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We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or ...
Many graph mining and network analysis problems rely on the availability of the full network over a set of nodes. But inferring a full network is sometimes non-trivial if the raw data is in the form of many small {\em patches} or subgraphs, of the true net ...
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective fu ...
In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some circumstances that we clarif ...
Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. ...
This thesis is devoted to the understanding of topological graphs. We consider the following four problems: 1. A \emph{simple topological graph} is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any t ...
Neurons are endowed with dendrites: tree-like structures that collect and transform inputs. These arborizations are believed to substantially enhance the computational repertoire of neurons. While it has long been known that dendrites are not iso-potential ...
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the sim ...
This paper examines the learning mechanism of adaptive agents over weakly connected graphs and reveals an interesting behavior on how information flows through such topologies. The results clarify how asymmetries in the exchange of data can mask local info ...
It is shown that fora constant t is an element of N, every simple topological graph on n vertices has 0(n) edges if the graph has no two sets of t edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of th ...
