Skip to main content
Top

2018 | OriginalPaper | Chapter

34. Linear Layout Problems

Authors : Eduardo G. Pardo, Rafael Martí, Abraham Duarte

Published in: Handbook of Heuristics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The term layout problem comes from the context of Very Large-Scale Integration (VLSI) circuit design. Graph layouts are optimization problems where the main objective is to project an original graph into a predefined host graph, usually a horizontal line. In this paper, some of the most relevant linear layout problems are reviewed, where the purpose is to minimize the objective function: the Cutwidth, the Minimum Linear Arrangement, the Vertex Separation, the SumCut, and the Bandwidth. Each problem is presented with its formal definition and it is illustrated with a detailed example. Additionally, the most relevant heuristic methods in the associated literature are reviewed together with the instances used in their evaluation. Since linear layouts represent a challenge for optimization methods in general and, for heuristics in particular, this review pays special attention to the strategies and methodologies which provide high-quality solutions.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Adolphson DL (1977) Single machine job sequencing with precedence constraints. SIAM J Comput 6:50–54 Adolphson DL (1977) Single machine job sequencing with precedence constraints. SIAM J Comput 6:50–54
2.
go back to reference Adolphson DL, Hu TC (1973) Optimal linear ordering. SIAM J Appl Math 25(3):403–423 Adolphson DL, Hu TC (1973) Optimal linear ordering. SIAM J Appl Math 25(3):403–423
3.
go back to reference Álvarez C, Cases R, Díaz J, Petit J, Serna M (2000) Approximation and randomized algorithms in communication networks. In: Routing trees problems on random graphs. ICALP workshops 2000. Carleton Scientific, p 99111 Álvarez C, Cases R, Díaz J, Petit J, Serna M (2000) Approximation and randomized algorithms in communication networks. In: Routing trees problems on random graphs. ICALP workshops 2000. Carleton Scientific, p 99111
4.
go back to reference Andrade DV, Resende MGC (2007) GRASP with evolutionary path-relinking. In: Seventh metaheuristics international conference (MIC), Montreal Andrade DV, Resende MGC (2007) GRASP with evolutionary path-relinking. In: Seventh metaheuristics international conference (MIC), Montreal
5.
go back to reference Andrade DV, Resende MGC (2007) GRASP with path-relinking for network migration scheduling. In: Proceedings of international network optimization conference (INOC), Spa Andrade DV, Resende MGC (2007) GRASP with path-relinking for network migration scheduling. In: Proceedings of international network optimization conference (INOC), Spa
6.
go back to reference Bezrukov SL, Chavez JD, Harper LH, öttger MR, Schroeder UP (2000) The congestion of n-cube layout on a rectangular grid. Discret Math 213:13–19 Bezrukov SL, Chavez JD, Harper LH, öttger MR, Schroeder UP (2000) The congestion of n-cube layout on a rectangular grid. Discret Math 213:13–19
7.
go back to reference Blin G, Fertin G, Hermelin D, Vialette S (2008) Fixed-parameter algorithms for protein similarity search under mRNA structure constraints. J Discret Algorithms 6:618–626 Blin G, Fertin G, Hermelin D, Vialette S (2008) Fixed-parameter algorithms for protein similarity search under mRNA structure constraints. J Discret Algorithms 6:618–626
8.
go back to reference Bodlaender HL, Gilbert JR, Hafsteinsson H, Kloks T (1995) Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. J Algorithms 18(2):238–255 Bodlaender HL, Gilbert JR, Hafsteinsson H, Kloks T (1995) Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. J Algorithms 18(2):238–255
9.
go back to reference Bodlaender HL, Gustedt J, Telle JA (1998) Linear-time register allocation for a fixed number of registers. In: Proceedings of the ninth annual ACM-SIAM symposium on discrete algorithms (SODA’98). Society for Industrial and Applied Mathematics, Philadelphia, pp 574–583 Bodlaender HL, Gustedt J, Telle JA (1998) Linear-time register allocation for a fixed number of registers. In: Proceedings of the ninth annual ACM-SIAM symposium on discrete algorithms (SODA’98). Society for Industrial and Applied Mathematics, Philadelphia, pp 574–583
10.
go back to reference Bodlaender HL, Kloks T, Kratsch D (1993) Treewidth and pathwidth of permutation graphs. In: Lingas A, Karlsson R, Carlsson S (eds) Automata, languages and programming. Lecture notes in computer science, vol 700. Springer, Berlin/Heidelberg, pp 114–125 Bodlaender HL, Kloks T, Kratsch D (1993) Treewidth and pathwidth of permutation graphs. In: Lingas A, Karlsson R, Carlsson S (eds) Automata, languages and programming. Lecture notes in computer science, vol 700. Springer, Berlin/Heidelberg, pp 114–125
11.
go back to reference Bodlaender HL, Kloks T, Kratsch D (1995) Treewidth and pathwidth of permutation graphs. SIAM J Discret Math 8(4):606–616 Bodlaender HL, Kloks T, Kratsch D (1995) Treewidth and pathwidth of permutation graphs. SIAM J Discret Math 8(4):606–616
12.
