Space efficient data structures for nearest larger neighbor

Given a sequence of n elements from a totally ordered set, and a position in the sequence, the nearest larger neighbor (NLN) query returns the position of the element which is closest to the query position, and is larger than the element at the query position. The problem of finding the nearest larger neighbors of all the elements in a one-dimensional array has attracted interest due to its applications for parenthesis matching and in computational geometry 1-3. We consider a data structure version of this problem, which is to preprocess a given sequence of elements to construct a data structure that can answer NLN queries efficiently. We consider time-space tradeoffs for the problem in both the indexing and the encoding models when the input is in a one dimensional array, and also initiate the study of this problem on two-dimensional arrays.

[1]  S. Srinivasa Rao,et al.  Space Efficient Data Structures for Nearest Larger Neighbor , 2014, IWOCA.

[2]  Uzi Vishkin,et al.  Optimal Doubly Logarithmic Parallel Algorithms Based on Finding All Nearest Smaller Values , 1993, J. Algorithms.

[3]  Guy Jacobson,et al.  Space-efficient static trees and graphs , 1989, 30th Annual Symposium on Foundations of Computer Science.

[4]  Johannes Fischer.  Combined data structure for previous- and next-smaller-values , 2011, Theor. Comput. Sci..

[5]  David G. Kirkpatrick,et al.  Time-Space Tradeoffs for All-Nearest-Larger-Neighbors Problems , 2013, WADS.

[6]  Gerth Stølting Brodal,et al.  The Encoding Complexity of Two Dimensional Range Minimum Data Structures , 2013, ESA.

[7]  Gonzalo Navarro,et al.  Faster entropy-bounded compressed suffix trees , 2009, Theor. Comput. Sci..

[8]  Rajeev Raman,et al.  Succinct Representations of Binary Trees for Range Minimum Queries , 2012, COCOON.

[9]  Rajeev Raman,et al.  Compact Encodings and Indexes for the Nearest Larger Neighbor Problem , 2015, WALCOM.

[10]  Sergey Bereg,et al.  Finding Nearest Larger Neighbors , 2009, Efficient Algorithms.

[11]  Moshe Lewenstein,et al.  Two dimensional range minimum queries and Fibonacci lattices , 2012, Theor. Comput. Sci..

[12]  Peter Elias,et al.  Universal codeword sets and representations of the integers , 1975, IEEE Trans. Inf. Theory.

[13]  Johannes Fischer,et al.  Optimal Succinctness for Range Minimum Queries , 2008, LATIN.

[14]  Kunihiko Sadakane,et al.  Practical Entropy-Compressed Rank/Select Dictionary , 2006, ALENEX.

[15]  Rajeev Raman,et al.  Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets , 2007, ACM Trans. Algorithms.

[16]  Rajeev Raman,et al.  Encoding 2D Range Maximum Queries , 2011, ISAAC.

[17]  John Iacono,et al.  Encoding 2-D Range Maximum Queries , 2016, Theor. Comput. Sci..

[18]  Volker Heun,et al.  Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays , 2011, SIAM J. Comput..

[19]  S. Srinivasa Rao,et al.  On Space Efficient Two Dimensional Range Minimum Data Structures , 2011, Algorithmica.

[20]  Gad M. Landau,et al.  On Cartesian Trees and Range Minimum Queries , 2009, Algorithmica.