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ABSTRACT
Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. This survey considers their motivation, complexity, approximation properties, upper and lower bounds, heuristics and probabilistic analysis on random graphs. The result is a complete view of the current state of the art with respect to layout problems from an algorithmic point of view.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
1
|
|
| |
2
|
Adolphson, D. 1977. Single machine job sequencing with precedence constraints. SIAM J. Comput. 6, 40--54.
|
| |
3
|
Adolphson, D. and Hu, T. C. 1973. Optimal linear ordering. SIAM J. Appl. Mathem. 25, 3, 403--423.
|
| |
4
|
Alon, N. and Milman, V. 1985. λ1, isoperimetric inequalities for graphs and superconcentrators. J. Combinatorial Theory. Series B 38, 73--88.
|
| |
5
|
Àlvarez, C., Cases, R., Díaz, J., Petit, J., and Serna, M. 2000. Routing trees problems on random graphs. In Approximation and Randomized Algorithms in Communication Networks, J. Rolim et al., Ed. ICALP Workshops 2000. Carleton Scientific, 99--111.
|
| |
6
|
Àlvarez, C., Díaz, J., and Serna, M. 1998. Intervalizing colored graphs is NP-complete for caterpillars with hair length 2. Technical report LSI 98-9-R, Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya.
|
| |
7
|
Àlvarez, C., Díaz, J., and Serna, M. 2001. The hardness of intervalizing four colored caterpillars. Discrete Mathematics 235, 19--27.
|
| |
8
|
Àlvarez, C. and Serna, M. 1999. The proper interval colored graph problem for caterpillar trees. Technical report LSI 99-12-R, Dept. de Llenguatges i Sistemes Informàtics, Univ. Politècnica de Catalunya.
|
| |
9
|
|
| |
10
|
|
| |
11
|
Assman, S. F., Peck, G. W., Syslo, M. M., and Zak, J. 1981. The bandwidth of caterpillars with hair of lengths 1 and 2. SIAM J. Algebraic and Discrete Meth. 2, 387--393.
|
| |
12
|
Giorgio Ausiello , M. Protasi , A. Marchetti-Spaccamela , G. Gambosi , P. Crescenzi , V. Kann, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer-Verlag New York, Inc., Secaucus, NJ, 1999
|
| |
13
|
Azizoğlu, C. and Eğecioğlu, Ö. 2002. The isoperimetric number and the bisection width of generalized cylinders. Discrete Mathematics. To appear.
|
| |
14
|
|
| |
15
|
Barnard, S. T., Pothen, A., and Simon, H. 1995. A spectral algorithm for envelope reduction of sparse matrices. Numerical Linear Algebra with Applications 2, 4, 317--334.
|
| |
16
|
Barnard, S. T. and Simon, H. D. 1994. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency: Practice and Experience 6, 101--107.
|
| |
17
|
Barth, D., Pellegrini, F., Raspaud, A., and Roman, J. 1995. On bandwidth, cutwidth, and quotient graphs. RAIRO Informatique Théorique et Applications. 29, 6, 487--508.
|
| |
18
|
|
| |
19
|
Berger-Wolf, T. Y. and Reingold, E. M. 2002. Index assignment for multichannel communication under failure. IEEE Trans. Inform. Th.
|
| |
20
|
Bernhart, F. and Kainen, P. C. 1979. The book thickness of a graph. Journal of Combinatorial Theory. Series B 27, 3, 320--331.
|
| |
21
|
|
| |
22
|
Bezrukov, S. L. 1999. Edge isoperimetric problems on graphs (a survey). In Graph Theory and Combinatorial Biology (Balatonlelle, 1996), L. Lovasz, A. Gyarfas, G. O. H. Katona, A. Recski, and L. Szekely, Eds. János Bolyai Math. Soc., 157--197.
|
| |
23
|
|
| |
24
|
|
| |
25
|
Bhatt, S. N. and Leighton, F. T. 1984. A framework for solving VLSI graph layout problems. J. Comput. Syst. Sci. 28, 300--343.
