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Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when available.The first is a multi-level method exploiting a…
Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of…
We propose a novel approach for optimizing the graph ratio-cut by modeling the binary assignments as random variables. We provide an upper bound on the expected ratio-cut, as well as an unbiased estimate of its gradient, to learn the…
We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…
We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in $\widetilde{O}(D + \sqrt{n})$ rounds on every graph, recovering the recent result of Dory, Efron,…
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…
Decision trees are one of the most popular classifiers in the machine learning literature. While the most common decision tree learning algorithms treat data as a batch, numerous algorithms have been proposed to construct decision trees…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
Attempting to recognize a tree inside a phylogenetic network is a fundamental undertaking in evolutionary analysis. In the last few years, therefore, tree-based phylogenetic networks, which are defined by a spanning tree called a…
Neighborhood algorithms may take a considerable percentage of computer time in discrete element methods (DEM). While the sort-and-sweep algorithm is ideal in some ways, as it only deal with particles whose relative positions change in one…
Real root finding of polynomial equations is a basic problem in computer algebra. This task is usually divided into two parts: isolation and refinement. In this paper, we propose two algorithms LZ1 and LZ2 to refine real roots of univariate…
We provide finite sample guarantees for the classical Chow-Liu algorithm (IEEE Trans.~Inform.~Theory, 1968) to learn a tree-structured graphical model of a distribution. For a distribution $P$ on $\Sigma^n$ and a tree $T$ on $n$ nodes, we…
We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…
Recursive maps of high order of convergence $m$ (say $m=2^{10}$ or $m=2^{20}$) induce certain monotone step functions from which one can filter relevant information needed to globally separate and compute the real roots of a function on a…
Univariate polynomial root-finding has been studied for four millennia and very intensively in the last decades. Our new near-optimal root-finders approximate all zeros of a polynomial p almost as fast as one accesses its coefficients with…
Discretization based approaches to solving online reinforcement learning problems have been studied extensively in practice on applications ranging from resource allocation to cache management. Two major questions in designing…
We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…
We introduce the Stochastic Monotone Aggregated Root-Finding (SMART) algorithm, a new randomized operator-splitting scheme for finding roots of finite sums of operators. These algorithms are similar to the growing class of incremental…
The antenna-subtraction technique has demonstrated remarkable effectiveness in providing next-to-next-to-leading order in $\alpha_s$ (NNLO) predictions for a wide range of processes relevant for the Large Hadron Collider. In a previous…