go back to reference Bodlaender HL, Möhring RH (1990) The pathwidth and treewidth of cographs. SIAM J Discret Math 6(6):181–188 Bodlaender HL, Möhring RH (1990) The pathwidth and treewidth of cographs. SIAM J Discret Math 6(6):181–188
13.
go back to reference Bollobás B, Leader I (1991) Edge-isoperimetric inequalities in the grid. Combinatorica 11(4):299–314 Bollobás B, Leader I (1991) Edge-isoperimetric inequalities in the grid. Combinatorica 11(4):299–314
14.
go back to reference Botafogo RA (1993) Cluster analysis for hypertext systems. In: 16th annual international ACM-SIGIR conference on research and development in information retrieval, Pittsburgh, PA, USA, pp 116–125 Botafogo RA (1993) Cluster analysis for hypertext systems. In: 16th annual international ACM-SIGIR conference on research and development in information retrieval, Pittsburgh, PA, USA, pp 116–125
15.
go back to reference Campos V, Piñana E, Martí R (2011) Adaptive memory programming for matrix bandwidth minimization. Ann Oper Res 183(1):7–23 Campos V, Piñana E, Martí R (2011) Adaptive memory programming for matrix bandwidth minimization. Ann Oper Res 183(1):7–23
16.
go back to reference Chinn PZ, Chvátalová J, Dewdney AK, Gibbs NE (1982) The bandwidth problem for graphs and matricesa survey. J Graph Theory 6(3):223–254 Chinn PZ, Chvátalová J, Dewdney AK, Gibbs NE (1982) The bandwidth problem for graphs and matricesa survey. J Graph Theory 6(3):223–254
17.
go back to reference Chung MJ, Makedon F, Sudborough IH, Turner J (1982) Polynomial time algorithms for the min cut problem on degree restricted trees. In: Proceedings of the 23rd annual symposium on foundations of computer science (SFCS’82). IEEE Computer Society, Washington, DC, pp 262–271 Chung MJ, Makedon F, Sudborough IH, Turner J (1982) Polynomial time algorithms for the min cut problem on degree restricted trees. In: Proceedings of the 23rd annual symposium on foundations of computer science (SFCS’82). IEEE Computer Society, Washington, DC, pp 262–271
18.
go back to reference Cohoon J, Sahni S (1983) Exact algorithms for special cases of the board permutation problem. In: Proceedings of the allerton conference on communication, control and computing, Monticello, pp 246–255 Cohoon J, Sahni S (1983) Exact algorithms for special cases of the board permutation problem. In: Proceedings of the allerton conference on communication, control and computing, Monticello, pp 246–255
19.
go back to reference Cohoon J, Sahni S (1987) Heuristics for backplane ordering. J VLSI Comput Syst 2:37–61 Cohoon J, Sahni S (1987) Heuristics for backplane ordering. J VLSI Comput Syst 2:37–61
21.
go back to reference Cuthill E, McKee J (1969) Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th national conference. ACM, New York, pp 157–172 Cuthill E, McKee J (1969) Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th national conference. ACM, New York, pp 157–172
22.
go back to reference Corso GMD, Manzini G (1999) Finding exact solutions to the bandwidth minimization problem. Computing 62(3):189–203 Corso GMD, Manzini G (1999) Finding exact solutions to the bandwidth minimization problem. Computing 62(3):189–203
23.
go back to reference Díaz J, Gibbons A, Pantziou GE, Serna MJ, Spirakis PG, Torán J (1997) Parallel algorithms for the minimum cut and the minimum length tree layout problems. Theor Comput Sci 181:267–287 Díaz J, Gibbons A, Pantziou GE, Serna MJ, Spirakis PG, Torán J (1997) Parallel algorithms for the minimum cut and the minimum length tree layout problems. Theor Comput Sci 181:267–287
24.
go back to reference Díaz J, Gibbons A, Paterson M, Torán J (1991) The minsumcut problem. In: Dehne F, Sack J-R, Santoro N (eds) WADS. Lecture notes in computer science, vol 519. Springer, Berlin/Heidelberg, pp 65–89 Díaz J, Gibbons A, Paterson M, Torán J (1991) The minsumcut problem. In: Dehne F, Sack J-R, Santoro N (eds) WADS. Lecture notes in computer science, vol 519. Springer, Berlin/Heidelberg, pp 65–89
25.
go back to reference Díaz J, Penrose MD, Petit J, Serna MJ (2000) Convergence theorems for some layout measures on random lattice and random geometric graphs. Comb Probab Comput 9: 489–511 Díaz J, Penrose MD, Petit J, Serna MJ (2000) Convergence theorems for some layout measures on random lattice and random geometric graphs. Comb Probab Comput 9: 489–511
26.
go back to reference Díaz J, Petit J, Serna MJ (2002) A survey of graph layout problems. ACM Comput Surv (CSUR) 34(3):313–356 Díaz J, Petit J, Serna MJ (2002) A survey of graph layout problems. ACM Comput Surv (CSUR) 34(3):313–356
27.
