메뉴 건너뛰기




Volumn 9, Issue 2, 2007, Pages 253-275

Ramsey partitions and proximity data structures

Author keywords

Approximate distance oracle; Metric Ramsey theorem; Proximity data structure

Indexed keywords


EID: 33846646989     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/79     Document Type: Article
Times cited : (86)

References (33)
  • 2
    • 0032201716 scopus 로고    scopus 로고
    • An optimal algorithm for approximate nearest neighbor searching
    • Zbl 1065.68650 MR 1678846
    • Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., Wu, A. Y.: An optimal algorithm for approximate nearest neighbor searching. J. ACM 45, 891-923 (1998) Zbl 1065.68650 MR 1678846
    • (1998) J. ACM , vol.45 , pp. 891-923
    • Arya, S.1    Mount, D.M.2    Netanyahu, N.S.3    Silverman, R.4    Wu, A.Y.5
  • 3
    • 0032057919 scopus 로고    scopus 로고
    • Near-linear time construction of sparse neighborhood covers
    • Zbl 0943.05079 MR 1630481
    • Awerbuch, B., Berger, B., Cowen, L., Peleg, D.: Near-linear time construction of sparse neighborhood covers. SIAM J. Comput. 28, 263-277 (1999) Zbl 0943.05079 MR 1630481
    • (1999) SIAM J. Comput , vol.28 , pp. 263-277
    • Awerbuch, B.1    Berger, B.2    Cowen, L.3    Peleg, D.4
  • 4
    • 0030393774 scopus 로고    scopus 로고
    • Probabilistic approximations of metric spaces and its algorithmic application
    • IEEE Comput. Soc. Press, MR 1450616
    • Bartal, Y.: Probabilistic approximations of metric spaces and its algorithmic application. In: 37th Annual Symposium on Foundations of Computer Science, IEEE Comput. Soc. Press, 184-193 (1996) MR 1450616
    • (1996) 37th Annual Symposium on Foundations of Computer Science , pp. 184-193
    • Bartal, Y.1
  • 5
    • 28944451802 scopus 로고    scopus 로고
    • On metric Ramsey type phenomena
    • Zbl pre05042684 MR 2183280
    • Bartal, Y., Linial, N., Mendel, M., Naor, A.: On metric Ramsey type phenomena. Ann. of Math. (2) 162, 643-709 (2005) Zbl pre05042684 MR 2183280
    • (2005) Ann. of Math. (2) , vol.162 , pp. 643-709
    • Bartal, Y.1    Linial, N.2    Mendel, M.3    Naor, A.4
  • 7
    • 2442516025 scopus 로고    scopus 로고
    • The level ancestor problem simplified
    • Zbl 1068.68047 MR 2067397
    • Bender, M. A., Farach-Colton, M.: The level ancestor problem simplified. Theoret. Comput. Sci. 321, 5-12 (2004) Zbl 1068.68047 MR 2067397
    • (2004) Theoret. Comput. Sci , vol.321 , pp. 5-12
    • Bender, M.A.1    Farach-Colton, M.2
  • 8
    • 51249179297 scopus 로고
    • On Hilbertian subsets of finite metric spaces
    • Zbl 0634.46008 MR 0868175
    • Bourgain, J., Figiel, T., Milman, V.: On Hilbertian subsets of finite metric spaces. Israel J. Math. 55, 147-152 (1986) Zbl 0634.46008 MR 0868175
    • (1986) Israel J. Math , vol.55 , pp. 147-152
    • Bourgain, J.1    Figiel, T.2    Milman, V.3
  • 9
    • 18444387163 scopus 로고    scopus 로고
    • Approximation algorithms for the 0-extension problem
    • Zbl pre02135840 MR 2124008
    • Calinescu, G., Karloff, H., Rabani, Y.: Approximation algorithms for the 0-extension problem. SIAM J. Comput. 34, 358-372 (2004/05) Zbl pre02135840 MR 2124008
    • (2005) SIAM J. Comput , vol.34 , pp. 358-372
