Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index str...Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.展开更多
The Fermat–Pramanik series are like below: .The mathematical principle has been established by factorization principle. The Fermat-Pramanik tree can be grown. It produces branched Fermat-Pramanik series using same pr...The Fermat–Pramanik series are like below: .The mathematical principle has been established by factorization principle. The Fermat-Pramanik tree can be grown. It produces branched Fermat-Pramanik series using same principle making Fermat-Pramanik chain. Branched chain can be propagated at any point of the main chain with indefinite length using factorization principle as follows: Same principle is applicable for integer solutions of A<sup>M</sup>+B<sup>2</sup>=C<sup>2</sup>which produces series of the type . It has been shown that this equation is solvable with N{A, B, C, M}. where , , M=M<sub>1</sub>+M<sub>2</sub> and M<sub>1</sub>>M<sub>2</sub>. Subsequently, it has been shown that using M= M<sub>1</sub>+M<sub>2</sub>+M<sub>3</sub>+... The combinations of Ms should be taken so that the values of both the parts (C<sub>n</sub>+B<sub>n</sub>) and (C<sub>n</sub>-B<sub>n</sub>) should be even or odd for obtaining Z{B,C}. Hence, it has been shown that the Fermat triple can generate a) Fermat-Pramanik multiplate, b) Fermat-Pramanik Branched multiplate and c) Fermat-Pramanik deductive series. All these formalisms are useful for development of new principle of cryptography. .展开更多
基金the National Research Foundation of Korea(NRF,www.nrf.re.kr)grant funded by the Korean government(MSIT,www.msit.go.kr)(No.2018R1A2B6009188)(received by W.-K.Loh).
文摘Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.
文摘The Fermat–Pramanik series are like below: .The mathematical principle has been established by factorization principle. The Fermat-Pramanik tree can be grown. It produces branched Fermat-Pramanik series using same principle making Fermat-Pramanik chain. Branched chain can be propagated at any point of the main chain with indefinite length using factorization principle as follows: Same principle is applicable for integer solutions of A<sup>M</sup>+B<sup>2</sup>=C<sup>2</sup>which produces series of the type . It has been shown that this equation is solvable with N{A, B, C, M}. where , , M=M<sub>1</sub>+M<sub>2</sub> and M<sub>1</sub>>M<sub>2</sub>. Subsequently, it has been shown that using M= M<sub>1</sub>+M<sub>2</sub>+M<sub>3</sub>+... The combinations of Ms should be taken so that the values of both the parts (C<sub>n</sub>+B<sub>n</sub>) and (C<sub>n</sub>-B<sub>n</sub>) should be even or odd for obtaining Z{B,C}. Hence, it has been shown that the Fermat triple can generate a) Fermat-Pramanik multiplate, b) Fermat-Pramanik Branched multiplate and c) Fermat-Pramanik deductive series. All these formalisms are useful for development of new principle of cryptography. .
