en>Addbot: Bot: Removing Orphan Tag (No longer an Orphan) (Report Errors)

2013-01-09T02:42:15Z

Bot: Removing Orphan Tag (No longer an Orphan) (Report Errors)

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			Given an array <math>A[1,n]</math> of <math>n</math> objects taken from a [[Well-order\|well-ordered set]] (such as numbers), a '''Range Minimum Query''' (or '''RMQ''') from <math>i</math> to <math>j</math> asks for the position of a minimum element in the sub-array <math>A[i,j]</math>.

			For example, when <math>A=[0,5,2,5,4,3,1,6,3]</math>, then the answer to the range minimum query for the <math>A[3,8]=[2,5,4,3,1,6]</math> is <math>7</math>, as <math>A[7]=1</math>.

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			It is known that a <math>O(n)</math>-time preprocessing is sufficient to answer subsequent queries in <math>O(1)</math> time. The space of the resulting scheme is actually very small, namely <math>O(n)</math> bits (see {{harvtxt\|Fischer\|Heun\|2007}}).

			RMQs can be used to solve the [[lowest common ancestor]] problem, and is used as a tool for many tasks in exact and approximate [[string matching]].

			== References ==
			*{{citation
			\| last1 = Berkman \| first1 = Omer
			\| last2 = Vishkin \| first2 = Uzi \| author2-link = Uzi Vishkin
			\| title = Recursive Star-Tree Parallel Data Structure
			\| journal = SIAM Journal on Computing
			\| volume = 22
			\| issue = 2
			\| pages = 221–242
			\| year = 1993
			\| doi = 10.1137/0222017}}
			*{{citation
			\| last1 = Bender \| first = Michael
			\| last2 = Farach-Colton \| first2 = Martin
			\| contribution = The LCA Problem Revisited
			\| publisher = Springer-Verlag
			\| series = Lecture Notes in Computer Science
			\| volume = 1776
			\| year = 2000
			\| pages = 88–94
			\| doi = 10.1007/10719839_9}}
			*{{citation
			\| last1 = Fischer \| first1 = Johannes
			\| last2 = Heun \| first2 = Volker
			\| contribution = A New Succinct Representation of RMQ-Information and Improvements in the Enhanced Suffix Array.
			\| title = Proceedings of the International Symposium on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
			\| publisher = Springer-Verlag
			\| series = Lecture Notes in Computer Science
			\| volume = 4614
			\| year = 2007
			\| pages = 459–470
			\| doi = 10.1007/978-3-540-74450-4_41}}

			==External links==
			*[http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=lowestCommonAncestor#Range_Minimum_Query_%28RMQ%29 An article on Range Minimum Queries on TopCoder]
			*[http://wcipeg.com/wiki/RMQ Range Minimum Query article on PEGWiki / P3G]

			[[Category:Search algorithms]]

en>Tom Morris: cleanup, replaced: due to the fact that → because using AWB

2011-03-02T22:53:39Z

cleanup, replaced: due to the fact that → because using AWB

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en>Addbot: Bot: Removing Orphan Tag (No longer an Orphan) (Report Errors)

en>Tom Morris: cleanup, replaced: due to the fact that → because using AWB