAM J. Discrete Math. doi: 10.1137/0403033 – ident: 10.1016/j.tcs.2013.03.024_br000215 doi: 10.1109/SFCS.1998.743431 – volume: 2 start-page: 387 year: 1981 ident: 10.1016/j.tcs.2013.03.024_br000010 article-title: The bandwidth of caterpillars with hairs of length 1 and 2 publication-title: SIAM J. Algebr. Discrete doi: 10.1137/0602041 – volume: 159 start-page: 1954 issue: 17 year: 2011 ident: 10.1016/j.tcs.2013.03.024_br000030 article-title: Approximation of max independent set, min vertex cover and related problems by moderately exponential algorithms publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2011.07.009 – volume: 95 start-page: 218 issue: 2 year: 1991 ident: 10.1016/j.tcs.2013.03.024_br000175 article-title: On finding the minimum bandwidth of interval graphs publication-title: Inf. Comput. doi: 10.1016/0890-5401(91)90045-4 – volume: 51 start-page: 60 issue: 1 year: 2008 ident: 10.1016/j.tcs.2013.03.024_br000180 article-title: Parameterized complexity and approximation algorithms publication-title: Comput. J. doi: 10.1093/comjnl/bxm048 – volume: 109 start-page: 950 issue: 16 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000035 article-title: Approximation of min coloring by moderately exponential algorithms publication-title: Inform. Process. Lett. doi: 10.1016/j.ipl.2009.05.002 – ident: 10.1016/j.tcs.2013.03.024_br000120 doi: 10.1007/978-3-642-11269-0_14 – volume: 32 start-page: 41 issue: 1 year: 1999 ident: 10.1016/j.tcs.2013.03.024_br000165 article-title: Approximating the bandwidth for asteroidal triple-free graphs publication-title: J. Algorithms doi: 10.1006/jagm.1998.0997 – ident: 10.1016/j.tcs.2013.03.024_br000005 doi: 10.1007/978-3-642-02927-1_8 – volume: 7 start-page: 505 issue: 4 year: 1986 ident: 10.1016/j.tcs.2013.03.024_br000185 article-title: The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete publication-title: SIAM J. Algebr. Discrete doi: 10.1137/0607057 – volume: 34 start-page: 477 issue: 3 year: 1978 ident: 10.1016/j.tcs.2013.03.024_br000125 article-title: Complexity results for bandwidth minimization publication-title: SIAM J. Appl. Math. doi: 10.1137/0134037 – volume: 5 start-page: 531 issue: 4 year: 1984 ident: 10.1016/j.tcs.2013.03.024_br000130 article-title: Improved dynamic programming algorithms for bandwidth minimization and the MinCut Linear Arrangement problem publication-title: J. Algorithms doi: 10.1016/0196-6774(84)90006-3 – volume: 7 start-page: 533 issue: 4 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000135 article-title: Bandwidth of bipartite permutation graphs in polynomial time publication-title: J. Discrete Algorithms doi: 10.1016/j.jda.2008.11.001 – ident: 10.1016/j.tcs.2013.03.024_br000060 doi: 10.1145/1007352.1007391 – volume: 41 start-page: 563 issue: 3 year: 2007 ident: 10.1016/j.tcs.2013.03.024_br000200 article-title: Efficient exact algorithms through enumerating maximal independent sets and other techniques publication-title: Theory Comput. Syst. doi: 10.1007/s00224-007-1334-2 – volume: 7 start-page: 213 year: 1994 ident: 10.1016/j.tcs.2013.03.024_br000210 article-title: An O(nlogn) algorithm for bandwidth of interval graphs publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480192232333 – volume: 13 start-page: 31 year: 1997 ident: 10.1016/j.tcs.2013.03.024_br000225 article-title: The Bandwidth problem in cographs publication-title: Tamsui Oxf. J. Math. Sci. – volume: 57 start-page: 398 issue: 2 year: 2010 ident: 10.1016/j.tcs.2013.03.024_br000050 article-title: Fixed-parameter approximation: conceptual framework and approximability results publication-title: Algorithmica doi: 10.1007/s00453-008-9223-x – ident: 10.1016/j.tcs.2013.03.024_br000025 doi: 10.1145/195058.195229 – ident: 10.1016/j.tcs.2013.03.024_br000110 doi: 10.1007/3-540-44985-X_2 – volume: 16 start-page: 392 issue: 4–5 year: 1996 ident: 10.1016/j.tcs.2013.03.024_br000150 article-title: A mildly exponential approximation algorithm for the permanent publication-title: Algorithmica doi: 10.1007/BF01940871 – volume: 411 start-page: 3055 issue: 34–36 year: 2010 ident: 10.1016/j.tcs.2013.03.024_br000045 article-title: Approximating the max-edge-coloring problem publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2010.04.031 – volume: 160 start-page: 494 issue: 4–5 year: 2012 ident: 10.1016/j.tcs.2013.03.024_br000070 article-title: Bandwidth and distortion revisited publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2011.10.032 – volume: 113 start-page: 81 issue: 1–3 year: 2001 ident: 10.1016/j.tcs.2013.03.024_br000085 article-title: MAX SAT approximation beyond the limits of polynomial-time approximation publication-title: Ann. Pure Appl. Logic doi: 10.1016/S0168-0072(01)00052-5 – ident: 10.1016/j.tcs.2013.03.024_br000205 doi: 10.1007/978-3-642-22685-4_28 – volume: 411 start-page: 3701 issue: 40–42 year: 2010 ident: 10.1016/j.tcs.2013.03.024_br000080 article-title: Exact and approximate bandwidth publication-title: Theoret. Comput. Sci. doi: 10.1016/j.tcs.2010.06.018 – ident: 10.1016/j.tcs.2013.03.024_br000095 doi: 10.1007/3-540-44666-4_26 – volume: 41 start-page: 590 issue: 4 year: 2009 ident: 10.1016/j.tcs.2013.03.024_br000155 article-title: Volume distortion for subsets of euclidean spaces publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-009-9135-9 – ident: 10.1016/j.tcs.2013.03.024_br000090 doi: 10.1007/11847250_11 – ident: 10.1016/j.tcs.2013.03.024_br000190 |
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| SubjectTerms | Approximation algorithm Bucket decomposition Exponential time algorithm Graph bandwidth |
| Title | An exponential time 2-approximation algorithm for bandwidth |
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