Decomposition of Geometric Set Systems and Graphs

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The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

In this paper, we formulate a mixed integer linear program (MILP) for the simulated maximum likelihood estimation (MLSE) problem and devise a Benders decomposition approach to speed up the solution process. This framework can be applied to any advanced dis ...

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

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We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

Decomposition of Geometric Set Systems and Graphs

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Stochastic distributed learning with gradient quantization and double-variance reduction

On the robustness of the metric dimension of grid graphs to adding a single edge

A Benders decomposition for maximum simulated likelihood estimation of advanced discrete choice models

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Quadratic serendipity element shape functions on general planar polygons

On The Convergence Of Stochastic Primal-Dual Hybrid Gradient

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Proximal Point Imitation Learning

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Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy