Related papers: An exact algorithm for higher-dimensional orthogon…

Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate…

Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…

Consensus maximization is widely used for robust fitting in computer vision. However, solving it exactly, i.e., finding the globally optimal solution, is intractable. A* tree search, which has been shown to be fixed-parameter tractable, is…

In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…

Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…

Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…

The two-dimensional non-oriented bin packing problem with due dates packs a set of rectangular items, which may be rotated by 90 degrees, into identical rectangular bins. The bins have equal processing times. An item's lateness is the…

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by…

Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…

We address the bin packing problem (BPP), which aims to maximize bin utilization when packing a variety of items. The offline problem, where the complete information about the item set and their sizes is known in advance, is proven to be…

Bipartite matching systems arise in many settings where agents or tasks from two distinct sets must be paired dynamically under compatibility constraints. We consider a high-dimensional bipartite matching system under uncertainty and seek…

We consider the problem of constructing an an optimal-weight tree from the 3*(n choose 4) weighted quartet topologies on n objects, where optimality means that the summed weight of the embedded quartet topologiesis optimal (so it can be the…

We consider the problem of finding all enclosing rectangles of minimum area that can contain a given set of rectangles without overlap. Our rectangle packer chooses the x-coordinates of all the rectangles before any of the y-coordinates. We…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…

Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether or not an item can be placed feasibly at a certain position, and the optimization challenge…