    • Calinescu, G.1    Karloff, H.2    Rabani, Y.3
  • 10
    • 33846602127 scopus 로고    scopus 로고
    • Callahan, P. B.: Dealing with higher dimensions: the well-separated pair decomposition and its applications. Ph.D. thesis, Dept. Comput. Sci., Johns Hopkins Univ., Baltimore, MD (1995)
    • Callahan, P. B.: Dealing with higher dimensions: the well-separated pair decomposition and its applications. Ph.D. thesis, Dept. Comput. Sci., Johns Hopkins Univ., Baltimore, MD (1995)
  • 11
    • 0029239056 scopus 로고
    • A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields
    • Zbl 0886.68078 MR 1370371
    • Callahan, P. B., Kosaraju, S.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. ACM 42, 67-90 (1995) Zbl 0886.68078 MR 1370371
    • (1995) J. ACM , vol.42 , pp. 67-90
    • Callahan, P.B.1    Kosaraju, S.2
  • 12
    • 20744432321 scopus 로고    scopus 로고
    • Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
    • Philadelphia, PA, SIAM
    • Chawla, S., Gupta, A., Räcke, H.: Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut. In: SODA '05: Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms (Philadelphia, PA), SIAM, 102-111 (2005)
    • (2005) SODA '05: Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms , pp. 102-111
    • Chawla, S.1    Gupta, A.2    Räcke, H.3
  • 13
    • 33846591739 scopus 로고    scopus 로고
    • Clarkson, K. L.: Nearest-neighbor searching and metric space dimensions. In: Nearest-Neighbor Methods for Learning and Vision: Theory and Practice. MIT Press (2005); available at http://cm.bell-labs.com/who/clarkson/nn_survey/p.pdf [14] Cohen, E.: Fast algorithms for constructing t-spanners and paths with stretch t. SIAM J. Comput. 28, 210-236 (1999) Zbl 0915.68077 MR 1630461
    • Clarkson, K. L.: Nearest-neighbor searching and metric space dimensions. In: Nearest-Neighbor Methods for Learning and Vision: Theory and Practice. MIT Press (2005); available at http://cm.bell-labs.com/who/clarkson/nn_survey/p.pdf [14] Cohen, E.: Fast algorithms for constructing t-spanners and paths with stretch t. SIAM J. Comput. 28, 210-236 (1999) Zbl 0915.68077 MR 1630461
  • 14
    • 33846563777 scopus 로고    scopus 로고
    • Cormen, T. H., Leiserson, C. E., Rivest, R. L.: Introduction to Algorithms. MIT Press (1990) Zbl 1047.68161 MR 1066870
    • Cormen, T. H., Leiserson, C. E., Rivest, R. L.: Introduction to Algorithms. MIT Press (1990) Zbl 1047.68161 MR 1066870
  • 15
    • 33846592661 scopus 로고    scopus 로고
    • Erdo″s, P.: Extremal problems in graph theory. In: Theory of Graphs and its Applications (Smolenice, 1963), Publ. House Czechoslovak Acad. Sci., Prague, 29-36 (1964) Zbl 0161.20501 MR 0180500
    • Erdo″s, P.: Extremal problems in graph theory. In: Theory of Graphs and its Applications (Smolenice, 1963), Publ. House Czechoslovak Acad. Sci., Prague, 29-36 (1964) Zbl 0161.20501 MR 0180500
  • 16
    • 4544291996 scopus 로고    scopus 로고
    • A tight bound on approximating arbitrary metrics by tree metrics
    • Zbl 1071.68082 MR 2087946
    • Fakcharoenphol, J., Rao, S., Talwar, K.: A tight bound on approximating arbitrary metrics by tree metrics. J. Comput. System Sci. 69, 485-497 (2004) Zbl 1071.68082 MR 2087946
