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Volumn 46, Issue 3-4, 2006, Pages 505-527

Optimal coding and sampling of triangulations

Author keywords

Bijection; Enumeration; Orientations; Schnyder trees

Indexed keywords

ENUMERATION; PLANE TRIANGULATIONS; POLYGONS; SCHNYDER TREES;

EID: 33846889519     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-006-0114-8     Document Type: Conference Paper
Times cited : (86)

References (40)
  • 1
    • 4244169180 scopus 로고
    • Geometry of a two-dimensional quantum gravity: Numerical study
    • M.E. Agishtein and A.A. Migdal. Geometry of a two-dimensional quantum gravity: numerical study. Nuclear Phys. B, 350:690-728, 1991.
    • (1991) Nuclear Phys. B , vol.350 , pp. 690-728
    • Agishtein, M.E.1    Migdal, A.A.2
  • 2
    • 0042689495 scopus 로고    scopus 로고
    • A linear-time algorithm for the generation of trees
    • L. Alonso, J.-L. Remy, and R. Schott. A linear-time algorithm for the generation of trees. Algorithmica, 17(2):162-183, 1997.
    • (1997) Algorithmica , vol.17 , Issue.2 , pp. 162-183
    • Alonso, L.1    Remy, J.-L.2    Schott, R.3
  • 4
    • 0003643205 scopus 로고    scopus 로고
    • Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge
    • J. Ambjørn, B. Durhuus, and T. Jonsson. Quantum Geometry. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, 1997.
    • (1997) Quantum Geometry
    • Ambjørn, J.1    Durhuus, B.2    Jonsson, T.3
  • 6
    • 35248872866 scopus 로고    scopus 로고
    • A bijection between realizers of maximal plane graphs and pairs of non-crossing dyck paths
    • N. Bonichon. A bijection between realizers of maximal plane graphs and pairs of non-crossing dyck paths. In Proc. FPSAC, 2002.
    • (2002) Proc. FPSAC
    • Bonichon, N.1
  • 7
    • 21144437215 scopus 로고    scopus 로고
    • An information-theoretic upper bound of planar graphs using triangulation
    • N. Bonichon, C. Gavoille, and N. Hanusse. An information-theoretic upper bound of planar graphs using triangulation. In Proc. STACS, 2003.
    • (2003) Proc. STACS
    • Bonichon, N.1    Gavoille, C.2    Hanusse, N.3
  • 9
    • 5344250647 scopus 로고    scopus 로고
    • The degree distribution in bipartite planar maps: Applications to theIsing model
    • arXiv:math.CO/0211070
    • M. Bousquet-Melou and G. Schaeffer. The degree distribution in bipartite planar maps: applications to theIsing model. 2002, arXiv:math.CO/0211070.
    • (2002)
    • Bousquet-Melou, M.1    Schaeffer, G.2
  • 10
    • 0041633154 scopus 로고    scopus 로고
    • 3-Orientations and Schnyder 3-tree-decompositions
    • Master's thesis, FB Mathematik und Informatik, Freie Universität Berlin
    • E. Brehm. 3-Orientations and Schnyder 3-tree-decompositions. Master's thesis, FB Mathematik und Informatik, Freie Universität Berlin, 2000.
    • (2000)
    • Brehm, E.1
  • 11
    • 0039176253 scopus 로고
    • Enumeration of triangulations of the disk
    • W. Brown. Enumeration of triangulations of the disk. Proc. London Math. Soc. (3), 14:746-768, 1964.
    • (1964) Proc. London Math. Soc. (3) , vol.14 , pp. 746-768
    • Brown, W.1
  • 12
    • 26844436915 scopus 로고    scopus 로고
    • Succinct representation of triangulations with a boundary
    • Proc. WADS, Springer, Berlin
    • L. Castelli Aleardi, O. Devillers, and G. Schaeffer. Succinct representation of triangulations with a boundary. In Proc. WADS, pages 139-195. LNCS 3608, Springer, Berlin, 2005.
    • (2005) LNCS , vol.3608 , pp. 139-195
    • Castelli Aleardi, L.1    Devillers, O.2    Schaeffer, G.3
  • 13
    • 84878620879 scopus 로고    scopus 로고
    • Compact encodings of planar graphs via canonical orderings
    • R. C.-N. Chuang, A. Garg, X. He, M.-Y. Kao, and H.-I Lu. Compact encodings of planar graphs via canonical orderings. In Proc. ICALP, pages 118-129, 1998.
