Geometric graphs | Geometric algorithms

Geometric spanner

A geometric spanner or a t-spanner graph or a t-spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a t-path between any pair of vertices for a fixed parameter t. A t-path is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner. In computational geometry, the concept was first discussed by L.P. Chew in 1986, although the term "spanner" was not used in the original paper. The notion of graph spanners has been known in graph theory: t-spanners are spanning subgraphs of graphs with similar dilation property, where distances between graph vertices are defined in graph-theoretical terms. Therefore geometric spanners are graph spanners of complete graphs embedded in the plane with edge weights equal to the distances between the embedded vertices in the corresponding metric. Spanners may be used in computational geometry for solving some proximity problems. They have also found applications in other areas, such as in motion planning, in telecommunication networks: network reliability, optimization of roaming in mobile networks, etc. (Wikipedia).

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From playlist Introduction to Vectors

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From playlist Trigonometry: Dynamic Interactives!

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From playlist Geometric Algebra

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From playlist Geometrical Optics

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From playlist Geometry: Dynamic Interactives!

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From playlist Handmade geometric toys

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From playlist Introduction to Vectors

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From playlist MIT 6.824 Distributed Systems (Spring 2020)

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From playlist Part 2 lectures (2021 zoom)

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From playlist A-Level Maths Mechanics

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From playlist Geometrical Optics

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From playlist GCSE Physics Revision

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From playlist Forces, motion and simple harmonic motion

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Motion planning | Graph theory | Triangulation | Stretch factor | Yao graph | Computational geometry | Euclidean distance | Complete graph | Minimum spanning tree | Well-separated pair decomposition | Glossary of graph theory | Degree (graph theory) | Graph embedding | Proximity problems | Delaunay triangulation | Theta graph