|
| |
26
|
Bilski, T. 1993. Embedding graphs in books with prespecified order of vertices. Poznańskie Towarzystwo Przyjaciól Nauk. Wydzial Nauk Technicznych. Prace Komisji Automatyki i Informatyki. Studia z Automatyki 18, 5--12.
|
| |
27
|
Blache, G., Karpinski, M., and Wirtgen, J. 1998. On approximation intractability of the bandwidth problem. Technical report TR98-014, Electronic Colloquium on Computational Complexity.
|
| |
28
|
|
 |
29
|
Hans L. Bodlaender , Michael R. Fellows , Michael T. Hallett, Beyond NP-completeness for problems of bounded width (extended abstract): hardness for the W hierarchy, Proceedings of the twenty-sixth annual ACM symposium on Theory of computing, p.449-458, May 23-25, 1994, Montreal, Quebec, Canada
[doi> 10.1145/195058.195229]
|
| |
30
|
Bodlaender, H. L. 1993. A tourist guide through treewidth. Acta Cybernetica 11, 1-2, 1--21.
|
| |
31
|
|
| |
32
|
|
| |
33
|
Hans L. Bodlaender , John R. Gilbert , Hjálmtýr Hafsteinsson , Ton Kloks, Approximating treewidth, pathwidth, frontsize, and shortest elimination tree, Journal of Algorithms, v.18 n.2, p.238-255, March 1995
[doi> 10.1006/jagm.1995.1009]
|
| |
34
|
|
| |
35
|
|
| |
36
|
Bollobás, B. 1985. Random Graphs. Academic Press, London.
|
| |
37
|
Bollobás, B. and Leader, I. 1991. Edge--isoperimetric inequalities in the grid. Combinatorica 4, 299--314.
|
| |
38
|
Boppana, R. 1987. Eigenvalues and graph bisection: An average case analysis. In Proceedings of the 28th Annual Symposium on Foundations of Computer Science. 280--285.
|
| |
39
|
|
 |
40
|
|
| |
41
|
|
| |
42
|
|
| |
43
|
Caprara, A., Malucelli, F., and Pretolani, D. 2002. On bandwidth-2 graphs. Discrete Applied Mathematics. 117, 1--13.
|
| |
44
|
|
| |
45
|
Chang, G. J. and Lai, Y.-L. 2001. On the profile of the corona of two graphs. Manuscript (provided by S. Bezrukov).
|
| |
46
|
Chinn, P., Chvátalová, J., Dewdney, A., and Gibbs, N. 1982. The bandwidth problem for graphs and matrices---A survey. Journal of Graph Theory 6, 223--254.
|
| |
47
|
Chinn, P. Z., Lin, Y. X., and Yuan, J. J. 1992. The bandwidth of the corona of two graphs. In Proceedings of the Twenty-third Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Congressus Numerantium, vol. 91. Utilitas Math., 141--152.
|
| |
48
|
Chinn, P. Z., Lin, Y. X., Yuan, J. J., and Williams, K. 1995. Bandwidth of the composition of certain graph powers. Ars Combinatoria 39, 167--173.
|
| |
49
|
Chirravuri, S., Bhandarkar, S. M., and Arnold, J. 1996. Parallel computing of physical maps---A comparative study in SIMD and MIMD parallelism. Journal of Computational Biology 3, 4, 503--528.
|
| |
50
|
Chung, F. R. K. 1988. Labelings of Graphs. Academic Press, San Diego, 151--168.
|
| |
51
|
|
| |
52
|
Chung, M., Makedon, F., Sudborough, I. H., and Turner, J. 1982. Polynomial time algorithms for the min cut problem on degree restricted trees. In Proceedings of the 23th Annual Symposium on Foundations of Computer Science. 262--271.
|
| |
53
|
Chvátalová, J. 1975. Optimal labelling of a product of two paths. Discrete Mathematics 11, 249--253.
|
| |
54
|
Chvátalová, J., Dewdney, A., Gibbs, N., and Korfhage, R. 1975. The bandwidth problem for graphs---A collection of recent results. Technical report CS 75020, Dept. of Computer Science, Southern Methodist University.