    • (1998) Proc. ICALP , pp. 118-129
    • Chuang, R.C.-N.1    Garg, A.2    He, X.3    Kao, M.-Y.4    Lu, H.-I.5
  • 14
    • 84957568828 scopus 로고
    • Regular orientations, arboricity and augmentation
    • Proc. Graph Drawing, Springer, Berlin
    • H. de Fraysseix and P. Ossona de Mendez. Regular orientations, arboricity and augmentation. In Proc. Graph Drawing, pages 111-118. LNCS 894, Springer, Berlin, 1995.
    • (1995) LNCS , vol.894 , pp. 111-118
    • de Fraysseix, H.1    Ossona de Mendez, P.2
  • 16
    • 84972528638 scopus 로고
    • The asymptotic density of certain sets of real numbers
    • A. Dvoretzky and Th. Motzkin. The asymptotic density of certain sets of real numbers. Duke Math. J., 14:315-321, 1947.
    • (1947) Duke Math. J , vol.14 , pp. 315-321
    • Dvoretzky, A.1    Motzkin, T.2
  • 17
    • 0042382767 scopus 로고    scopus 로고
    • Convex drawings of planar graphs and the order dimension of 3-poly topes
    • S. Felsner. Convex drawings of planar graphs and the order dimension of 3-poly topes. Order, 18:19-37, 2001.
    • (2001) Order , vol.18 , pp. 19-37
    • Felsner, S.1
  • 18
    • 3042526859 scopus 로고    scopus 로고
    • S. Felsner. Lattice structures from planar graphs. Electron. J. Combin., 11:#15, 24 pp., 2004.
    • S. Felsner. Lattice structures from planar graphs. Electron. J. Combin., 11:#15, 24 pp., 2004.
  • 19
    • 0028498498 scopus 로고
    • A calculus for random generation of labelled combinatorial structures
    • P. Flajolet, P. Zimmermann, and B. Van Cutsem. A calculus for random generation of labelled combinatorial structures. Theoret. Comput. Sci., 132(2):1-35, 1994.
    • (1994) Theoret. Comput. Sci , vol.132 , Issue.2 , pp. 1-35
    • Flajolet, P.1    Zimmermann, P.2    Van Cutsem, B.3
  • 20
    • 20744447325 scopus 로고    scopus 로고
    • Dissections and trees, with applications to optimal mesh encoding and to random sampling
    • E. Fusy, D. Poulalhon, and G. Schaeffer. Dissections and trees, with applications to optimal mesh encoding and to random sampling. In Proc. SODA, pages 690-699, 2005.
    • (2005) Proc. SODA , pp. 690-699
    • Fusy, E.1    Poulalhon, D.2    Schaeffer, G.3
  • 21
    • 0036996256 scopus 로고    scopus 로고
    • P.-M. Gandoin and O. Devillers. Progressive lossless compression of arbitrary simplicial complexes. ACM Trans. Gmphics, 21(3):372-379, 2002.
    • P.-M. Gandoin and O. Devillers. Progressive lossless compression of arbitrary simplicial complexes. ACM Trans. Gmphics, 21(3):372-379, 2002.
  • 22
    • 0346874324 scopus 로고    scopus 로고
    • Enumeration of rooted planar triangulations with respect to diagonal flips
    • Z. Gao and J. Wang. Enumeration of rooted planar triangulations with respect to diagonal flips. J. Combin. Theory Ser: A, 88(2):276-296, 1999.
    • (1999) J. Combin. Theory Ser: A , vol.88 , Issue.2 , pp. 276-296
    • Gao, Z.1    Wang, J.2
  • 23
    • 33846861348 scopus 로고    scopus 로고
    • O. Gimenez and M. Noy. Asymptotic enumeration and limit law of labelled planar graphs. Preprint available on arXiv.org,2005.
    • O. Gimenez and M. Noy. Asymptotic enumeration and limit law of labelled planar graphs. Preprint available on arXiv.org,2005.
  • 24
    • 0001740837 scopus 로고    scopus 로고
    • Linear-time succinct encodings of planar graphs via canonical orderings
    • X. He, M.-Y. Kao, and H.-I. Lu. Linear-time succinct encodings of planar graphs via canonical orderings. SIAM J. Discrete Math., 12(3):317-325, 1999.
    • (1999) SIAM J. Discrete Math , vol.12 , Issue.3 , pp. 317-325
    • He, X.1    Kao, M.-Y.2    Lu, H.-I.3
  • 25
    • 0034941107 scopus 로고    scopus 로고
    • A fast general methodology for information-theoretically optimal encodings of graphs
