\begin{thebibliography}{10}

\bibitem{AHU74}
A.~V. Aho, J.~E. Hopcroft, and J.~D. Ullman.
\newblock {\em The Design and Analysis of Computer Algorithms}.
\newblock Addison-Wesley Publishing Company, 1974.

\bibitem{Aleksandrov1996}
L.~Aleksandrov and H.~Djidjev.
\newblock Linear algorithms for partitioning embedded graphs of bounded genus.
\newblock {\em SIAM J. Discret. Math.}, 9(1):129--150, February 1996.

\bibitem{Aleksandrov2007}
Lyudmil Aleksandrov, Hristo Djidjev, Hua Guo, and Anil Maheshwari.
\newblock Partitioning planar graphs with costs and weights.
\newblock {\em J. Exp. Algorithmics}, 11, February 2007.

\bibitem{alon2004probabilistic}
N.~Alon and J.~H. Spencer.
\newblock {\em The probabilistic method}.
\newblock John Wiley \& Sons, 3rd edition, 2007.

\bibitem{Indyk06}
A.~Andoni and P.~Indyk.
\newblock Near-optimal hashing algorithms for approximate nearest neighbor in
  high dimensions.
\newblock In {\em Foundations of Computer Science, 2006. FOCS '06. 47th Annual
  IEEE Symposium on}, pages 459--468, 2006.

\bibitem{Appel2002}
Martin J.~B. Appel and Ralph~P. Russo.
\newblock {The connectivity of a graph on uniform points on $[0,1]^d$}.
\newblock {\em Statistics \& Probability Letters}, 60(4):351--357, 2002.

\bibitem{balister2008percolation}
P.~Balister, A.~Sarkar, and B.~Bollob{\'a}s.
\newblock Percolation, connectivity, coverage and colouring of random geometric
  graphs.
\newblock In {\em Handbook of Large-Scale Random Networks}, pages 117--142.
  Springer, 2008.

\bibitem{BKMS15}
Ahmad Biniaz, Evangelos Kranakis, Anil Maheshwari, and Michiel Smid.
\newblock Plane and planarity thresholds for random geometric graphs.
\newblock In {\em Proc.\ ALGOSENSORS 2015 (Patras, Greece)}, Lecture Notes in
  Computer Science, Berlin, Germany, 2015. Springer.

\bibitem{bollobas2001random}
B.~Bollob{\'a}s.
\newblock {\em Random graphs}.
\newblock Cambridge University Press, 2001.

\bibitem{Bollobas1987}
B{\'{e}}la Bollob{\'{a}}s and Andrew Thomason.
\newblock Threshold functions.
\newblock {\em Combinatorica}, 7(1):35--38, 1987.

\bibitem{Bollobas1998}
Béla Bollobás.
\newblock {\em Modern Graph Theory}.
\newblock Graduate texts in mathematics. Springer, Heidelberg, corrected
  edition, 1998.

\bibitem{Bondy1976}
J.~A. Bondy and U.~S.~R. Murty.
\newblock {\em Graph Theory with Applications}.
\newblock Elsevier, New York, 1976.

\bibitem{boruuvka1926a}
Otakar Borůvka.
\newblock O jist{\'e}m probl{\'e}mu minim{\'a}ln{\'\i}m.
\newblock {\em Práce mor. přírodověd. spol. v Brně III}, 3:37--58, 1926.

\bibitem{boruuvka1926b}
Otakar Borůvka.
\newblock P{\v{r}}{\'\i}sp{\v{e}}vek k {\v{r}}e{\v{s}}en{\'\i} ot{\'a}zky
  ekonomick{\'e} stavby elektrovodn{\'\i}ch s{\'\i}t{\'\i}.
\newblock {\em Elektrotechnick{\`y} obzor}, 15:153--154, 1926.

\bibitem{Bou85}
J.~Bourgain.
\newblock On lipschitz embedding of finite metric spaces in hilbert space.
\newblock {\em Israel Journal of Mathematics}, 52(1-2):46--52, 1985.