|
| |
55
|
|
| |
56
|
|
 |
57
|
|
| |
58
|
Deo, N., Krishnamoorthy, M. S., and Langston, M. A. 1987. Exact and approximate solutions for the gate matrix layout problem. IEEE Transactions on Computer Aided Design 6, 1, 79--84.
|
| |
59
|
Dewdney, A. K. 1976. The bandwidth of a graph---some recent results. In Proceedings of the Seventh Southeastern Conference on Combinatorics, Graph Theory, and Computing. Number 17 in Congressus Numerantium. Utilitas Math., 273--288.
|
| |
60
|
Díaz, J. 1979. The Δ-operator. In Fundamentals of Computation Theory, L. Budach, Ed. Akademie--Verlag, 105--111.
|
| |
61
|
|
| |
62
|
Josep Díaz , Alan Gibbons , Grammati E. Pantziou , Maria J. Serna , Paul G. Spirakis , Jacobo Toran, Parallel algorithms for the minimum cut and the minimum length tree layout problems, Theoretical Computer Science, v.181 n.2, p.267-287, July 30, 1997
[doi> 10.1016/S0304-3975(96)00274-5]
|
| |
63
|
Díaz, J., Gibbons, A. M., Paterson, M. S., and Torán, J. 1991. The Minsumcut problem. In Algorithms and Data Structures, F. Dehen, R. J. Sack, and N. Santoro, Eds. Lecture Notes in Computer Science, vol. 519. Springer-Verlag, 65--79.
|
| |
64
|
|
| |
65
|
|
| |
66
|
Díaz, J., Petit, J., and Serna, M. 2001b. Faulty random geometric networks. Parallel Processing Letters 10, 4, 343--357.
|
| |
67
|
Díaz, J., Petit, J., Serna, M., and Trevisan, L. 2001c. Approximating layout problems on random graphs. Discrete Mathematics 235, 1--3, 245--253.
|
| |
68
|
|
| |
69
|
|
| |
70
|
Diekmann, R., Lüling, R., Monien, B., and Spräner, C. 1996. Combining helpful sets and parallel simulated annealing for the graph-partitioning problem. Parallel Algorithms and Applications 8, 61--84.
|
| |
71
|
Diekmann, R., Monien, B., and Preis, R. 1995. Using helpful sets to improve graph bisections. In Interconnection Networks and Mapping and Scheduling Parallel Computations, D. F. Hsu, A. L. Rosenberg, and D. Sotteau, Eds. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. AMS Press, 57--73.
|
| |
72
|
|
| |
73
|
|
| |
74
|
|
| |
75
|
|
| |
76
|
Downey, R. G. and Fellows, M. R. 1999. Parameterized Complexity. Springer-Verlag, New York.
|
| |
77
|
|
| |
78
|
|
| |
79
|
Elsner, U. 1997. Graph partitioning---A survey. Technical Report 393, Technische Universitat Chemnitz.
|
| |
80
|
|
 |
81
|
|
| |
82
|
Even, S. and Itai, A. 1971. Queues, stacks, and graphs. In Theory of Machines and Computations. Academic Press, 71--86.
|
| |
83
|
Even, S. and Shiloach, Y. 1975. NP-completeness of several arrangement problems. Technical Report TR-43, Dept. of Computer Science, Technion, Haifa.
|
| |
84
|
Everstine, G. C. 1979. A comparison of three resequencing algorithms for the reduction of matrix profile and wavefront. Int. J. Num. Meth. Eng. 14, 837--853.
|
| |
85
|
|
| |
86
|
Feige, U. and Krauthgamer, R. 1998. Improved performance guarantees for bandwidth minimization heuristics (draft). Technical Report, Computer Science Dept., Weizmann Inst. Tech.
|
| |
87
|
|
| |
88
|
Feige, U., Krauthgamer, R., and Nissim, K. 2002. Approximating the minimum bisection size. Discrete Applied Mathematics.
