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A basic algorithm of 3D sparse matrix multiplication (BASMM) is presented using one dimensional (1D) arrays which is used further for multiplying two 3D sparse matrices using Linked Lists. In this algorithm, a general concept is derived in which we enter non- zeros elements in 1st and 2nd sparse matrices (3D) but store that values in 1D arrays and linked lists so that zeros could be removed or ignored to store in memory. The positions of that non-zero value are also stored in memory like row and column position. In this way space complexity is decreased. There are two ways to store the sparse matrix in memory. First is row major order and another is column major order. But, in this algorithm, row major order is used. Now multiplying those two matrices with the help of BASMM algorithm, time complexity also decreased. For the implementation of this, simple c programming and concepts of data structures are used which are very easy to understand for everyone.
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A sum labeling is a mapping λ from the vertices of G into the positive integers such that, for any two vertices u, v ϵ V (G) with labels λ(u) and λ(v), respectively, (uv) is an edge iff λ(u) + λ(v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is known as the sum number of the graph. In this paper, we will obtain optimal sum labeling scheme for path union of split graph of star, K_(1,m)⨀Spl(P_n) and K_(1,m)⨀Spl(K_(1,n)).
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This is short overview of research paper. We present a practical algorithm for the automatic generation of a map that describes the operation environment of an indoor mobile service robot. The input is a CAD description of a building consisting of line segments that represent the walls. The algorithm is based on the exact cell decomposition obtained when these segments are extended to infinite lines, resulting in a line arrangement. The cells are represented by nodes in a connectivity graph. The map consists of the connectivity graph and additional environmental information that is calculated for each cell. The method takes into account both the path planning and position verification requirements of the robot and has been implemented.
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Anbu Alagan
This presentation provides a summary of chapter 13 of book "Computational Geometry: Algorithms and Applications" by Mark de Berg.
Ultimate Goals In Robotics
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Farzad Nozarian
Lesson 48
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andreagoings
A basic algorithm of 3D sparse matrix multiplication (BASMM) is presented using one dimensional (1D) arrays which is used further for multiplying two 3D sparse matrices using Linked Lists. In this algorithm, a general concept is derived in which we enter non- zeros elements in 1st and 2nd sparse matrices (3D) but store that values in 1D arrays and linked lists so that zeros could be removed or ignored to store in memory. The positions of that non-zero value are also stored in memory like row and column position. In this way space complexity is decreased. There are two ways to store the sparse matrix in memory. First is row major order and another is column major order. But, in this algorithm, row major order is used. Now multiplying those two matrices with the help of BASMM algorithm, time complexity also decreased. For the implementation of this, simple c programming and concepts of data structures are used which are very easy to understand for everyone.
Multiplication of two 3 d sparse matrices using 1d arrays and linked lists
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Dr Sandeep Kumar Poonia
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A sum labeling is a mapping λ from the vertices of G into the positive integers such that, for any two vertices u, v ϵ V (G) with labels λ(u) and λ(v), respectively, (uv) is an edge iff λ(u) + λ(v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is known as the sum number of the graph. In this paper, we will obtain optimal sum labeling scheme for path union of split graph of star, K_(1,m)⨀Spl(P_n) and K_(1,m)⨀Spl(K_(1,n)).
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This is short overview of research paper. We present a practical algorithm for the automatic generation of a map that describes the operation environment of an indoor mobile service robot. The input is a CAD description of a building consisting of line segments that represent the walls. The algorithm is based on the exact cell decomposition obtained when these segments are extended to infinite lines, resulting in a line arrangement. The cells are represented by nodes in a connectivity graph. The map consists of the connectivity graph and additional environmental information that is calculated for each cell. The method takes into account both the path planning and position verification requirements of the robot and has been implemented.
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PC8-8 3DTransformation Matrices
1.
Transformation Matrices in
3-D Space Precalculus 8-8 p. 535
2.
3.
4.
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