\bibitem{Bourgain1998}
Jean Bourgain and Gil Kalai.
\newblock Threshold intervals under group symmetries.
\newblock {\em Convex Geometric Analysis MSRI Publications Volume 34}, pages
  59--63, 1998.

\bibitem{Bradonjic2014}
Milan Bradonji\'{c} and Will Perkins.
\newblock On sharp thresholds in random geometric graphs.
\newblock In {\em Approximation, Randomization, and Combinatorial Optimization.
  Algorithms and Techniques, {APPROX/RANDOM}}, pages 500--514, 2014.

\bibitem{Broder98}
Andrei~Z. Broder, Moses Charikar, Alan~M. Frieze, and Michael Mitzenmacher.
\newblock Min-wise independent permutations.
\newblock {\em Journal of Computer and System Sciences}, 60:327--336, 1998.

\bibitem{Broder97}
A.Z. Broder.
\newblock On the resemblance and containment of documents.
\newblock In {\em Compression and Complexity of Sequences 1997. Proceedings},
  pages 21--29, 1997.

\bibitem{chan1998}
Timothy~M. Chan.
\newblock Backwards analysis of the {K}arger-{K}lein-{T}arjan algorithm for
  minimum spanning.
\newblock {\em Inf. Process. Lett.}, 67(6):303--304, 1998.

\bibitem{CLRS}
T.~H. Cormen, C.~E. Leiserson, R.~L. Rivest, and C.~Stein.
\newblock {\em Introduction to Algorithms}.
\newblock The MIT Press, 3rd edition, 2009.

\bibitem{clrs2009}
Thomas~H. Cormen, Charles~E. Leiserson, Ronald~L. Rivest, and Clifford Stein.
\newblock {\em Introduction to Algorithms, Third Edition}.
\newblock The MIT Press, 3rd edition, 2009.

\bibitem{DG02}
Sanjoy Dasgupta and Anupam Gupta.
\newblock An elementary proof of a theorem of {J}ohnson and {L}indenstrauss.
\newblock {\em Random Struct. Algorithms}, 22(1):60--65, 2003.

\bibitem{Indyk04}
Mayur Datar and Piotr Indyk.
\newblock Locality-sensitive hashing scheme based on p-stable distributions.
\newblock In {\em In SCG ’04: Proceedings of the twentieth annual symposium
  on Computational geometry}, pages 253--262. ACM Press, 2004.

\bibitem{dePaula10}
L.B. de~Paula, R.S. Villaca, and M.F. Magalhaes.
\newblock A locality sensitive hashing approach for conceptual classification.
\newblock In {\em Semantic Computing (ICSC), 2010 IEEE Fourth International
  Conference on}, pages 408--413, 2010.

\bibitem{dijkstra1959}
E.W. Dijkstra.
\newblock A note on two problems in connexion with graphs.
\newblock {\em Numerische Mathematik}, 1(1):269--271, 1959.

\bibitem{dixon1992}
B.~Dixon, M.~Rauch, and R.~Tarjan.
\newblock Verification and sensitivity analysis of minimum spanning trees in
  linear time.
\newblock {\em SIAM Journal on Computing}, 21(6):1184--1192, 1992.

\bibitem{DP09}
D.P. Dubhashi and A.~Panconesi.
\newblock {\em Concentration of measure for the analysis of randomized
  algorithms}.
\newblock Cambridge University Press, 2009.

\bibitem{erd6s1960evolution}
P.~Erd\"{o}s and A.~R{\'e}nyi.
\newblock On the evolution of random graphs.
\newblock {\em Publ. Math. Inst. Hungar. Acad. Sci}, 5:17--61, 1960.

\bibitem{Even79}
Shimon Even.
\newblock {\em Graph Algorithms}.
\newblock W. H. Freeman \& Co., New York, NY, USA, 1979.