|
| |
89
|
|
| |
90
|
|
| |
91
|
|
| |
92
|
|
| |
93
|
|
| |
94
|
Ford, L. R. and Fulkerson, D. R. 1962. Flows in Networks. Princeton University Press.
|
| |
95
|
|
| |
96
|
Gallian, J. 1998. A dynamic survey of graph labeling. Electronic Journal of Combininatorics 5, 1.
|
| |
97
|
Garey, M. R., Graham, R. L., Johnson, D. S., and Knuth, D. 1978. Complexity results for bandwidth minimization. SIAM J. Appl. Mathem. 34, 477--495.
|
| |
98
|
|
| |
99
|
Garey, M. R., Johnson, D. S., Miller, G. L., and Papadimitriou, C. H. 1980. The complexity of coloring circular arcs and chords. SIAM J. Algeb. Discrete Meth. 1, 2, 216--227.
|
| |
100
|
Garey, M. R., Johnson, D. S., and Stockmeyer, L. 1976. Some simplified NP-complete graph problems. Theoretical Computer Science 1, 237--267.
|
| |
101
|
Gavril, F. 1977. Some NP-complete problems on graphs. In 11th Conference on Information Sciences and Systems. John Hopkins University, Baltimore, 91--95.
|
| |
102
|
Gibbs, N. E., Poole, Jr., W. G., and Stockmeyer, P. K. 1976. An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J. Num. Anal. 13, 2, 236--250.
|
| |
103
|
|
| |
104
|
Goldberg, M. and Miller, Z. 1988. A parallel algorithm for bisection width in trees. Computers & Mathematics with Applications 15, 4, 259--266.
|
| |
105
|
Goldberg, M. K. and Klipker, I. A. 1976. An algorithm for minimal numeration of tree vertices. Sakharth. SSR Mecn. Akad. Moambe 81, 3, 553--556. In Russian.
|
| |
106
|
Goldberg, P. W., Golumbic, M. C., Kaplan, H., and Shamir, R. 1995. Four strikes against physical mapping of DNA. J. Comput. Biol. 2, 1, 139--152.
|
| |
107
|
Golovach, P. A. 1997. The total vertex separation number of a graph. Diskretnaya Matematika 9, 4, 86--91. In Russian.
|
| |
108
|
Golovach, P. A. and Fomin, F. V. 1998. The total vertex separation number and the profile of graphs. Diskretnaya Matematika 10, 1, 87--94. In Russian.
|
| |
109
|
Golumbic, M. C. 1980. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York.
|
| |
110
|
|
| |
111
|
|
 |
112
|
|
| |
113
|
Gomory, R. E. and Hu, T. C. 1975. Multi-Terminal Flows in a Network. Studies in Mathematics, vol. 11. MAA, 172--199.
|
| |
114
|
|
| |
115
|
Grimmett, G. R. 1999. Percolation, second ed. Springer-Verlag, Heidelberg.
|
| |
116
|
|
| |
117
|
Gurari, E. and Sudborough, I. H. 1984. Improved dynamic programming algorithms for the bandwidth minimization and the mincut linear arrangement problem. J. Algor. 5, 531--546.
|
| |
118
|
|
| |
119
|
|
| |
120
|
Hansen, M. D. 1989. Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems. In 30th Annual Symposium on Foundations of Computer Science. 604--609.
|
| |
121
|
Haralambides, J. and Makedon, F. 1997. Approximation algorithms for the bandwidth minimization problem for a large class of trees. Theory of Computing Systems 30, 67--90.
|
| |
122
|
Haralambides, J., Makedon, F., and Monien, B. 1991. Bandwidth minimization: an approximation algorithm for caterpillars. Mathematical Systems Theory 24, 169--177.
|
| |
123
|
Harary, F. 1967. Problem 16. In Graph Theory and Computing, M. Fiedler, Ed. Czechoslovak Academy Sciences, 161.
|
| |
124
|
Harper, L. H. 1964. Optimal assignments of numbers to vertices. J. SIAM 12, 1, 131--135.
|
| |
125
|
Harper, L. H. 1966. Optimal numberings and isoperimetric problems on graphs. J. Combinatorial Theory 1, 3, 385--393.
