Untangled monotonic chains and adaptive range search (original) (raw)

Range queries over untangled chains

2010

We present a practical implementation of the first adaptive data structure for orthogonal range queries in 2D Arroyuelo et al., ISAAC 2009. The structure is static, requires only linear space for its representation, and can even be made implicit. The running time for a query is O (lgklgn+ min (k, m) lgn+ m) O (\ lg k\ lg n+\ min (k, m)\ lg n+ m), where k is the number of non-crossing monotonic chains in which we can partition the set of points, and m is the size of the output. The space consumption of our implementation is 2n+ o (n) words.

An Optimal Algorithm for Range Search on Multidimensional Points

2016

This paper proposes an efficient and novel method to address range search on multidimensional points in theta(t)\\theta(t)theta(t) time, where ttt is the number of points reported in Rek\\Re^kRek space. This is accomplished by introducing a new data structure, called BITS kkkd-tree. This structure also supports fast updation that takes theta(1)\\theta(1)theta(1) time for insertion and O(logn)O(\\log n)O(logn) time for deletion. The earlier best known algorithm for this problem is O(logkn+t)O(\\log^k n+t)O(logkn+t) time in the pointer machine model.

ON MULTI-LEVEL k-RANGES FOR RANGE SEARCH

International Journal of Computational Geometry & Applications, 2005

We investigate an implementation of the multi-level or ℓ-level k-range data structure. The ℓ-level k-range is compared to naive and R*tree search over N randomly generated k-dimensional points. Results indicate that multi-level k-ranges are not competitive due to their (previously unreported) complexity. We show that storage is S(N,k,ℓ) = O(N1+2(k-1)/ℓ) and S(N,k) = Θ(N1+2(k-1)/ log 2N). Our results also indicate that the ℓ-level k-range requires Q(N,k,ℓ) = O((2ℓ)k( log N + A)) time for range search, for A = number of points reported in range.

IJERT-Indexing Structures for Range Searching with Point Objects: A Survey

International Journal of Engineering Research and Technology (IJERT), 2016

https://www.ijert.org/indexing-structures-for-range-searching-with-point-objects-a-survey https://www.ijert.org/research/indexing-structures-for-range-searching-with-point-objects-a-survey-IJERTV5IS010388.pdf This paper discusses the various indexing structures for range queries. Attention is directed to point objects because of its correlation to tuples of the tables of relational databases. It discusses the structures in details and possible ways of implementing them in relational databases. A special attention is given to structures that are relatively efficient for range searching in multidimensional space.

Indexing Structures for Range Searching with Point Objects: A Survey

International journal of engineering research and technology, 2016

This paper discusses the various indexing structures for range queries. Attention is directed to point objects because of its correlation to tuples of the tables of relational databases. It discusses the structures in details and possible ways of implementing them in relational databases. A special attention is given to structures that are relatively efficient for range searching in multidimensional space. Keywords—Range; Searching; Query; Indexing; Structures; Multidimensional; Geometric Objects