go back to reference Díaz J, Petit J, Serna MJ, Trevisan L (1998) Approximating layout problems on random sparse graphs. Technical report LSI-98-44-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya (Presented in the fifth Czech-Slovak international symposium on combinatorics, graph theory, algorithms and applications) Díaz J, Petit J, Serna MJ, Trevisan L (1998) Approximating layout problems on random sparse graphs. Technical report LSI-98-44-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya (Presented in the fifth Czech-Slovak international symposium on combinatorics, graph theory, algorithms and applications)
28.
go back to reference Ding G, Oporowski B (1995) Some results on tree decomposition of graphs. J Graph Theory 20(4):481–499 Ding G, Oporowski B (1995) Some results on tree decomposition of graphs. J Graph Theory 20(4):481–499
29.
go back to reference Dorigo M (1992) Optimization, learning and natural algorithms. PhD thesis, Politecnico di Milano, Italia Dorigo M (1992) Optimization, learning and natural algorithms. PhD thesis, Politecnico di Milano, Italia
30.
go back to reference Duarte A, Escudero LF, Martí R, Mladenović N, Pantrigo JJ, Sánchez-Oro J (2012) Variable neighborhood search for the vertex separation problem. Comput Oper Res 39(12): 3247–3255 Duarte A, Escudero LF, Martí R, Mladenović N, Pantrigo JJ, Sánchez-Oro J (2012) Variable neighborhood search for the vertex separation problem. Comput Oper Res 39(12): 3247–3255
31.
go back to reference Duarte A, Pantrigo JJ, Pardo EG, Mladenović N (2015) Multi-objective variable neighborhood search: an application to combinatorial optimization problems. J Glob Optim 63(3):515–536 Duarte A, Pantrigo JJ, Pardo EG, Mladenović N (2015) Multi-objective variable neighborhood search: an application to combinatorial optimization problems. J Glob Optim 63(3):515–536
32.
go back to reference Duarte A, Pantrigo JJ, Pardo EG, Sánchez-Oro J (2016) Parallel variable neighbourhood search strategies for the cutwidth minimization problem. IMA J Manag Math 27(1):55–73 Duarte A, Pantrigo JJ, Pardo EG, Sánchez-Oro J (2016) Parallel variable neighbourhood search strategies for the cutwidth minimization problem. IMA J Manag Math 27(1):55–73
33.
go back to reference Dueck G, Jeffs J (1995) A heuristic bandwidth reduction algorithm. J comb math comput 18:97–108 Dueck G, Jeffs J (1995) A heuristic bandwidth reduction algorithm. J comb math comput 18:97–108
34.
go back to reference Duff IS, Grimes RG, Lewis JG (1989) Sparse matrix test problems. ACM Trans Math Softw 15(1):1–14 Duff IS, Grimes RG, Lewis JG (1989) Sparse matrix test problems. ACM Trans Math Softw 15(1):1–14
35.
go back to reference Duff IS, Grimes RG, Lewis JG (1992) User’s guide for the harwell-boeing sparse matrix collection (release I), Rutherford Appleton Laboratory, Chilton Duff IS, Grimes RG, Lewis JG (1992) User’s guide for the harwell-boeing sparse matrix collection (release I), Rutherford Appleton Laboratory, Chilton
36.
go back to reference Dujmovic V, Fellows MR, Kitching M, Liotta G, McCartin C, Nishimura N, Ragde P, Rosamond F, Whitesides S, Wood DR (2008) On the parameterized complexity of layered graph drawing. Algorithmica 52(2):267–292 Dujmovic V, Fellows MR, Kitching M, Liotta G, McCartin C, Nishimura N, Ragde P, Rosamond F, Whitesides S, Wood DR (2008) On the parameterized complexity of layered graph drawing. Algorithmica 52(2):267–292
37.
go back to reference Ellis JA, Sudborough IH, Turner JS (1994) The vertex separation and search number of a graph. Inf Comput 113(1):50–79 Ellis JA, Sudborough IH, Turner JS (1994) The vertex separation and search number of a graph. Inf Comput 113(1):50–79
38.
go back to reference Ellis JA, Markov M (2004) Computing the vertex separation of unicyclic graphs. Inf Comput 192(2):123–161 Ellis JA, Markov M (2004) Computing the vertex separation of unicyclic graphs. Inf Comput 192(2):123–161
39.
go back to reference Fellows MR, Langston MA (1994) On search, decision, and the efficiency of polynomial-time algorithms. J Comput Syst Sci 49(3):769–779 Fellows MR, Langston MA (1994) On search, decision, and the efficiency of polynomial-time algorithms. J Comput Syst Sci 49(3):769–779
40.
go back to reference Feo TA, Resende MGC (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8(2):67–71 Feo TA, Resende MGC (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8(2):67–71
41.
go back to reference Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Glob Optim 6(2):109–133 Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Glob Optim 6(2):109–133
42.
