1 research outputs found
Efficiently Sampling Multiplicative Attribute Graphs Using a Ball-Dropping Process
We introduce a novel and efficient sampling algorithm for the Multiplicative
Attribute Graph Model (MAGM - Kim and Leskovec (2010)}). Our algorithm is
\emph{strictly} more efficient than the algorithm proposed by Yun and
Vishwanathan (2012), in the sense that our method extends the \emph{best} time
complexity guarantee of their algorithm to a larger fraction of parameter
space. Both in theory and in empirical evaluation on sparse graphs, our new
algorithm outperforms the previous one. To design our algorithm, we first
define a stochastic \emph{ball-dropping process} (BDP). Although a special case
of this process was introduced as an efficient approximate sampling algorithm
for the Kronecker Product Graph Model (KPGM - Leskovec et al. (2010)}), neither
\emph{why} such an approximation works nor \emph{what} is the actual
distribution this process is sampling from has been addressed so far to the
best of our knowledge. Our rigorous treatment of the BDP enables us to clarify
the rational behind a BDP approximation of KPGM, and design an efficient
sampling algorithm for the MAGM