\bibitem{Frederickson1987}
Greg~N. Frederickson.
\newblock Fast algorithms for shortest paths in planar graphs, with
  applications.
\newblock {\em SIAM J. Comput.}, 16(6):1004--1022, 1987.

\bibitem{Frederickson1991}
Greg~N. Frederickson.
\newblock Optimal algorithms for tree partitioning.
\newblock In {\em Proceedings of the Second Annual ACM-SIAM Symposium on
  Discrete Algorithms}, SODA '91, pages 168--177, Philadelphia, PA, USA, 1991.
  Society for Industrial and Applied Mathematics.

\bibitem{friedgut1996every}
E.~Friedgut and G.~Kalai.
\newblock Every monotone graph property has a sharp threshold.
\newblock {\em Proceedings of the American Mathematical Society},
  124(10):2993--3002, 1996.

\bibitem{GS72}
D.~Gale and L.~S. Shapley.
\newblock College admissions and the stability of marriage.
\newblock {\em The American Mathematical Monthly}, 69(1):9--15, 1972.

\bibitem{gilbert1959random}
E.~Gilbert.
\newblock Random graphs.
\newblock {\em The Annals of Mathematical Statistics}, pages 1141--1144, 1959.

\bibitem{gilbert1961random}
E.~Gilbert.
\newblock Random plane networks.
\newblock {\em Journal of the Society for Industrial \& Applied Mathematics},
  9(4):533--543, 1961.

\bibitem{Indyk97}
Aristides Gionis, Piotr Indyk, and Rajeev Motwani.
\newblock Similarity search in high dimensions via hashing.
\newblock pages 518--529, 1997.

\bibitem{Godehardt1996}
Erhard Godehardt and Jerzy Jaworski.
\newblock On the connectivity of a random interval graph.
\newblock {\em Random Struct. Algorithms}, 9(1-2):137--161, 1996.

\bibitem{goel2004sharp}
A.~Goel, S.~Rai, and B.~Krishnamachari.
\newblock Sharp thresholds for monotone properties in random geometric graphs.
\newblock In {\em Proceedings of STOC}, pages 580--586. ACM, 2004.

\bibitem{Gorisse12}
D.~Gorisse, M.~Cord, and F.~Precioso.
\newblock Locality-sensitive hashing for chi2 distance.
\newblock {\em Pattern Analysis and Machine Intelligence, IEEE Transactions
  on}, 34(2):402--409, 2012.

\bibitem{Gupta1998}
Piyush Gupta and P.~R. Kumar.
\newblock Critical power for asymptotic connectivity in wireless networks.
\newblock In {\em Stochastic Analysis, Control, Optimization and Applications},
  pages 547--566, 1998.

\bibitem{hagerup2010}
Torben Hagerup.
\newblock An even simpler linear-time algorithm for verifying minimum spanning
  trees.
\newblock In Christophe Paul and Michel Habib, editors, {\em Graph-Theoretic
  Concepts in Computer Science}, volume 5911 of {\em Lecture Notes in Computer
  Science}, pages 178--189. Springer Berlin Heidelberg, 2010.

\bibitem{HR88}
Torben Hagerup and Christine R{\"u}b.
\newblock A guided tour of {C}hernoff bounds.
\newblock {\em Inf. Process. Lett.}, 33(6):305--308, 1990.

\bibitem{hall1985coverage}
P.~Hall.
\newblock On the coverage of $ k $-dimensional space by $ k $-dimensional
  spheres.
\newblock {\em The Annals of Probability}, 13(3):991--1002, 1985.

\bibitem{H-Book69}
Frank Harary.
\newblock {\em Graph theory}.
\newblock Addison-Wesley, 1991.

\bibitem{harel1984}
D.~Harel and R.~Tarjan.
\newblock Fast algorithms for finding nearest common ancestors.
\newblock {\em SIAM Journal on Computing}, 13(2):338--355, 1984.