|
| |
126
|
Harper, L. H. 1970. Chassis layout and isoperimetric problems. Technical Report SPS 37--66, vol II, Jet Propulsion Laboratory.
|
| |
127
|
Harper, L. H. 1977. Stabilization and the edgesum problem. Ars Combinatoria 4, 225--270.
|
| |
128
|
Harper, L. H. 2001. On the bandwidth of a hamming graph. Manuscript.
|
| |
129
|
|
| |
130
|
|
| |
131
|
|
| |
132
|
Heath, L. S., Pemmaraju, S. V., and Ribbens, C. J. 1993. Sparse Matrix-Vector Multiplication on a Small Linear Array. Springer-Verlag.
|
| |
133
|
|
| |
134
|
|
| |
135
|
|
| |
136
|
Helmberg, C., Rendl, F., Mohar, B., and Poljak, S. 1995. A spectral approach to bandwidth and separator problems in graphs. Linear and Multilinear Algebra 39, 1-2, 73--90.
|
| |
137
|
|
| |
138
|
Hendrickson, B. and Leland, R. 1997. The Chaco user's guide: version 2.0. Technical Report SAND94--2692, Sandia National Laboratories. ftp://ftp.cs.sandia.gov/pub/papers/bahendr/guide.ps.gz.
|
| |
139
|
Hromkovi&cbreve;, J. and Monien, B. 1992. The Bisection Problem for Graphs of Degree 4 (Configuring Transputer Systems). Teubner, Stuttgart, 215--233.
|
| |
140
|
Hu, T. C. 1974. Optimum communication spanning trees. SIAM J. Comput. 3, 188--195.
|
| |
141
|
Janson, S., Luczak, T., and Rucinski, A. 2000. Random Graphs. Wiley, New York.
|
| |
142
|
|
| |
143
|
|
| |
144
|
Johnson, D. S., Lenstra, J. K., and Kan, A. H. G. R. 1978. The complexity of the network design problem. Networks 8, 4, 279--285.
|
| |
145
|
|
| |
146
|
|
| |
147
|
Kadluczka, P. and Wala, K. 1995. Tabu search and genetic algorithms for the generalized graph partitioning problem. Control and Cybernetics 24, 4, 459--476.
|
| |
148
|
|
| |
149
|
Kaplan, H. and Shamir, R. 1999. Bounded degree interval sandwich problems. Algorithmica 24, 2, 96--104.
|
| |
150
|
|
| |
151
|
|
 |
152
|
|
| |
153
|
Karpinski, M., Wirtgen, J., and Zelikovsky, A. 1997. An approximating algorithm for the bandwidth problem on dense graphs. Technical Report TR 97-017, Electronic Colloquium on Computational Complexity.
|
| |
154
|
Karypis, G. 2001. Metis's home page. Web page. http://www-users.cs.umn.edu/∼karypis/metis.
|
| |
155
|
Kendall, D. G. 1969. Incidence matrices, interval graphs, and seriation in archeology. Pacific J. Mathem. 28, 565--570.
|
| |
156
|
Kernighan, B. W. and Lin, S. 1970. An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291--307.
|
| |
157
|
King, I. P. 1970. An automatic reordering schema for simultaneous equations derived from network system. Int. J. Numer. Meth. Eng. 2, 523--533.
|
| |
158
|
|
| |
159
|
|
| |
160
|
|
| |
161
|
|
| |
162
|
|
| |
163
|
Kloks, T., Kratsch, D., and Müller, H. 1999. Approximating the bandwidth for asteroidal triple-free graphs. J. Algor. 32, 1, 41--57.
|
| |
164
|
|
| |
165
|
Kumfert, G. and Pothen, A. 1997. Two improved algorithms for reducing the envelope and wavefront. BIT 37, 3, 001--032.
|
| |
166
|
|
| |
167
|
|
| |
168
|
Lai, Y.-L. 2001. On the profile of the tensor product of path with complete bipartite graphs. Manuscript (provided by S. Bezrukov).