go back to reference Garey MR, Johnson DS (1979) Computers and intractability: a Guide to the theory of np-completeness. W.H. Freeman, San Francisco Garey MR, Johnson DS (1979) Computers and intractability: a Guide to the theory of np-completeness. W.H. Freeman, San Francisco
43.
go back to reference Gavril F (1977) Some NP-complete problems on graphs. In: Proceedings of the eleventh conference on information sciences and systems, Baltimore, pp 91–95 Gavril F (1977) Some NP-complete problems on graphs. In: Proceedings of the eleventh conference on information sciences and systems, Baltimore, pp 91–95
44.
go back to reference Gibbs NE, Poole WG Jr, Stockmeyer PK (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 13(2):236–250 Gibbs NE, Poole WG Jr, Stockmeyer PK (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 13(2):236–250
45.
go back to reference Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166 Glover F (1977) Heuristics for integer programming using surrogate constraints. Decis Sci 8(1):156–166
46.
go back to reference Glover F (1997) Tabu search and adaptive memory programming—advances, applications and challenges. Springer, Boston, pp 1–75 Glover F (1997) Tabu search and adaptive memory programming—advances, applications and challenges. Springer, Boston, pp 1–75
47.
go back to reference Glover F, Laguna M (1997) Tabu search. Kluwer Academic Publishers, Norwell Glover F, Laguna M (1997) Tabu search. Kluwer Academic Publishers, Norwell
48.
go back to reference Golberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addion wesley 1989:102 Golberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addion wesley 1989:102
49.
go back to reference Golovach P (2009) The total vertex separation number of a graph. Discret Math Appl 6(7):631–636 Golovach P (2009) The total vertex separation number of a graph. Discret Math Appl 6(7):631–636
50.
go back to reference Harper LH (1964) Optimal assignments of numbers to vertices. J Soc Ind Appl Math 12(1):131–135 Harper LH (1964) Optimal assignments of numbers to vertices. J Soc Ind Appl Math 12(1):131–135
51.
go back to reference Harper LH (1966) Optimal numberings and isoperimetric problems on graphs. J Comb Theory 1:385–393 Harper LH (1966) Optimal numberings and isoperimetric problems on graphs. J Comb Theory 1:385–393
52.
go back to reference Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann Arbor Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann Arbor
53.
go back to reference Hu TC (1974) Optimum communication spanning trees. SIAM J Comput 3(3):188–195 Hu TC (1974) Optimum communication spanning trees. SIAM J Comput 3(3):188–195
54.
go back to reference Johnson DS, Lenstra JK, Kan AHGR (1978) The complexity of the network design problem. Networks 8(4):279–285 Johnson DS, Lenstra JK, Kan AHGR (1978) The complexity of the network design problem. Networks 8(4):279–285
55.
go back to reference Juvan M, Marincek J, Mohar B (1995) Embedding a graph into the torus in linear time. Springer, Berlin/Heidelberg, pp 360–363 Juvan M, Marincek J, Mohar B (1995) Embedding a graph into the torus in linear time. Springer, Berlin/Heidelberg, pp 360–363
56.
go back to reference Juvan M, Mohar B 1992 Optimal linear labelings and eigenvalues of graphs. Discret Appl Math 36:153–168 Juvan M, Mohar B 1992 Optimal linear labelings and eigenvalues of graphs. Discret Appl Math 36:153–168
57.
go back to reference Karger DR (1999) A randomized fully polynomial time approximation scheme for the all-terminal network reliability problem. SIAM J Comput 29(2):492–514 Karger DR (1999) A randomized fully polynomial time approximation scheme for the all-terminal network reliability problem. SIAM J Comput 29(2):492–514
58.
go back to reference Karp RM (1993) Mapping the genome: some combinatorial problems arising in molecular biology. In: Proceedings of the twenty-fifth annual ACM symposium on theory of computing. ACM, New York, pp 278–285 Karp RM (1993) Mapping the genome: some combinatorial problems arising in molecular biology. In: Proceedings of the twenty-fifth annual ACM symposium on theory of computing. ACM, New York, pp 278–285
59.
go back to reference Kendall D (1969) Incidence matrices, interval graphs and seriation in archeology. Pac J math 28(3):565–570 Kendall D (1969) Incidence matrices, interval graphs and seriation in archeology. Pac J math 28(3):565–570
60.
go back to reference Kennedy J Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, Yokohama, vol 4, pp 1942–1948 Kennedy J Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, Yokohama, vol 4, pp 1942–1948
61.
go back to reference Kinnersley NG (1992) The vertex separation number of a graph equals its path-width. Inf Process Lett 42(6):345–350 Kinnersley NG (1992) The vertex separation number of a graph equals its path-width. Inf Process Lett 42(6):345–350
62.
go back to reference Kirkpatrick S, Gelatt CD, Vecchi MP 1983 Optimization by simulated annealing. Science 220(4598):671–680 Kirkpatrick S, Gelatt CD, Vecchi MP 1983 Optimization by simulated annealing. Science 220(4598):671–680
63.
