Abstract
Window queries are basic but important query tasks in geospatial databases. The Hilbert curve has good clustering properties, which can be used to effectively improve the execution efficiency of window queries. The ideal goal of a window query using Hilbert curve code is to quickly convert the query window to the corresponding monotonic continuous Hilbert code segments. However, existing algorithms have shortcomings in conversion calculations and Hilbert code segments properties. We propose the state vectors that are used to describe the filling rules of a three-dimensional Hilbert curve. In addition, we designed a direct generation algorithm for monotonically increasing Hilbert code segments (MI-HCS) for a three-dimensional window query. The MI-HCS algorithm is characterized by the direct generation of a monotonically increasing code segment set without the need to traverse all grid elements or the requirement of separate sorting steps. For a given query window <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$W\left ({{x,y,z,l,w,h} }\right)$ </tex-math></inline-formula> and a Hilbert curve of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T\times T\times T$ </tex-math></inline-formula> , the maximum complexity of our MI-HCS algorithm is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O\left ({{\alpha _{1} \times \alpha _{2} \times \left ({{\log _{2} T+1} }\right)} }\right)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha _{1} = \textrm {median}\left ({{l,w,h} }\right)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha _{2} = \textrm {max}\left ({{l,w,h} }\right)$ </tex-math></inline-formula> . The experimental results of the MI-HCS algorithm complexity are consistent with the specific theoretical analysis. The experimental results show that the Hilbert code segment generation efficiency of the proposed MI-HCS algorithm is 260.5% to 423.9% higher than that of existing algorithms.
Highlights
Spatial ordering can be defined as a reversible one-to-one correspondence between consecutive integers or key values and elements in a spatial entity set [1]
To realize the efficient conversion from a threedimensional query window to a Hilbert code segment, VOLUME 8, 2020 this paper proposes a direct algorithm for a monotonically increasing three-dimensional Hilbert code segment (MI-HCS) based on the study of the filling rule of three-dimensional Hilbert curves and the topological relationship between the query window and the space grid element
The recursive splitting of the query process in the monotonically increasing Hilbert code segments (MI-HCS) algorithm is similar to the multidimensional tree search process in [23], but because [23] does not specify the search order when searching for tree nodes, the resulting final set of Hilbert code segments may not be monotonically increasing, requiring all code segments to be sorted before the continuous code segment merging step is performed
Summary
Spatial ordering can be defined as a reversible one-to-one correspondence between consecutive integers or key values and elements in a spatial entity set [1]. After studying the filling order of the two-dimensional Hilbert curve [22], a code segment generation algorithm for recursive quad splitting of the query window is proposed. The efficiency of this algorithm is greatly improved compared with that in [18]. To realize the efficient conversion from a threedimensional query window to a Hilbert code segment, VOLUME 8, 2020 this paper proposes a direct algorithm for a monotonically increasing three-dimensional Hilbert code segment (MI-HCS) based on the study of the filling rule of three-dimensional Hilbert curves and the topological relationship between the query window and the space grid element. T (su+1) → sE[u][0], sE[u][1], sE[u][2], sE[u][3], sE[u][4], sE[u][5], sE[u][6], sE[u][7], sE[u][8] (3)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
