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Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…
Graph workloads pose a particularly challenging problem for query optimizers. They typically feature large queries made up of entirely many-to-many joins with complex correlations. This puts significant stress on traditional cardinality…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings…
Cutting rectangular items from stock sheets to satisfy demands while minimizing waste is a central manufacturing task. The Two-Dimensional Single Stock Size Cutting Stock Problem (2D-CSSP) generalizes bin packing by requiring multiple…
The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We propose a dynamic graph representation method, showcasing its rich representational capacity and establishing some of its theoretical properties. Our representation falls under the bind-and-sum approach in hyperdimensional computing…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…