    • (2004) J. Comput. System Sci , vol.69 , pp. 485-497
    • Fakcharoenphol, J.1    Rao, S.2    Talwar, K.3
  • 17
    • 33846644783 scopus 로고    scopus 로고
    • Ann. of Math, to appear; available at
    • m smooth functions to data I. Ann. of Math., to appear; available at http://www.math.princeton.edu/ facultypapers/Fefferman/FittingData_Part_I.pdf (2005)
    • (2005) m smooth functions to data I
    • Fefferman, C.1    Klartag, B.2
  • 18
    • 84968754795 scopus 로고    scopus 로고
    • Gudmundsson, J., Levcopoulos, C., Narasimhan, G., Smid, M.: Approximate distance oracles for geometric graphs. In: SODA '02: Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (Philadelphia, PA, 2002), SIAM, 828-837 (2002) Zbl 1058.65028
    • Gudmundsson, J., Levcopoulos, C., Narasimhan, G., Smid, M.: Approximate distance oracles for geometric graphs. In: SODA '02: Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (Philadelphia, PA, 2002), SIAM, 828-837 (2002) Zbl 1058.65028
  • 19
    • 33749260659 scopus 로고    scopus 로고
    • Fast construction of nets in low dimensional metrics and their applications
    • MR 2217141
    • Har-Peled, S., Mendel, M.: Fast construction of nets in low dimensional metrics and their applications. SIAM J. Comput. 35, 1148-1184 (2006) MR 2217141
    • (2006) SIAM J. Comput , vol.35 , pp. 1148-1184
    • Har-Peled, S.1    Mendel, M.2
  • 20
    • 0021426157 scopus 로고
    • Fast algorithms for finding nearest common ancestors
    • Zbl 0535.68022 MR 0739994
    • Harel, D., Tarjan, R. E.: Fast algorithms for finding nearest common ancestors. SIAM J. Comput. 13, 338-355 (1984) Zbl 0535.68022 MR 0739994
    • (1984) SIAM J. Comput , vol.13 , pp. 338-355
    • Harel, D.1    Tarjan, R.E.2
  • 21
    • 33846632190 scopus 로고    scopus 로고
    • Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext, Springer, New York (2001) Zbl 0985.46008 MR 1800917
    • Heinonen, J.: Lectures on Analysis on Metric Spaces. Universitext, Springer, New York (2001) Zbl 0985.46008 MR 1800917
  • 22
    • 24644489770 scopus 로고    scopus 로고
    • Nearest neighbors in high-dimensional spaces
    • 2nd ed, CRC Press, Boca Raton, FL
    • Indyk, P.: Nearest neighbors in high-dimensional spaces. In: Handbook of Discrete and Computational Geometry, 2nd ed., CRC Press, Boca Raton, FL, 877-892 (2004)
    • (2004) Handbook of Discrete and Computational Geometry , pp. 877-892
    • Indyk, P.1
  • 23
    • 26844509176 scopus 로고    scopus 로고
    • Measured descent: A new embedding method for finite metrics
    • Zbl pre02228663
    • Krauthgamer, R., Lee, J. R., Mendel, M., Naor, A.: Measured descent: A new embedding method for finite metrics. Geom. Funct. Anal. 15, 839-858 (2005) Zbl pre02228663
    • (2005) Geom. Funct. Anal , vol.15 , pp. 839-858
    • Krauthgamer, R.1    Lee, J.R.2    Mendel, M.3    Naor, A.4
  • 24
    • 15544369683 scopus 로고    scopus 로고
    • Extending Lipschitz functions via random metric partitions
    • Zbl 1074.46004 MR 2129708
    • Lee, J. R., Naor, A.: Extending Lipschitz functions via random metric partitions. Invent. Math. 160, 59-95 (2005) Zbl 1074.46004 MR 2129708
    • (2005) Invent. Math , vol.160 , pp. 59-95