\bibitem{harel1980}
Dov Harel.
\newblock A linear time algorithm for the lowest common ancestors problem.
\newblock In {\em Foundations of Computer Science, 1980., 21st Annual Symposium
  on}, pages 308--319, 1980.

\bibitem{Hu05}
S.~Hu.
\newblock Efficient video retrieval by locality sensitive hashing.
\newblock In {\em Acoustics, Speech, and Signal Processing, 2005. Proceedings.
  (ICASSP '05). IEEE International Conference on}, volume~2, pages 449--452,
  2005.

\bibitem{Indyk98}
Piotr Indyk and Rajeev Motwani.
\newblock Approximate nearest neighbors: Towards removing the curse of
  dimensionality.
\newblock In {\em Proceedings of the Thirtieth Annual ACM Symposium on Theory
  of Computing}, STOC '98, pages 604--613, New York, NY, USA, 1998. ACM.

\bibitem{Ir85}
Robert~W. Irving.
\newblock An efficient algorithm for the "stable roommates" problem.
\newblock {\em J. Algorithms}, 6(4):577--595, 1985.

\bibitem{janson1986random}
S.~Janson.
\newblock Random coverings in several dimensions.
\newblock {\em Acta Mathematica}, 156(1):83--118, 1986.

\bibitem{Jeon12}
Woojay Jeon and Yan-Ming Cheng.
\newblock Efficient speaker search over large populations using kernelized
  locality-sensitive hashing.
\newblock In {\em Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE
  International Conference on}, pages 4261--4264, 2012.

\bibitem{Jing08}
Yushi Jing and S.~Baluja.
\newblock Visualrank: Applying pagerank to large-scale image search.
\newblock {\em Pattern Analysis and Machine Intelligence, IEEE Transactions
  on}, 30(11):1877--1890, 2008.

\bibitem{Kala13}
K.A. Kala and K.~Chitharanjan.
\newblock Locality sensitive hashing based incremental clustering for creating
  affinity groups in hadoop; hdfs - an infrastructure extension.
\newblock In {\em Circuits, Power and Computing Technologies (ICCPCT), 2013
  International Conference on}, pages 1243--1249, 2013.

\bibitem{Kang04}
Zixiang Kang, Wei~Tsang Ooi, and Qibin Sun.
\newblock Hierarchical, non-uniform locality sensitive hashing and its
  application to video identification.
\newblock In {\em Multimedia and Expo, 2004. ICME '04. 2004 IEEE International
  Conference on}, volume~1, pages 743--746 Vol.1, 2004.

\bibitem{karger1995}
David~R. Karger, Philip~N. Klein, and Robert~E. Tarjan.
\newblock A randomized linear-time algorithm to find minimum spanning trees.
\newblock {\em J. ACM}, 42(2):321--328, March 1995.

\bibitem{king1997}
V.~King.
\newblock A simpler minimum spanning tree verification algorithm.
\newblock {\em Algorithmica}, 18(2):263--270, 1997.

\bibitem{king1995}
Valerie King.
\newblock A simpler minimum spanning tree verification algorithm.
\newblock In SelimG. Akl, Frank Dehne, Jörg-Rüdiger Sack, and Nicola Santoro,
  editors, {\em Algorithms and Data Structures}, volume 955 of {\em Lecture
  Notes in Computer Science}, pages 440--448. Springer Berlin Heidelberg, 1995.

\bibitem{klein1994}
Philip~N. Klein and Robert~E. Tarjan.
\newblock A randomized linear-time algorithm for finding minimum spanning
  trees.
\newblock In {\em Proceedings of the twenty-sixth annual ACM symposium on
  Theory of computing}, STOC '94, pages 9--15, New York, NY, USA, 1994. ACM.

\bibitem{KT05}
Jon Kleinberg and Eva Tardos.
\newblock {\em Algorithm Design}.
\newblock Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 2005.

