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JCT
1998
122views more  JCT 1998»
13 years 9 months ago
Counting 1-Factors in Regular Bipartite Graphs
We show that any k-regular bipartite graph with 2n vertices has at least ((k−1)k−1 kk−2 )n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent...
Alexander Schrijver
WWW
2010
ACM
14 years 4 months ago
Distributed nonnegative matrix factorization for web-scale dyadic data analysis on mapreduce
The Web abounds with dyadic data that keeps increasing by every single second. Previous work has repeatedly shown the usefulness of extracting the interaction structure inside dya...
Chao Liu, Hung-chih Yang, Jinliang Fan, Li-Wei He,...
FCSC
2008
88views more  FCSC 2008»
13 years 9 months ago
Fraction-free matrix factors: new forms for LU and QR factors
Gaussian elimination and LU factoring have been greatly studied from the algorithmic point of view, but much less from the point view of the best output format. In this paper, we g...
Wenqin Zhou, David J. Jeffrey
DAM
2010
95views more  DAM 2010»
13 years 10 months ago
Excessive factorizations of bipartite multigraphs
Let G be a multigraph. We say that G is 1-extendable if every edge of G is contained in a 1-factor. Suppose G is 1-extendable. An excessive factorization of G is a set F = {F1, F2...
David Cariolaro, Romeo Rizzi
WWW
2011
ACM
13 years 4 months ago
Counting triangles and the curse of the last reducer
The clustering coefficient of a node in a social network is a fundamental measure that quantifies how tightly-knit the community is around the node. Its computation can be reduce...
Siddharth Suri, Sergei Vassilvitskii