go back to reference Kirousis LM, Papadimitriou CH (1985) Interval graphs and searching. Discret Math 55(2):181–184 Kirousis LM, Papadimitriou CH (1985) Interval graphs and searching. Discret Math 55(2):181–184
64.
go back to reference Kirousis LM, Papadimitriou CH (1986) Searching and pebbling. Theor Comput Sci 47(0):205–218 Kirousis LM, Papadimitriou CH (1986) Searching and pebbling. Theor Comput Sci 47(0):205–218
65.
go back to reference Klugerman M, Russell A, Sundaram R (1998) On embedding complete graphs into hypercubes. Discret Math 186(13):289–293 Klugerman M, Russell A, Sundaram R (1998) On embedding complete graphs into hypercubes. Discret Math 186(13):289–293
66.
go back to reference Laguna M, Martí R (2012) Scatter search: methodology and implementations in C, vol 24. Springer Science & Business Media, New York Laguna M, Martí R (2012) Scatter search: methodology and implementations in C, vol 24. Springer Science & Business Media, New York
67.
go back to reference Leiserson CE (1980) Area-efficient graph layouts (for vlsi). In: IEEE symposium on foundations of computer science, Syracuse, pp 270–281 Leiserson CE (1980) Area-efficient graph layouts (for vlsi). In: IEEE symposium on foundations of computer science, Syracuse, pp 270–281
68.
go back to reference Lewis JG (1982) The gibbs-poole-stockmeyer and gibbs-king algorithms for reordering sparse matrices. ACM Trans Math Softw (TOMS) 8(2):190–194 Lewis JG (1982) The gibbs-poole-stockmeyer and gibbs-king algorithms for reordering sparse matrices. ACM Trans Math Softw (TOMS) 8(2):190–194
69.
go back to reference Lewis RR (1994) Simulated annealing for profile and fill reduction of sparse matrices. Int J Numer Methods Eng 37(6):905–925 Lewis RR (1994) Simulated annealing for profile and fill reduction of sparse matrices. Int J Numer Methods Eng 37(6):905–925
70.
go back to reference Lim A, Lin J, Rodrigues B, Xiao F (2006) Ant colony optimization with hill climbing for the bandwidth minimization problem. Appl Soft Comput 6(2):180–188 Lim A, Lin J, Rodrigues B, Xiao F (2006) Ant colony optimization with hill climbing for the bandwidth minimization problem. Appl Soft Comput 6(2):180–188
71.
go back to reference Lim A, Lin J, Xiao F (2007) Particle swarm optimization and hill climbing for the bandwidth minimization problem. Appl Intell 26(3):175–182 Lim A, Lin J, Xiao F (2007) Particle swarm optimization and hill climbing for the bandwidth minimization problem. Appl Intell 26(3):175–182
72.
go back to reference Lim A, Rodrigues B, Xiao F (2006) Heuristics for matrix bandwidth reduction. Eur J Oper Res 174(1):69–91 Lim A, Rodrigues B, Xiao F (2006) Heuristics for matrix bandwidth reduction. Eur J Oper Res 174(1):69–91
73.
go back to reference Lin YX (1994) Two-dimensional bandwidth problem. In: Combinatorics, graph theory, algorithms and applications 1993, Beijing, pp 223–232 Lin YX (1994) Two-dimensional bandwidth problem. In: Combinatorics, graph theory, algorithms and applications 1993, Beijing, pp 223–232
74.
go back to reference Lipton RJ, Tarjan RE (1979) A separator theorem for planar graphs. SIAM J Appl Math 36(2):177–189 Lipton RJ, Tarjan RE (1979) A separator theorem for planar graphs. SIAM J Appl Math 36(2):177–189
75.
go back to reference Livingston M, Stout QF (1988) Embeddings in hypercubes. Math Comput Model 11(0): 222–227 Livingston M, Stout QF (1988) Embeddings in hypercubes. Math Comput Model 11(0): 222–227
76.
go back to reference López-Locés MC, Castillo-García N, Huacuja HJF, Bouvry P, Pecero JE, Rangel RAP, Barbosa JJG, Valdez F (2014) A new integer linear programming model for the cutwidth minimization problem of a connected undirected graph. In: Recent advances on hybrid approaches for designing intelligent systems. Springer, Cham, pp 509–517 López-Locés MC, Castillo-García N, Huacuja HJF, Bouvry P, Pecero JE, Rangel RAP, Barbosa JJG, Valdez F (2014) A new integer linear programming model for the cutwidth minimization problem of a connected undirected graph. In: Recent advances on hybrid approaches for designing intelligent systems. Springer, Cham, pp 509–517
77.
go back to reference Lozano M, Duarte A, Gortázar F, Martí R (2013) A hybrid metaheuristic for the cyclic antibandwidth problem. Knowl-Based Syst 54:103–113 Lozano M, Duarte A, Gortázar F, Martí R (2013) A hybrid metaheuristic for the cyclic antibandwidth problem. Knowl-Based Syst 54:103–113
78.
go back to reference Luttamaguzi J, Pelsmajer M, Shen Z, Yang B (2005) Integer programming solutions for several optimization problems in graph theory. Technical report, Center for Discrete Mathematics and Theoretical Computer Science, DIMACS Luttamaguzi J, Pelsmajer M, Shen Z, Yang B (2005) Integer programming solutions for several optimization problems in graph theory. Technical report, Center for Discrete Mathematics and Theoretical Computer Science, DIMACS
79.
