Related papers: Few Cuts Meet Many Point Sets
We consider large-scale nonlinear least squares problems with sparse residuals, each of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
In this paper we study the partitioning approach for multiprocessor real-time scheduling. This approach seems to be the easiest since, once the partitioning of the task set has been done, the problem reduces to well understood uniprocessor…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…
Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the…
Cutwidth is a widely studied parameter that quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth…
3D part segmentation is an essential step in advanced CAM/CAD workflow. Precise 3D segmentation contributes to lower defective rate of work-pieces produced by the manufacturing equipment (such as computer controlled CNCs), thereby improving…
We propose an approach to find low-makespan solutions to multi-robot multi-task planning problems in environments where robots block each other from completing tasks simultaneously. We introduce a formulation of the problem that allows for…
Let $G = (V, E)$ be an undirected graph and let $B \subseteq V \times V$ be a set of terminal pairs. A node/edge multicut is a subset of vertices/edges of $G$ whose removal destroys all the paths between every terminal pair in $B$. The…
In this article we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of Support Points (SP), which was initially developed for finding the optimal…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work…
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…