    • X. He, M.-Y. Kao, and H.-I Lu. A fast general methodology for information-theoretically optimal encodings of graphs. SIAM J. Comput. 30(3):838-846, 2000.
    • (2000) SIAM J. Comput , vol.30 , Issue.3 , pp. 838-846
    • He, X.1    Kao, M.-Y.2    Lu, H.-I.3
  • 26
    • 0002648128 scopus 로고    scopus 로고
    • G. Kant. Drawing planar graphs using the canonical ordering. Algorithmica, 16:4-32, 1996. (also Proc. FOCS 92).
    • G. Kant. Drawing planar graphs using the canonical ordering. Algorithmica, 16:4-32, 1996. (also Proc. FOCS 92).
  • 27
    • 0002405531 scopus 로고    scopus 로고
    • Guaranteed 3.67v bit encoding of planar triangle graphs
    • D. King and J. Rossignac. Guaranteed 3.67v bit encoding of planar triangle graphs. In Proc. CCCG, #39, 1999.
    • (1999) Proc. CCCG , Issue.39
    • King, D.1    Rossignac, J.2
  • 28
    • 84968911974 scopus 로고    scopus 로고
    • Linear-time compression of bounded-genus graphs into information-theoretically optimal number of bits
    • H.-I. Lu. Linear-time compression of bounded-genus graphs into information-theoretically optimal number of bits. In Proc. SODA, pages 223-224, 2002.
    • (2002) Proc. SODA , pp. 223-224
    • Lu, H.-I.1
  • 29
    • 0036306861 scopus 로고    scopus 로고
    • Succint representation of balanced parantheses and static trees
    • J. I. Munro and V. Raman. Succint representation of balanced parantheses and static trees. SIAM J. Comput., 31:762-776, 2001.
    • (2001) SIAM J. Comput , vol.31 , pp. 762-776
    • Munro, J.I.1    Raman, V.2
  • 30
    • 0038626215 scopus 로고    scopus 로고
    • On random planar graphs, the number of planar graphs and their triangulations
    • May
    • D. Osthus, H.J. Prömel, and A. Taraz. On random planar graphs, the number of planar graphs and their triangulations. J. Combin. Theory, Ser. B, 88(1):119-134, May 2003.
    • (2003) J. Combin. Theory, Ser. B , vol.88 , Issue.1 , pp. 119-134
    • Osthus, D.1    Prömel, H.J.2    Taraz, A.3
  • 31
    • 0141748173 scopus 로고    scopus 로고
    • A bijection for triangulations of a polygon with interior points and multiple edges
    • D. Poulalhon and G. Schaeffer. A bijection for triangulations of a polygon with interior points and multiple edges. Theoret. Comput. Sci., 307(2):385-401, 2003.
    • (2003) Theoret. Comput. Sci , vol.307 , Issue.2 , pp. 385-401
    • Poulalhon, D.1    Schaeffer, G.2
  • 33
    • 0032674171 scopus 로고    scopus 로고
    • Edgebreaker: Connectivity compression for triangle meshes
    • J. Rossignac. Edgebreaker: connectivity compression for triangle meshes. IEEE Trans. Visual. Comput. Graphics, 5(1):47-61, 1999.
    • (1999) IEEE Trans. Visual. Comput. Graphics , vol.5 , Issue.1 , pp. 47-61
    • Rossignac, J.1
  • 34
    • 13744253226 scopus 로고    scopus 로고
    • G. Schaeffer. Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees. Electron. J. Combin., 4(1):# 20, 14 pp., 1997.
    • G. Schaeffer. Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees. Electron. J. Combin., 4(1):# 20, 14 pp., 1997.
  • 36
    • 0032628274 scopus 로고    scopus 로고
    • Random sampling of large planar maps and convex polyhedra
    • G. Schaeffer. Random sampling of large planar maps and convex polyhedra. In Proc. STOC, pages 760-769, 1999.
    • (1999) Proc. STOC , pp. 760-769
    • Schaeffer, G.1
  • 37
    • 84962950301 scopus 로고
    • Embedding planar graphs on the grid
    • W. Schnyder. Embedding planar graphs on the grid. In Proc. SODA, pages 138-148, 1990.
    • (1990) Proc. SODA , pp. 138-148
    • Schnyder, W.1
  • 38
  • 39
    • 0001853980 scopus 로고
    • A census of planar triangulations
    • W. T. Tutte. A census of planar triangulations. Canad. J. Math., 14:21-38, 1962.
    • (1962) Canad. J. Math , vol.14 , pp. 21-38
    • Tutte, W.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.