|
| |
169
|
Lai, Y.-L., Liu, J., and Williams, K. 1994. Bandwidth for the sum of k graphs. Ars Combinatoria 37, 149--155.
|
| |
170
|
Lai, Y.-L. and Williams, K. 1994. The edgesum of the sum of k sum deterministic graphs. In Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, vol. 102. Utilitas Math., 231--236.
|
| |
171
|
Lai, Y.-L. and Williams, K. 1995. Bandwidth of the strong product of paths and cycles. In Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, vol. 109. Utilitas Math., 123--128.
|
| |
172
|
|
| |
173
|
Lai, Y.-L. and Williams, K. 1999. A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs. J. Graph Theory 31, 2, 75--94.
|
| |
174
|
|
| |
175
|
|
 |
176
|
|
| |
177
|
Leiserson, C. E. 1980. Area-efficient graph layouts (for VLSI). In Proceedings of the 21st Annual Symposium on Foundations of Computer Science. 270--281.
|
| |
178
|
Leland, R. and Hendrickson, B. 1994. An empirical study of static load balancing algorithms. In Scalable High-Performance Computing Conference. IEEE Computer Society Press, 682--685.
|
| |
179
|
Lengauer, T. 1981. Black-white pebbles and graph separation. Acta Informatica 16, 465--475.
|
| |
180
|
Lengauer, T. 1982. Upper and lower bounds on the complexity of the min-cut linear arrangements problem on trees. SIAM J. Algeb. Discrete Meth. 3, 99--113.
|
| |
181
|
Lepin, V. V. 1986. Profile minimization problem of matrices and graphs. Academy of Sciences of Belarus. Institute of Mathematics. 33, 269. In Russian.
|
| |
182
|
Lewis, R. 1994. Simulated annealing for profile and fill reduction of sparse matrices. Int. J. Num. Meth. Eng. 37, 6.
|
| |
183
|
Lin, Y. X. 1994. Two-dimensional bandwidth problem. In Combinatorics, Graph Theory, Algorithms and Applications (Beijing, 1993). World Sci. Publishing, 223--232.
|
| |
184
|
Lin, Y. X. and Yuan, J. 1994a. Profile minimization problem for matrices and graphs. Acta Mathematicae Applicatae Sinica. English Series 10, 1, 107--112.
|
| |
185
|
Lin, Y. X. and Yuan, J. J. 1994b. Profile minimization problem for matrices and graphs. Acta Mathematicae Applicatae Sinica. English Series. Yingyong Shuxue Xuebao 10, 1, 107--112.
|
| |
186
|
Lindsey, J. H. 1964. Assignments of numbers to vertices. American Mathematical Monthly 71, 508--516.
|
| |
187
|
Lipton, R. J. and Tarjan, R. E. 1979. A separator theorem for planar graphs. SIAM J. Appl. Mathem. 36, 177--189.
|
| |
188
|
Liu, H. E. and Yuan, J. J. 1995. The cutwidth problem for graphs. Gaoxiao Yingyong Shuxue Xuebao. Applied Mathematics. A Journal of Chinese Universities. Series A 10, 3, 339--348. In Chinese.
|
| |
189
|
Liu, J. 1992. On bandwidth sum for the composition of paths and cycles. Technical Report Rep/92-06, Dept. of Computer Science, Western Michigan Univ.
|
| |
190
|
|
| |
191
|
|
| |
192
|
|
| |
193
|
|
| |
194
|
Mai, J. H. 1996. Profiles of some classes of condensable graphs. J. Syst. Sci. Mathem. Sci. Xitong Kexue yu Shuxue 16, 2, 141--148.
|
| |
195
|
Mai, J. H. and Luo, H. P. 1984. Some theorems on the bandwidth of a graph. Acta Mathematicae Applicatae Sinica. Yingyong Shuxue Xuebao 7, 1, 86--95.
|
| |
196
|
Makedon, F., Papadimitriou, C. H., and Sudborough, I. H. 1985. Topological bandwidth. SIAM J. Algeb. Discrete Meth. 6, 3, 418--444.