80.
go back to reference Martí R, Campos V, Piñana E (2008) A branch and bound algorithm for the matrix bandwidth minimization. Eur J Oper Res 186(2):513–528MathSciNetCrossRef Martí R, Campos V, Piñana E (2008) A branch and bound algorithm for the matrix bandwidth minimization. Eur J Oper Res 186(2):513–528MathSciNetCrossRef
81.
go back to reference Martí R, Laguna M, Glover F, Campos V (2001) Reducing the bandwidth of a sparse matrix with tabu search. Eur J Oper Res 135(2):450–459MathSciNetCrossRef Martí R, Laguna M, Glover F, Campos V (2001) Reducing the bandwidth of a sparse matrix with tabu search. Eur J Oper Res 135(2):450–459MathSciNetCrossRef
82.
go back to reference Martí R, Pantrigo JJ, Duarte A, Campos V, Glover F (2011) Scatter search and path relinking: a tutorial on the linear arrangement problem. Int J Swarm Intell Res (IJSIR) 2(2): 1–21CrossRef Martí R, Pantrigo JJ, Duarte A, Campos V, Glover F (2011) Scatter search and path relinking: a tutorial on the linear arrangement problem. Int J Swarm Intell Res (IJSIR) 2(2): 1–21CrossRef
83.
go back to reference Martí R, Pantrigo JJ, Duarte A, Pardo EG (2013) Branch and bound for the cutwidth minimization problem. Comput Oper Res 40(1):137–149MathSciNetCrossRef Martí R, Pantrigo JJ, Duarte A, Pardo EG (2013) Branch and bound for the cutwidth minimization problem. Comput Oper Res 40(1):137–149MathSciNetCrossRef
84.
go back to reference Mcallister AJ (1999) A new heuristic algorithm for the linear arrangement problem. Technical report, University of New Brunswick Mcallister AJ (1999) A new heuristic algorithm for the linear arrangement problem. Technical report, University of New Brunswick
85.
go back to reference Miller Z, Sudborough IH 1991 A polynomial algorithm for recognizing bounded cutwidth in hypergraphs. Theory Comput Syst 24:11–40MathSciNetMATH Miller Z, Sudborough IH 1991 A polynomial algorithm for recognizing bounded cutwidth in hypergraphs. Theory Comput Syst 24:11–40MathSciNetMATH
86.
88.
go back to reference Mladenović N, Urošević D, Pérez-Brito D (2014) Variable neighborhood search for minimum linear arrangement problem. Yugosl J Oper Res 24(2):2334–6043. ISSN:0354-0243 Mladenović N, Urošević D, Pérez-Brito D (2014) Variable neighborhood search for minimum linear arrangement problem. Yugosl J Oper Res 24(2):2334–6043. ISSN:0354-0243
89.
go back to reference Mladenović N, Urošević D, Pérez-Brito D, García-González CG (2010) Variable neighbourhood search for bandwidth reduction. Eur J Oper Res 200(1):14–27MathSciNetCrossRef Mladenović N, Urošević D, Pérez-Brito D, García-González CG (2010) Variable neighbourhood search for bandwidth reduction. Eur J Oper Res 200(1):14–27MathSciNetCrossRef
90.
go back to reference Mutzel P (1995) A polyhedral approach to planar augmentation and related problems. In: Proceedings of the third annual European symposium on algorithms, ESA’95. Springer, London, pp 494–507 Mutzel P (1995) A polyhedral approach to planar augmentation and related problems. In: Proceedings of the third annual European symposium on algorithms, ESA’95. Springer, London, pp 494–507
91.
go back to reference Palubeckis G, Rubliauskas D (2012) A branch-and-bound algorithm for the minimum cut linear arrangement problem. J comb optim 24(4):540–563MathSciNetCrossRef Palubeckis G, Rubliauskas D (2012) A branch-and-bound algorithm for the minimum cut linear arrangement problem. J comb optim 24(4):540–563MathSciNetCrossRef
92.
go back to reference Pantrigo JJ, Martí R, Duarte A, Pardo EG (2012) Scatter search for the cutwidth minimization problem. Ann Oper Res 199:285–304MathSciNetCrossRef Pantrigo JJ, Martí R, Duarte A, Pardo EG (2012) Scatter search for the cutwidth minimization problem. Ann Oper Res 199:285–304MathSciNetCrossRef
93.