\bibitem{K1}
Donald~E. Knuth.
\newblock {\em The art of computer programming, volume 1-3}.
\newblock Addison Wesley Longman Publishing Co., Inc., Redwood City, CA, USA,
  1998.

\bibitem{komlos1984}
J.~Komlos.
\newblock Linear verification for spanning trees.
\newblock In {\em Foundations of Computer Science, 1984. 25th Annual Symposium
  on}, pages 201--206, 1984.

\bibitem{komlos1985}
J.~Komlós.
\newblock Linear verification for spanning trees.
\newblock {\em Combinatorica}, 5(1):57--65, 1985.

\bibitem{Kozen}
D.~Kozen.
\newblock {\em The design and analysis of algorithms}.
\newblock Springer, 1992.

\bibitem{Krishnamachari2002}
Bhaskar Krishnamachari, Stephen~B. Wicker, R\'{a}mon B\'{e}jar, and Marc
  Pearlman.
\newblock Critical density thresholds in distributed wireless networks.
\newblock In {\em Communications, information and network security}, 2002.

\bibitem{Kulis12}
B.~Kulis and K.~Grauman.
\newblock Kernelized locality-sensitive hashing.
\newblock {\em Pattern Analysis and Machine Intelligence, IEEE Transactions
  on}, 34(6):1092--1104, 2012.

\bibitem{LT79}
Richard~J. Lipton and Robert~E. Tarjan.
\newblock A separator theorem for planar graphs.
\newblock {\em SIAM Journal on Applied Mathematics}, 36(2):177--189, 1979.

\bibitem{LP-Matching86}
L.~Lov\'asz and M.D. Plummer.
\newblock {\em Matching Theory}.
\newblock Akad\'emiai Kiad\'o, Budapest, 1986.
\newblock Also published as Vol. 121 of the North-Holland Mathematics Studies,
  North-Holland Publishing, Amsterdam.

\bibitem{AM12}
A.~Maheshwari and M.~Smid.
\newblock {\em Introduction to Theory of Computation}.
\newblock Free Online, 2012.

\bibitem{Manber94}
Udi Manber.
\newblock Finding similar files in a large file system.
\newblock In {\em in Proceedings of the USENIX Winter 1994 Technical
  Conference}, pages 1--10, 1994.

\bibitem{Mat02}
Jiri Matousek.
\newblock {\em Lectures on Discrete Geometry}.
\newblock Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2002.

\bibitem{Mat96}
Jiří Matoušek.
\newblock On the distortion required for embedding finite metric spaces into
  normed spaces.
\newblock {\em Israel Journal of Mathematics}, 93(1):333--344, 1996.

\bibitem{Mccolm2001}
Gregory~L. Mccolm.
\newblock Threshold functions for random graphs on a line segment.
\newblock {\em Combinatorics, Probability and Computing}, 13:373--387, 2001.

\bibitem{M70}
P.L. Meyer.
\newblock {\em Introductory probability and statistical applications}.
\newblock Addison-Wesley, Boston, MA, USA, 1970.

\bibitem{Miller1997}
Gary~L. Miller, Shang-Hua Teng, William Thurston, and Stephen~A. Vavasis.
\newblock Separators for sphere-packings and nearest neighbor graphs.
\newblock {\em J. ACM}, 44(1):1--29, January 1997.

\bibitem{MU05}
Michael Mitzenmacher and Eli Upfal.
\newblock {\em Probability and Computing: Randomized Algorithms and
  Probabilistic Analysis}.
\newblock Cambridge University Press, New York, NY, USA, 2005.

\bibitem{Mondal13}
Tanmoy Mondal, Nicolas Ragot, Jean-Yves Ramel, and Umapada Pal.
\newblock A fast word retrieval technique based on kernelized locality
  sensitive hashing.
\newblock In {\em Document Analysis and Recognition (ICDAR), 2013 12th
  International Conference on}, pages 1195--1199, 2013.

