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Encoding Range Minimum Queries∗
"... We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to preprocess A and create a data structure that can answer the query RMQ(i, j), which returns the index containing the smallest element in A[i..j], without access to the ar ..."
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We consider the problem of encoding range minimum queries (RMQs): given an array A[1..n] of distinct totally ordered values, to preprocess A and create a data structure that can answer the query RMQ(i, j), which returns the index containing the smallest element in A[i..j], without access
On Cartesian Trees and Range Minimum Queries
"... We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cacheoblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree of a tree for the bottleneck edge query problem on trees and undirected graphs, ..."
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We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cacheoblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree of a tree for the bottleneck edge query problem on trees and undirected graphs
Optimal Succinctness for Range Minimum Queries
"... Abstract. For an array A of n objects from a totally ordered universe, a range minimum query rmq A(i, j) asks for the position of the minimum element in the subarray A[i, j]. We focus on the setting where the array A is static and known in advance, and can hence be preprocessed into a scheme in ord ..."
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Cited by 35 (4 self)
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Abstract. For an array A of n objects from a totally ordered universe, a range minimum query rmq A(i, j) asks for the position of the minimum element in the subarray A[i, j]. We focus on the setting where the array A is static and known in advance, and can hence be preprocessed into a scheme
TwoDimensional Range Minimum Queries
, 2007
"... We consider the twodimensional Range Minimum Query problem: for a static (m × n)matrix of size N = mn which may be preprocessed, answer online queries of the form “where is the position of a minimum element in an axisparallel rectangle?”. Unlike the onedimensional version of this problem which ..."
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Cited by 13 (2 self)
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We consider the twodimensional Range Minimum Query problem: for a static (m × n)matrix of size N = mn which may be preprocessed, answer online queries of the form “where is the position of a minimum element in an axisparallel rectangle?”. Unlike the onedimensional version of this problem which
Data structures for range minimum queries in multidimensional arrays
 In Proceedings of the 20th Annual ACMSIAM Symposium on Discrete Algorithms
, 2010
"... Given a ddimensional array A with N entries, the Range Minimum Query (RMQ) asks for the minimum element within a contiguous subarray of A. The 1D RMQ problem has been studied intensively because of its relevance to the Nearest Common Ancestor problem and its important use in stringology. If constan ..."
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Cited by 14 (0 self)
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Given a ddimensional array A with N entries, the Range Minimum Query (RMQ) asks for the minimum element within a contiguous subarray of A. The 1D RMQ problem has been studied intensively because of its relevance to the Nearest Common Ancestor problem and its important use in stringology
On (Dynamic) Range Minimum Queries in External Memory
"... Abstract. We study the onedimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + N+Q ..."
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Cited by 2 (1 self)
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Abstract. We study the onedimensional range minimum query (RMQ) problem in the external memory model. We provide the first spaceoptimal solution to the batched static version of the problem. On an instance with N elements and Q queries, our solution takes Θ(sort(N + N+Q
Two Dimensional Range Minimum Queries and Fibonacci Lattices
"... Abstract. Given a matrix of size N, two dimensional range minimum queries (2DRMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study tradeoffs between the query time and the additional space used by indexing data structures that support 2DRMQs. Using a ..."
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Cited by 4 (2 self)
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Abstract. Given a matrix of size N, two dimensional range minimum queries (2DRMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study tradeoffs between the query time and the additional space used by indexing data structures that support 2DRMQs. Using
Range Minimum Queries: Simple and Optimal, At Last!
, 2008
"... For an array A of n objects from a totally ordered universe, a range minimum query rmqA(i, j) asks for the position of the minimum element in the subarray A[i, j]. This fundamental algorithmic problem has applications in string processing, text indexing, text compression, document retrieval, and gr ..."
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For an array A of n objects from a totally ordered universe, a range minimum query rmqA(i, j) asks for the position of the minimum element in the subarray A[i, j]. This fundamental algorithmic problem has applications in string processing, text indexing, text compression, document retrieval
SpaceEfficient Preprocessing Schemes for Range Minimum Queries on Static Arrays
, 2009
"... Given a static array of n totally ordered object, the range minimum query problem is to build an additional data structure that allows to answer subsequent online queries of the form “what is the position of a minimum element in the subarray ranging from i to j? ” efficiently. We focus on two sett ..."
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Cited by 47 (3 self)
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Given a static array of n totally ordered object, the range minimum query problem is to build an additional data structure that allows to answer subsequent online queries of the form “what is the position of a minimum element in the subarray ranging from i to j? ” efficiently. We focus on two
Succinct representations of binary trees for range minimum queries, in:
 of Lecture Notes in Computer Science,
, 2012
"... Abstract. We provide two succinct representations of binary trees that can be used to represent the Cartesian tree of an array A of size n. Both the representations take the optimal 2n + o(n) bits of space in the worst case and support range minimum queries (RMQs) in O(1) time. The first one is a m ..."
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Cited by 12 (3 self)
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Abstract. We provide two succinct representations of binary trees that can be used to represent the Cartesian tree of an array A of size n. Both the representations take the optimal 2n + o(n) bits of space in the worst case and support range minimum queries (RMQs) in O(1) time. The first one is a
Results 1  10
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