|
| |
197
|
|
| |
198
|
|
| |
199
|
Manabe, Y., Hagihara, K., and Tokura, N. 1984. The minimum bisection widths of the cube-connected cycles graph and cube graph. Systems-Computers-Controls. The Transactions of the Institute of Electronics and Communication Engineers of Japan 15, 6, 9--18.
|
| |
200
|
Miller, Z. 1991. Multidimensional bandwidth in random graphs. In Graph Theory, Combinatorics, and Applications. Vol. 2 (Kalamazoo, MI, 1988). Wiley, New York, 861--870.
|
| |
201
|
|
| |
202
|
Mohar, B. and Poljak, S. 1993. Eigenvalues in combinatorial optimization. In Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A. Brualdi, S. Friedland, and V. Klee, Eds. IMA Volumes in Mathematics and its Applications, vol. 50. Springer-Verlag, 107--151.
|
| |
203
|
|
| |
204
|
|
| |
205
|
Monien, B. and Sudborough, I. H. 1990. Embedding one interconnection network in another. In Computational Graph Theory, G. Tinhofer, E. Mayr, H. Noltemeier, and M. M. Syslo, Eds. Computing Supplementa, vol. 7. Springer-Verlag, 257--282.
|
| |
206
|
Muradyan, D. 1999. Proceedings of Computer Science & Information Technologies Conference, Armenia.
|
| |
207
|
Muradyan, D. O. 1982. Minimal numberings of a two-dimensional cylinder. Akademiya Nauk Armyanskoĭ SSR. Doklady 75, 3, 114--119. In Russian.
|
| |
208
|
Muradyan, D. O. 1985. Some estimates for the length of an arbitrary graph. Mat. Voprosy Kibernet. Vychisl. Tekhn.14, 79--86, 126. In Russian.
|
| |
209
|
Muradyan, D. O. 1986. A polynomial algorithm for finding the bandwidth of interval graphs. Akademiya Nauk Armyanskoĭ SSR. Doklady 82, 2, 64--66. In Russian.
|
| |
210
|
Muradyan, D. O. and Piliposyan, T. E. 1980. Minimal numberings of vertices of a rectangular lattice. Akad. Nauk. Armjan. SRR 1, 70, 21--27. In Russian.
|
| |
211
|
Muradyan, D. O. and Piliposyan, T. E. 1980. The problem of finding the length and width of the complete p-partite graph. Uchen. Zapiski Erevan. Gosunivers. 2, 18--26. In Russian.
|
| |
212
|
|
| |
213
|
|
| |
214
|
Niepel, L. and Tomasta, P. 1981. Elevation of a graph. Czechoslovak Mathematical Journal 31(106), 3, 475--483.
|
| |
215
|
Papadimitriou, C. 1976. The NP-completeness of the bandwidth minimization problem. Computing 16, 263--270.
|
| |
216
|
Papadimitriou, C. H. and Sideri, M. 1996. The bisection width of grid graphs. Mathematical Systems Theory 29, 2, 97--110.
|
| |
217
|
|
| |
218
|
Penrose, M. 2000. Vertex ordering and partitioning problems for random spatial graphs. The Annals of Applied Probability 10, 517--538.
|
| |
219
|
Petit, J. 1998. Approximation heuristics and benchmarkings for the MinLA problem. In Alex '98---Building Bridges Between Theory and Applications, R. Battiti and A. Bertossi, Eds. 112--128.
|
| |
220
|
Petit, J. 2000. Combining spectral sequencing and parallel simulated annealing for the minLA problem. Technical Report LSI-01-13-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya.
|
| |
221
|
Petit, J. 2001a. Experiments for the MinLAP problem. Technical Report LSI-R01-7-R, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya.
|
| |
222
|
Petit, J. 2001b. Layout problems. Ph.D. thesis, Universitat Politècnica de Catalunya.
|
| |
223
|
Preis, R. and Diekmann, R. 1996. The Party partitioning library user guide. Technical Report TR-RSFB-96-024, Universität Paderborn.
