PPT-Generating Random Spanning Trees via Fast Matrix Multiplication

Keyulu Xu University of British Columbia Joint work with Nick Harvey TexPoint fonts used in EMF Read the TexPoint manual before you delete this box A A A What are random s panning . So to do fast multiplicationA = B x CReformat B and C before and A after. - S. Kapoor and H. Ramesh. Speakers: . 李孟韓. 1. , . 林蔚茵. 2. , . 莊秋芸. 3. , . 黃稚穎. 4. Reference. H. N. Gabow and E. W. Myers: Finding all spanning trees of directed and undirected graphs, . Subhypergraphs. with Polynomial Delay. Taishin Daigo (Kyushu Inst. of Tech.). Kouichi Hirata (Kyushu Inst. of Tech.). 1. On . Generating Maximal Acyclic . Subhypergraphs. with Polynomial Delay . Contents. Sources of randomness in a computer?. Methods for generating random numbers:. Time of day (Seconds since midnight). 10438901, 98714982747, 87819374327498,1237477,657418,. Gamma ray . counters. Rand Tables. and Counting Trees. Today’s Plan. Generating functions for basic sequences. Operations on generating functions. Counting. Solve recurrences. Catalan number. Counting Spanning Trees. Generating Functions. Communication Avoiding. Fast. Algorithm for. Sparse Matrix . Multiplication. Part I: Minimizing arithmetic operations. Oded Schwartz. CS294, Lecture #21 Fall, 2011. Communication-Avoiding Algorithms. Final presentation. One semester – winter 2014/15. By : Dana Abergel and Alex . Fonariov. Supervisor : . Mony. . Orbach. High Speed Digital System Laboratory. Abstract . Matrix multiplication is a complex mathematical operation.. Trees. Spring 2014. Sukumar Ghosh. What is a tree?. Rooted tree: recursive definition. Rooted tree terminology. Rooted tree terminology. A . subtree. Rooted tree terminology. Important properties of trees. and . Graph Algorithms. Uri Zwick. Tel Aviv University. February . 2015. Last updated: June 10, 2015. Algebraic matrix multiplication. Strassen. ’s algorithm. Rectangular matrix multiplication. Boolean matrix multiplication. Jianyu. Huang. , Leslie Rice,. Devin A. Matthews, Robert A. van de . Geijn. IPDPS2017, May 31. st. , Orlando, FL. Jianyu Huang. , Leslie Rice,. Devin A. Matthews, Robert A. van de . Geijn. The University of Texas at Austin. A . tree. is a connected undirected graph with no simple circuits.. Since a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops.. Therefore, any tree must be a . simple graph. Graph Algorithms. Uri Zwick. Tel Aviv University. Algebraic matrix multiplication. Strassen. ’s algorithm. Rectangular matrix multiplication. Boolean matrix multiplication. Simple reduction to integer matrix multiplication. Graph Algorithms. Uri Zwick. Tel Aviv University. November 2016. 1. Algebraic matrix multiplication. Strassen. ’s algorithm. Rectangular matrix multiplication. Boolean matrix multiplication. Simple reduction to integer matrix multiplication. Determinants. Square matrices have determinants, which are useful in other matrix operations, especially inversion. .. For a second-order . square. . matrix. , . A. ,. the determinant is. Consider the following bivariate raw data matrix.