    • Lee, J.R.1    Naor, A.2
  • 25
    • 0030445230 scopus 로고    scopus 로고
    • On the distortion required for embedding finite metric space into normed spaces
    • Zbl 0851.46007 MR 1380650
    • Matoušek, J.: On the distortion required for embedding finite metric space into normed spaces. Israel J. Math. 93, 333-344 (1996) Zbl 0851.46007 MR 1380650
    • (1996) Israel J. Math , vol.93 , pp. 333-344
    • Matoušek, J.1
  • 26
    • 4344706090 scopus 로고    scopus 로고
    • Euclidean quotients of finite metric spaces
    • Zbl pre02136510 MR 2101227
    • Mendel, M., Naor, A.: Euclidean quotients of finite metric spaces. Adv. Math. 189, 451-494 (2004) Zbl pre02136510 MR 2101227
    • (2004) Adv. Math , vol.189 , pp. 451-494
    • Mendel, M.1    Naor, A.2
  • 28
    • 23844459328 scopus 로고    scopus 로고
    • Informative labeling schemes for graphs
    • Zbl 1077.68078 MR 2160465
    • Peleg, D.: Informative labeling schemes for graphs. Theoret. Comput. Sci. 340, 577-593 (2005) Zbl 1077.68078 MR 2160465
    • (2005) Theoret. Comput. Sci , vol.340 , pp. 577-593
    • Peleg, D.1
  • 29
    • 26444492566 scopus 로고    scopus 로고
    • Roditty, L., Thorup, M., Zwick, U.: Deterministic constructions of approximate distance oracles and spanners. In: Automata, Languages and Programming, Lecture Notes in Comput. Sei. 3580, Springer, Berlin, 261-272 (2005) Zbl 1082.68087 MR 2184637
    • Roditty, L., Thorup, M., Zwick, U.: Deterministic constructions of approximate distance oracles and spanners. In: Automata, Languages and Programming, Lecture Notes in Comput. Sei. 3580, Springer, Berlin, 261-272 (2005) Zbl 1082.68087 MR 2184637
  • 30
    • 4544336800 scopus 로고    scopus 로고
    • Bypassing the embedding: Algorithms for low dimensional metrics
    • New York, ACM Press
    • Talwar, K.: Bypassing the embedding: algorithms for low dimensional metrics. In: STOC '04: Proc. 36th Annual ACM Symposium on Theory of Computing (New York, 2004). ACM Press, 281-290 (2004)
    • (2004) STOC '04: Proc. 36th Annual ACM Symposium on Theory of Computing , pp. 281-290
    • Talwar, K.1
  • 31
    • 26444519480 scopus 로고    scopus 로고
    • Approximate distance oracles
    • MR 2143683
    • Thorup, M., Zwick, U.: Approximate distance oracles. J. ACM 52, 1-24 (2005) MR 2143683
    • (2005) J. ACM , vol.52 , pp. 1-24
    • Thorup, M.1    Zwick, U.2
  • 32
    • 0000662711 scopus 로고    scopus 로고
    • Vaidya, P.M.: An O (n log n ) algorithm for the all-nearest-neighbors problem. Discrete Cornput. Geom. 4, 101-115 (1989) Zbl 0663.68058 MR 0973540
    • Vaidya, P.M.: An O (n log n ) algorithm for the all-nearest-neighbors problem. Discrete Cornput. Geom. 4, 101-115 (1989) Zbl 0663.68058 MR 0973540
  • 33
    • 84943271885 scopus 로고    scopus 로고
    • Zwick, U.: Exact and approximate distances in graphs - a survey. In: Algorithms - ESA 2001 (Århus), Lecture Notes in Comput. Sci. 2161, Springer, Berlin, 33-48 (2001) Zbl 1006.68543 MR 1913540
    • Zwick, U.: Exact and approximate distances in graphs - a survey. In: Algorithms - ESA 2001 (Århus), Lecture Notes in Comput. Sci. 2161, Springer, Berlin, 33-48 (2001) Zbl 1006.68543 MR 1913540


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.