94.
go back to reference Pardo EG, Mladenović N, Pantrigo JJ, Duarte A (2012) A variable neighbourhood search approach to the cutwidth minimization problem. Electron Notes Discret Math 39(0):67–74MathSciNetCrossRef Pardo EG, Mladenović N, Pantrigo JJ, Duarte A (2012) A variable neighbourhood search approach to the cutwidth minimization problem. Electron Notes Discret Math 39(0):67–74MathSciNetCrossRef
95.
go back to reference Pardo EG, Mladenović N, Pantrigo JJ, Duarte A (2013) Variable formulation search for the cutwidth minimization problem. Appl Soft Comput 13(5):2242–2252CrossRef Pardo EG, Mladenović N, Pantrigo JJ, Duarte A (2013) Variable formulation search for the cutwidth minimization problem. Appl Soft Comput 13(5):2242–2252CrossRef
97.
go back to reference Peng SL, Ho CW, Hsu TS, Ko MT, Tang C (1998) A linear-time algorithm for constructing an optimal node-search strategy of a tree. In: Hsu W-L, Kao M-Y (eds) Computing and combinatorics. Lecture notes in computer science, vol 1449. Springer, Berlin/Heidelberg, pp 279–289CrossRef Peng SL, Ho CW, Hsu TS, Ko MT, Tang C (1998) A linear-time algorithm for constructing an optimal node-search strategy of a tree. In: Hsu W-L, Kao M-Y (eds) Computing and combinatorics. Lecture notes in computer science, vol 1449. Springer, Berlin/Heidelberg, pp 279–289CrossRef
98.
go back to reference Petit J (2003) Combining spectral sequencing and parallel simulated annealing for the minla problem. Parallel Process Lett 13(1):77–91MathSciNetCrossRef Petit J (2003) Combining spectral sequencing and parallel simulated annealing for the minla problem. Parallel Process Lett 13(1):77–91MathSciNetCrossRef
99.
100.
go back to reference Piñana E, Plana I, Campos V, Martí R (2004) GRASP and path relinking for the matrix bandwidth minimization. Eur J Oper Res 153(1):200–210MathSciNetCrossRef Piñana E, Plana I, Campos V, Martí R (2004) GRASP and path relinking for the matrix bandwidth minimization. Eur J Oper Res 153(1):200–210MathSciNetCrossRef
101.
go back to reference Pop PC, Matei O (2011) An improved heuristic for the bandwidth minimization based on genetic programming. In: Hybrid artificial intelligent systems. Springer, Berlin, pp 67–74CrossRef Pop PC, Matei O (2011) An improved heuristic for the bandwidth minimization based on genetic programming. In: Hybrid artificial intelligent systems. Springer, Berlin, pp 67–74CrossRef
102.
go back to reference Raspaud A, Schröder H, Sỳkora O, Torok L, Vrto I (2009) Antibandwidth and cyclic antibandwidth of meshes and hypercubes. Discret Math 309(11):3541–3552 Raspaud A, Schröder H, Sỳkora O, Torok L, Vrto I (2009) Antibandwidth and cyclic antibandwidth of meshes and hypercubes. Discret Math 309(11):3541–3552
103.
go back to reference Ravi R, Agrawal A, Klein P (1991) Ordering problems approximated: single-processor scheduling and interval graph completion. In: Proceedings of the ICALP. Springer, Berlin, pp 751–762 Ravi R, Agrawal A, Klein P (1991) Ordering problems approximated: single-processor scheduling and interval graph completion. In: Proceedings of the ICALP. Springer, Berlin, pp 751–762
104.
go back to reference Resende MGC, Andrade DV (2009) Method and system for network migration scheduling. United States Patent Application Publication. US2009/0168665 Resende MGC, Andrade DV (2009) Method and system for network migration scheduling. United States Patent Application Publication. US2009/0168665
105.
go back to reference Rodriguez-Tello E, Hao J-K, Torres-Jimenez J (2008) An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem. Comput Oper Res 35(10):3331–3346CrossRef Rodriguez-Tello E, Hao J-K, Torres-Jimenez J (2008) An effective two-stage simulated annealing algorithm for the minimum linear arrangement problem. Comput Oper Res 35(10):3331–3346CrossRef
106.
go back to reference Rodriguez-Tello E, Hao J-K, Torres-Jimenez J (2008) An improved simulated annealing algorithm for bandwidth minimization. Eur J Oper Res 185(3):1319–1335CrossRef Rodriguez-Tello E, Hao J-K, Torres-Jimenez J (2008) An improved simulated annealing algorithm for bandwidth minimization. Eur J Oper Res 185(3):1319–1335CrossRef
107.
go back to reference Rolim J, Sýkora O, Vrt’o I (1995) Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes. In: Graph-theoretic concepts in computer science. Lecture notes in computer science, vol 1017. Springer, Berlin/Heidelberg, pp 252–264 Rolim J, Sýkora O, Vrt’o I (1995) Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes. In: Graph-theoretic concepts in computer science. Lecture notes in computer science, vol 1017. Springer, Berlin/Heidelberg, pp 252–264
108.
go back to reference Saad Y (2003) Iterative methods for sparse linear systems. SIAM, PhiladelphiaCrossRef Saad Y (2003) Iterative methods for sparse linear systems. SIAM, PhiladelphiaCrossRef
109.
