Silvio Lattanzi

Silvio Lattanzi
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Silvio Lattanzi
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Computer Science - Data Structures and Algorithms (5)
 
Statistics - Machine Learning (1)
 
Computer Science - Learning (1)
 
Computer Science - Networking and Internet Architecture (1)
 
Computer Science - Distributed; Parallel; and Cluster Computing (1)
 
Mathematics - Probability (1)

Publications Authored By Silvio Lattanzi

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise $\ell_p$-approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of low-rank approximation that work for every value of $p \geq 1$, including $p = \infty$. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix. Read More

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this question in the context of data streams, where elements arrive one at a time, and we want to design low-memory and fast update-time algorithms that maintain a good solution. Specifically, we focus on the sliding window model, where we are asked to maintain a solution that considers only the last $W$ items. Read More

Designing distributed and scalable algorithms to improve network connectivity is a central topic in peer-to-peer networks. In this paper we focus on the following well-known problem: given an $n$-node $d$-regular network for $d=\Omega(\log n)$, we want to design a decentralized, local algorithm that transforms the graph into one that has good connectivity properties (low diameter, expansion, etc.) without affecting the sparsity of the graph. Read More

People today typically use multiple online social networks (Facebook, Twitter, Google+, LinkedIn, etc.). Each online network represents a subset of their "real" ego-networks. Read More

Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms guarantee an output conductance of $\tilde{O}(\sqrt{\phi(A)})$ when the target set $A$ has conductance $\phi(A)\in[0,1]$. In this paper, we improve it to $$\tilde{O}\bigg( \min\Big\{\sqrt{\phi(A)}, \frac{\phi(A)}{\sqrt{\mathsf{Conn}(A)}} \Big\} \bigg)\enspace, $$ where the internal connectivity parameter $\mathsf{Conn}(A) \in [0,1]$ is defined as the reciprocal of the mixing time of the random walk over the induced subgraph on $A$. Read More