|
| |
224
|
|
| |
225
|
Raspaud, A., Sýkora, O., and Vr&tbreve;o, I. 1995. Cutwidth of the de Bruijn graph. RAIRO Informatique Théorique et Applications 29, 6, 509--514.
|
| |
226
|
Raspaud, A., Sýkora, O., and Vr&tbreve;o, I. 2000. Congestion and dilation, similarities and differences---a survey. In Proceedings 7th International Colloquium on Structural Information and Communication Complexity. Carleton Scientific, 269--280.
|
| |
227
|
|
| |
228
|
Robertson, N. and Seymour, P. D. 1985. Graph minors---a survey. In Surveys in Combinatorics. Cambridge University Press, 153--171.
|
| |
229
|
|
| |
230
|
|
| |
231
|
|
| |
232
|
Saxe, J. B. 1980. Dynamic-programming algorithms for recognizing small-bandwidth graphs in polynomial time. SIAM J. Algeb. Discrete Meth. 1, 4, 363--369.
|
| |
233
|
Seymour, P. D. 1995. Packing directed circuits fractionally. Combinatorica 15, 2, 281--288.
|
| |
234
|
Seymour, P. D. and Thomas, R. 1994. Call routing and the ratcatcher. Combinatorica 14, 2, 217--241.
|
| |
235
|
Shahrokhi, F., Sýkora, O., Székely, L. A., and Vr&tbreve;o, I. 1997. Crossing numbers: bounds and applications. János Bolyai Math. Soc., Budapest, 179--206.
|
| |
236
|
|
| |
237
|
Shiloach, Y. 1979. A minimum linear arrangement algorithm for undirected trees. SIAM J. Comput. 8, 1, 15--32.
|
| |
238
|
Shing, M. T. and Hu, T. C. 1986. Computational complexity of layout problems. In Layout Design and Verification, T. Ohtsuki, Ed. Advances in CAD for VLSI, vol. 4. North--Holland, Amsterdam, 267--294.
|
| |
239
|
|
| |
240
|
|
| |
241
|
Soumyanath, K. and Deogun, J. S. 1990. On the bisection width of partial k-trees. In Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing. Congressus Numerantium, vol. 74. Utilitas Math., 25--37.
|
| |
242
|
|
| |
243
|
|
| |
244
|
|
| |
245
|
|
| |
246
|
Tewarson, R. 1973. Sparse Matrices. Academic Press, New York.
|
| |
247
|
|
| |
248
|
|
 |
249
|
|
| |
250
|
|
| |
251
|
|
| |
252
|
|
| |
253
|
Vr&tbreve;o, I. 2000. Cutwidth of the r-dimensional mesh of d-ary trees. RAIRO Informatique Théorique et Applications 34, 6, 515--519.
|
| |
254
|
Vr&tbreve;o, I. 2002. Crossing numbers of graphs: A bibliography. ftp://ftp.ifi.savba.sk/pub/imrich/crobib.ps.gz.
|
| |
255
|
Williams, K. 1993. On the minimum sum of the corona of two graphs. In Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Congressus Numerantium, vol. 94. Utilitas Math., 43--49.
|
| |
256
|
Williams, K. 1994. On bandwidth and edgesum for the tensor product of paths with complete bipartite graphs. In Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, vol. 102. Utilitas Math., 183--190.
|
| |
257
|
Williams, K. 1996. On bandwidth for the tensor product of paths and cycles with complete graphs. Bulletin of the Institute of Combinatorics and its Applications 16, 41--48.
|
| |
258
|
Bang Ye Wu , Giuseppe Lancia , Vineet Bafna , Kun-Mao Chao , R. Ravi , Chuan Yi Tang, A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees, SIAM Journal on Computing, v.29 n.3, p.761-778, Dec. 1999 to Jan. 2000
[doi> 10.1137/S009753979732253X]
|
 |
259
|
|
| |
260
|
Yuan, J., Lin, Y., Liu, Y., and Wang, S. 1998. NP-completeness of the profile problem and the fill-in problem on cobipartite graphs. J. Mathem. Study 31, 3, 239--243.
|
| |
261
|
|
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|
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|
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