\bibitem{MR95}
Rajeev Motwani and Prabhakar Raghavan.
\newblock {\em Randomized algorithms}.
\newblock Cambridge University Press, New York, NY, USA, 1995.

\bibitem{motwani1995}
Rajeev Motwani and Prabhakar Raghavan.
\newblock {\em Randomized algorithms}.
\newblock Cambridge University Press, New York, NY, USA, 1995.

\bibitem{nesetril2001}
Jaroslav Nešetřil, Eva Milková, and Helena Nešetřilová.
\newblock Otakar borůvka on minimum spanning tree problem translation of both
  the 1926 papers, comments, history.
\newblock {\em Discrete Mathematics}, 233(1–3):3 -- 36, 2001.
\newblock <ce:title>Czech and Slovak 2</ce:title>.

\bibitem{Panchapakesan2001}
Padma Panchapakesan and D~Manjunath.
\newblock On the transmission range in dense ad hoc radio networks.
\newblock In {\em Proceedings of IEEE Signal Processing Communication (SPCOM)},
  2001.

\bibitem{penrose1997longest}
Mathew~D. Penrose.
\newblock The longest edge of the random minimal spanning tree.
\newblock {\em The annals of applied probability}, pages 340--361, 1997.

\bibitem{Penrose1999}
Mathew~D. Penrose.
\newblock On $k$-connectivity for a geometric random graph.
\newblock {\em Random Struct. Algorithms}, 15(2):145--164, 1999.

\bibitem{penrose2003random}
Mathew~D. Penrose.
\newblock {\em Random geometric graphs}, volume~5.
\newblock Oxford University Press Oxford, 2003.

\bibitem{RLU12}
Anand Rajaraman and Jeffrey~David Ullman.
\newblock {\em Mining of Massive Datasets}.
\newblock Cambridge University Press, New York, NY, USA, 2011.

\bibitem{Rasheed12}
Z.~Rasheed, H.~Rangwala, and D.~Barbara.
\newblock Lsh-div: Species diversity estimation using locality sensitive
  hashing.
\newblock In {\em Bioinformatics and Biomedicine (BIBM), 2012 IEEE
  International Conference on}, pages 1--6, 2012.

\bibitem{Rosen}
Kenneth~H. Rosen.
\newblock {\em Discrete Mathematics and Its Applications}.
\newblock McGraw-Hill Higher Education, 5th edition, 2002.

\bibitem{schieber1988}
Baruch Schieber and Uzi Vishkin.
\newblock On finding lowest common ancestors: Simplification and
  parallelization.
\newblock In JohnH. Reif, editor, {\em VLSI Algorithms and Architectures},
  volume 319 of {\em Lecture Notes in Computer Science}, pages 111--123.
  Springer New York, 1988.

\bibitem{spencer1987ten}
J.~H. Spencer.
\newblock {\em Ten lectures on the probabilistic method}, volume~52.
\newblock SIAM, 1987.

\bibitem{STRA69}
V.~Strassen.
\newblock Gaussian elimination is not optimal.
\newblock {\em Numerische Mathematik}, 13:354--356, 1969.

\bibitem{tarjan1983}
Robert Tarjan.
\newblock {\em Data Structures and Network Algorithms}, volume~44, chapter 6.
  Minimum Spanning Trees, pages 71--83.
\newblock SIAM, 1983.

\bibitem{tarjan1975}
Robert~Endre Tarjan.
\newblock Efficiency of a good but not linear set union algorithm.
\newblock {\em J. ACM}, 22(2):215--225, April 1975.

\bibitem{tarjan1979}
Robert~Endre Tarjan.
\newblock Applications of path compression on balanced trees.
\newblock {\em J. ACM}, 26(4):690--715, October 1979.

\bibitem{Wang12}
Qiang Wang, Zhiyuan Guo, Gang Liu, and Jun Guo.
\newblock Entropy based locality sensitive hashing.
\newblock In {\em Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE
  International Conference on}, pages 1045--1048, 2012.

\end{thebibliography}
