Abstract
We consider the problem of coding planar graphs by binary strings. Depending on whether O(1)-time queries for adjacency and degree are supported, we present three sets of coding schemes which all take linear time for encoding and decoding. The encoding lengths are significantly shorter than the previously known results in each case.
Research supported in part by NSF Grant CCR-9205982.
Research supported in part by NSF Grant CCR-9531028.
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References
T. Bell, J. G. Cleary, and I. Witten, Text Compression, Prentice-Hall, 1990.
D. R. Clark, Compact Pat Tree, PhD thesis, University of Waterloo, 1996.
H. D. Fraysseix, J. Pach, and R. Pollack, How to draw a planar graph on a grid, Combinatorica, 10 (1990), pp. 41–51.
H. Galperin and A. Wigderson, Succinct representations of graphs, Information and Control, 56 (1983), pp. 183–198.
A. Itai and M. Rodeh, Representation of graphs, Acta Informatica, 17 (1982), pp. 215–219.
G. Jacobson, Space-efficient static trees and graphs, in proc. 30th FOCS, 30 Oct.–1 Nov. 1989, pp. 549–554.
S. Kannan, N. Naor, and S. Rudich, Implicit representation of graphs, SIAM Journal on Discrete Mathematics, 5 (1992), pp. 596–603.
G. Kant, Drawing planar graphs using the lmc-ordering (extended abstract), in proc. 33rd FOCS, 24–27 Oct. 1992, pp. 101–110.
-, Algorithms for Drawing Planar Graphs, PhD thesis, Univ. of Utrecht, 1993.
G. Kant and X. He, Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems, TCS 172 (1997), pp. 175–193.
M. Y. Kao, M. Fürer, X. He, and B. Raghavachari, Optimal parallel algorithms for straight-line grid embeddings of planar graphs, SIAM Journal on Discrete Mathematics, 7 (1994), pp. 632–646.
M. Y. Kao and S. H. Teng, Simple and efficient compression schemes for dense and complement graphs, in Fifth Annual Symposium on Algorithms and Computation, LNCS 834, Beijing, China, 1994, Springer-Verlag, pp. 201–210.
K. Keeler and J. Westbrook, Short encodings of planar graphs and maps, Discrete Applied Mathematics, 58 (1995), pp. 239–252.
J. I. Munro, Tables, in proc. of 16th Conf. on Foundations of Software Technology and Theoret. Comp. Sci., LNCS 1180, 1996, Springer-Verlag, pp. 37–42.
J. I. Munro and V. Raman, Succinct representation of balanced parentheses, static trees and planar graphs, in proc. 38th FOCS 20–22 Oct. 1997.
M. Naor, Succinct representation of general unlabeled graphs, Discrete Applied Mathematics, 28 (1990), pp. 303–307.
C. H. Papadimitriou and M. Yannakakis, A note on succinct representations of graphs, Information and Control, 71 (1986), pp. 181–185.
W. Schnyder, Embedding planar graphs on the grid, in Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 138–148.
G. Turán, On the succinct representation of graphs, Discrete Applied Mathematics, 8 (1984), pp. 289–294.
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Chuang, R.CN., Garg, A., He, X., Kao, MY., Lu, HI. (1998). Compact encodings of planar graphs via canonical orderings and multiple parentheses. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055046
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DOI: https://doi.org/10.1007/BFb0055046
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