go back to reference Sánchez-Oro J, Duarte A (2012) An experimental comparison of variable neighborhood search variants for the minimization of the vertex-cut in layout problems. Electron Notes Discret Math 39:59–66MathSciNetCrossRef Sánchez-Oro J, Duarte A (2012) An experimental comparison of variable neighborhood search variants for the minimization of the vertex-cut in layout problems. Electron Notes Discret Math 39:59–66MathSciNetCrossRef
110.
go back to reference Sánchez-Oro J, Duarte A (2012) Grasp with path relinking for the sumcut problem. Int J Comb Optim Probl Inf 3:3–11 Sánchez-Oro J, Duarte A (2012) Grasp with path relinking for the sumcut problem. Int J Comb Optim Probl Inf 3:3–11
111.
go back to reference Sánchez-Oro J, Duarte A Grasp for the sumcut problem. In: XVII international congress on computer science research, Morelia (México), 26–28/10/2011 Sánchez-Oro J, Duarte A Grasp for the sumcut problem. In: XVII international congress on computer science research, Morelia (México), 26–28/10/2011
112.
go back to reference Sánchez-Oro J, Laguna M, Duarte A, Martí R (2015) Scatter search for the profile minimization problem. Networks 65(1):10–21MathSciNetCrossRef Sánchez-Oro J, Laguna M, Duarte A, Martí R (2015) Scatter search for the profile minimization problem. Networks 65(1):10–21MathSciNetCrossRef
113.
go back to reference Sánchez-Oro J, Pantrigo JJ, Duarte A (2014) Combining intensification and diversification strategies in VNS. An application to the vertex separation problem. Comput Oper Res 52(Part B):209–219 Sánchez-Oro J, Pantrigo JJ, Duarte A (2014) Combining intensification and diversification strategies in VNS. An application to the vertex separation problem. Comput Oper Res 52(Part B):209–219
114.
go back to reference Shahrokhi F, Sýkora O, Székely LA, Vrt’o I (2001) On bipartite drawings and the linear arrangement problem. SIAM J Comput 30(6):1773–1789MathSciNetCrossRef Shahrokhi F, Sýkora O, Székely LA, Vrt’o I (2001) On bipartite drawings and the linear arrangement problem. SIAM J Comput 30(6):1773–1789MathSciNetCrossRef
115.
116.
go back to reference Skodinis K (2000) Computing optimal linear layouts of trees in linear time. In: Proceedings of the 8th annual European symposium on algorithms, ESA’00. Springer, London, pp 403–414 Skodinis K (2000) Computing optimal linear layouts of trees in linear time. In: Proceedings of the 8th annual European symposium on algorithms, ESA’00. Springer, London, pp 403–414
117.
go back to reference Sýkora O, Torok L, Vrt’o I (2005) The cyclic antibandwidth problem. Electron Notes Discret Math 7th Int Colloq Graph Theory 22:223–227 Sýkora O, Torok L, Vrt’o I (2005) The cyclic antibandwidth problem. Electron Notes Discret Math 7th Int Colloq Graph Theory 22:223–227
118.
go back to reference Takagi K, Takagi N (1999) Minimum cut linear arrangement of p-q dags for VLSI layout of adder trees. IEICE Trans Fundam Electron Commun Comput Sci E82-A(5):767–774 Takagi K, Takagi N (1999) Minimum cut linear arrangement of p-q dags for VLSI layout of adder trees. IEICE Trans Fundam Electron Commun Comput Sci E82-A(5):767–774
119.
go back to reference Tewarson RP (1973) Sparse matrices, vol 69. Academic Press, New YorkMATH Tewarson RP (1973) Sparse matrices, vol 69. Academic Press, New YorkMATH
120.
go back to reference Thilikos DM, Serna MJ, Bodlaender HL (2005) Cutwidth II: algorithms for partial w-trees of bounded degree. J Algorithms 56(1):25–49MathSciNetCrossRef Thilikos DM, Serna MJ, Bodlaender HL (2005) Cutwidth II: algorithms for partial w-trees of bounded degree. J Algorithms 56(1):25–49MathSciNetCrossRef
121.
go back to reference Woodcock JR (2006) A faster algorithm for torus embedding. PhD thesis, University of Victoria Woodcock JR (2006) A faster algorithm for torus embedding. PhD thesis, University of Victoria
122.
123.
go back to reference Yuan J, Lin Y, Liu Y, Wang S (1998) NP-completeness of the profile problem and the fill-in problem on cobipartite graphs. J Math Study 31(3):239–243MathSciNetMATH Yuan J, Lin Y, Liu Y, Wang S (1998) NP-completeness of the profile problem and the fill-in problem on cobipartite graphs. J Math Study 31(3):239–243MathSciNetMATH
Metadata
Title
Linear Layout Problems
Authors
Eduardo G. Pardo
Rafael Martí
Abraham Duarte
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-07124-4_45

Premium Partner