11,794 research outputs found
Statistical Multiparty Computation Based on Random Walks on Graphs
With respect to a special class of access structures based on connectivity of graphs, we start from a linear secret sharing scheme
and turn it into a secret sharing scheme with perfect security and exponentially small error probability by randomizing the
reconstruction algorithm through random walks on graphs. It reduces the polynomial work space to logarithmic. Then we build the corresponding statistical multiparty computation protocol by using the secret sharing scheme. The results of this paper also imply the inherent connections and influences among secret sharing, randomized algorithms, and secure multi-party computation
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
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