Faster Spectral Sparsification and Numerical Algorithms for SDD Matrices
نویسندگان
چکیده
منابع مشابه
Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices
We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n logn/ 2) edges that provides a strong approximation of G. Namely, for all vectors x and any > 0, we have (1− )xLGx ≤ xLHx ≤ (1 + )xLGx, where LG and LH are the Laplacians of the two graphs. The first algorithm is a simple modification of the fastest ...
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Alternative definition: Then LG is the matrix with diagonal entries (LG)ii = di, and off-diagonal entries (LG)ij = −wij . Fact 1: The matrix L = LG is symmetric, non-diagonals entries are Lij = −wij , and its diagonal entries are Lii = di, where di = ∑ j:ij∈E wij is the degree of vertex i. It is useful to put these values in a diagonal matrixD = diag(d⃗). If G is unweighted, then L = D−A where A...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2016
ISSN: 1549-6325,1549-6333
DOI: 10.1145/2743021