- Title: Lightweight-Yet-Efficient: Revitalizing Ball-Tree for Point-to-Hyperplane Nearest Neighbor Search
- Картина панно рисунок Роспись ВЕСНА УВЛЕЧЕНИЕ point-to-point Дерево Краска
- Point to Point Network Topology
- Tree Network Topology Diagram
- Wireless Network Topology
- Daisy Chain Network Topology
- Grid Network Topology
- Toroidal Network Topology
- Complete Network Topology
- Hotel Network Topology Diagram
- Network Topologies
- Star Network Topology
Title: Lightweight-Yet-Efficient: Revitalizing Ball-Tree for Point-to-Hyperplane Nearest Neighbor Search
Abstract: Finding the nearest neighbor to a hyperplane (or Point-to-Hyperplane Nearest Neighbor Search, simply P2HNNS) is a new and challenging problem with applications in many research domains. While existing state-of-the-art hashing schemes (e.g., NH and FH) are able to achieve sublinear time complexity without the assumption of the data being in a unit hypersphere, they require an asymmetric transformation, which increases the data dimension from $d$ to $\Omega(d^2)$. This leads to considerable overhead for indexing and incurs significant distortion errors.
In this paper, we investigate a tree-based approach for solving P2HNNS using the classical Ball-Tree index. Compared to hashing-based methods, tree-based methods usually require roughly linear costs for construction, and they provide different kinds of approximations with excellent flexibility. A simple branch-and-bound algorithm with a novel lower bound is first developed on Ball-Tree for performing P2HNNS. Then, a new tree structure named BC-Tree, which maintains the Ball and Cone structures in the leaf nodes of Ball-Tree, is described together with two effective strategies, i.e., point-level pruning and collaborative inner product computing. BC-Tree inherits both the low construction cost and lightweight property of Ball-Tree while providing a similar or more efficient search. Experimental results over 16 real-world data sets show that Ball-Tree and BC-Tree are around 1.1$\sim$10$\times$ faster than NH and FH, and they can reduce the index size and indexing time by about 1$\sim$3 orders of magnitudes on average. The code is available at \url.
Comments: | Accepted by IEEE ICDE 2023 |
Subjects: | Databases (cs.DB) ; Computational Geometry (cs.CG); Data Structures and Algorithms (cs.DS); Information Retrieval (cs.IR) |
Cite as: | arXiv:2302.10626 [cs.DB] |
(or arXiv:2302.10626v1 [cs.DB] for this version) | |
https://doi.org/10.48550/arXiv.2302.10626 |
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Картина панно рисунок Роспись ВЕСНА УВЛЕЧЕНИЕ point-to-point Дерево Краска
Вот с этой ключницы все началось. Поскольку центральная часть квартиры выполнена в восточном ключе. давно была мечта о ключнице в соответствующих тенденциях. Наткнулась на работу в этой технике и давай ставить точки.
Остановиться потом было сложнее.
Совсем стало сложно остановиться))))
А расслабилась и давай получать удовольствие))))))))))))
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Point to Point Network Topology
This sample was created in ConceptDraw DIAGRAM diagramming and vector drawing software using the Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park.
This sample shows the Point-to-point network topology.
Network topology is the topological structure of the computer network.
Point-to-point network topology is a simple topology that displays the network of exactly two hosts (computers, servers, switches or routers) connected with a cable. Point-to-point topology is widely used in the computer networking and computer architecture.
Tree Network Topology Diagram
The Tree Network Topology Diagram examples was created using ConceptDraw DIAGRAM software with Computer and Networks solution.
Wireless Network Topology
Wireless network topology — logical topology.
Wireless network topology shows how the computers connect each other when there is no physical connection. The computers communicate each using the wireless devices.
Daisy Chain Network Topology
This sample was created in ConceptDraw DIAGRAM diagramming and vector drawing software using the Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park.
A Daisy Chain is the simple computer network. It is the easiest way to add more Ethernet devices into the network. In the Daisy Chain network one computer is connected to the next without any intervening devices, thus the message is sent from one computer to the next and then to the next and so on. A Daisy Chain can be linear or ring
Grid Network Topology
The grid network topology is a type of the network topology in which the each node of the network is connected with two neighboring nodes along one or more dimensions. If the chain of nodes has the circular form and the network is one-dimensional, the topology is named the Ring. The topology with n-dimensional grid network with circularly connection of the nodes is named the Torus.
Toroidal Network Topology
This sample was created in ConceptDraw DIAGRAM diagramming and vector drawing software using the Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park.
This is example of the Toroidal network topology
Network topology is the topological structure of the computer network.
Complete Network Topology
This sample was created in ConceptDraw DIAGRAM diagramming and vector drawing software using the Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park.
A complete (fully connected) topology is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are n(n-1)/2 direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the multiple paths for data that are provided by the large number of redundant links between nodes.
Hotel Network Topology Diagram
Hotel Network Topology Diagram — The Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park provides examples, templates and vector stencils library with symbols of local area network (LAN) and wireless LAN (WLAN) equipment.
Use it to draw the physical and logical network topology diagrams for wired and wireless computer communication networks.
Network Topologies
Running your own business or working for some company as IT specialist, one day you definitely face the need of connecting all network and computer devices existing on this enterprise’s balance sheet. Especially once this company grows you need more stuff and so elements of network such as laptops, servers, scanners, printers, fax machines, telephones, routers, so you definitely have to make network topology flowchart to arrange it all correctly to connect it with each other. In this case to use ConceptDraw DIAGRAM as a tool to make your topology diagram is the best decision ever! Test how simple it is to use our samples to create your diagrams in a short term! Whether you need to make logical or physical topologies you can always use the service of our software and with help of libraries to design whatever you need. The basic topologies types are: ring, mesh, bus, star, tree or fully connected one, and its examples are there in Solutions waiting for you on this site to use it all. Check it out and enjoy simplicity of using this application right now!
Star Network Topology
The Computer and Networks solution from Computer and Networks area of ConceptDraw Solution Park provides examples, templates and vector stencils library with symbols of local area network (LAN) and wireless LAN (WLAN) equipment.
Use it to draw the physical and logical network topology diagrams for wired and wireless computer communication networks.
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