Carathéodory's existence theorem: Difference between revisions

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[[File:Ken Clarkson SoCG 2011.jpg|thumb|Ken Clarkson at SoCG 2011]]
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'''Kenneth Lee Clarkson''' is an American [[computer scientist]] known for his research in [[computational geometry]]. He is a researcher at the [[IBM Almaden Research Center]], and co-editor-in-chief of the ''Journal of Computational Geometry''.<ref>[http://jocg.org/index.php/jocg/about/editorialTeam Editorial team], Journal of Computational Geometry. Retrieved 2009-05-30.</ref>


==Biography==
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Clarkson received his Ph.D. from [[Stanford University]] in 1984, under the supervision of [[Andrew Yao]].<ref>[http://sigact.acm.org/cgi-bin/genealogy.cgi?file=database-C.html&from=Clarkson,Ken&to=endhere TCS Genealogy], [[Association for Computing Machinery]].</ref> Until 2007 he worked for [[Bell Labs]].<ref>[http://cm.bell-labs.com/who/clarkson/ Clarkson's page at Bell Labs], retrieved January 15, 2009.</ref>
 
In 1998 he was co-chair of the [[Association for Computing Machinery|ACM]] [[Symposium on Computational Geometry]].
 
==Research==
Clarkson's primary research interests are in [[computational geometry]].
 
His most highly cited paper, with [[Peter Shor]], uses [[random sampling]] to devise optimal [[randomized algorithm]]s for several problems of constructing geometric structures, following up on an earlier singly-authored paper by Clarkson on the same subject.<ref>{{citation
| last = Clarkson | first = Kenneth L.
| doi = 10.1007/BF02187879
| issue = 2
| journal = [[Discrete and Computational Geometry]]
| mr = 884226
| pages = 195–222
| title = New applications of random sampling in computational geometry
| volume = 2
| year = 1987}}.</ref><ref>{{citation
| last1 = Clarkson | first1 = Kenneth L.
| last2 = Shor | first2 = Peter W. | author2-link = Peter Shor
| doi = 10.1007/BF02187740
| issue = 5
| journal = [[Discrete and Computational Geometry]]
| mr = 1014736
| pages = 387–421
| title = Applications of random sampling in computational geometry. II
| volume = 4
| year = 1989}}.</ref>
It includes algorithms for finding all <math>k</math> intersections among a set of <math>n</math> [[line segment]]s in the plane in expected time <math>O(k+n\log n)</math>, finding the [[diameter]] of a set of <math>n</math> points in three dimensions in expected time <math>O(n\log n)</math>, and constructing the [[convex hull]] of <math>n</math> points in <math>d</math>-dimensional [[Euclidean space]] in expected time <math>O(n^{\lfloor d/2\rfloor}+n\log n)</math>. The same paper also uses random sampling to prove bounds in [[discrete geometry]], and in particular to give tight bounds on the number of [[K-set (geometry)|≤''k''-sets]].
 
Clarkson has also written highly cited papers on the complexity of arrangements of curves and surfaces,<ref>{{citation
| last1 = Clarkson | first1 = Kenneth L.
| last2 = Edelsbrunner | first2 = Herbert | author2-link = Herbert Edelsbrunner
| last3 = Guibas | first3 = Leonidas J. | author3-link = Leonidas J. Guibas
| last4 = Sharir | first4 = Micha | author4-link = Micha Sharir
| last5 = Welzl | first5 = Emo | author5-link = Emo Welzl
| doi = 10.1007/BF02187783
| issue = 2
| journal = Discrete and Computational Geometry
| mr = 1032370
| pages = 99–160
| title = Combinatorial complexity bounds for arrangements of curves and spheres
| volume = 5
| year = 1990}}.</ref> [[nearest neighbor search]],<ref>{{citation
| last = Clarkson | first = Kenneth L.
| doi = 10.1137/0217052
| issue = 4
| journal = SIAM Journal on Computing
| mr = 953296
| pages = 830–847
| title = A randomized algorithm for closest-point queries
| volume = 17
| year = 1988}}.</ref><ref>{{citation
| last = Clarkson | first = K. L.
| doi = 10.1007/PL00009449
| issue = 1
| journal = [[Discrete and Computational Geometry]]
| mr = 1692615
| pages = 63–93
| title = Nearest neighbor queries in metric spaces
| volume = 22
| year = 1999}}.</ref> [[motion planning]],<ref>{{citation
| last = Clarkson | first = K.
| contribution = Approximation algorithms for shortest path motion planning
| doi = 10.1145/28395.28402
| pages = 56–65
| title = Proc. 19th ACM Symposium on Theory of Computing
| year = 1987}}.</ref> and low-dimensional [[linear programming]] and [[LP-type problem]]s.<ref>{{citation
| last = Clarkson | first = Kenneth L.
| doi = 10.1145/201019.201036
| issue = 2
| journal = [[Journal of the ACM]]
| mr = 1409744
| pages = 488–499
| title = Las Vegas algorithms for linear and integer programming when the dimension is small
| volume = 42
| year = 1995}}.</ref>
 
==Awards and honors==
In 2008 Clarkson was elected a [[Fellow]] of the ACM for his "contributions to computational geometry."<ref>[http://fellows.acm.org/fellow_citation.cfm?id=4491536&srt=year&year=2008 ACM Fellow citation].</ref>
 
==References==
{{reflist}}
 
==External links==
*[http://researcher.watson.ibm.com/researcher/view.php?person=us-klclarks Clarkson's web page at IBM]
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Clarkson, Kenneth L.
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION =
| DATE OF BIRTH    =
| PLACE OF BIRTH    =
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Clarkson, Kenneth L.}}
[[Category:Year of birth missing (living people)]]
[[Category:Living people]]
[[Category:Researchers in geometric algorithms]]
[[Category:Stanford University alumni]]
[[Category:Fellows of the Association for Computing Machinery]]

Latest revision as of 16:01, 7 February 2014

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