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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…

Data Structures and Algorithms · Computer Science 2007-05-23 Sandor P. Fekete , Joerg Schepers

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…

Tiling planar regions with dominoes is a classical problem in which the decision and counting problems are polynomial. We prove a variety of hardness results (both NP- and #P-completeness) for different generalizations of dominoes in three…

Combinatorics · Mathematics 2013-05-10 Igor Pak , Jed Yang

Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…

Data Structures and Algorithms · Computer Science 2017-04-04 Orlando Moreira , Merten Popp , Christian Schulz

We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant $\Delta$, and we are given a set of items each of which has a positive size. We…

Data Structures and Algorithms · Computer Science 2022-02-23 Asaf Levin

In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…

Computer Vision and Pattern Recognition · Computer Science 2025-09-09 Anuraag Mishra , Andrea Gilch , Benjamin Apeleo Zubiri , Jan Rolfes , Frauke Liers

The problem of Distance Edge Labeling is a variant of Distance Vertex Labeling (also known as $L_{2,1}$ labeling) that has been studied for more than twenty years and has many applications, such as frequency assignment. The Distance Edge…

Discrete Mathematics · Computer Science 2022-03-17 Dušan Knop , Tomáš Masařík

Ptychography is an emerging imaging technique that is able to provide wavelength-limited spatial resolution from specimen with extended lateral dimensions. As a scanning microscopy method, a typical two-dimensional image requires a number…

Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…

Artificial Intelligence · Computer Science 2013-08-02 Václav Lín

How can a stack of identical blocks be arranged to extend beyond the edge of a table as far as possible? We consider a generalization of this classic puzzle to blocks that differ in width and mass. Despite the seemingly simple premise, we…

Combinatorics · Mathematics 2026-02-13 Simon Gmeiner , Andreas S. Schulz

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…

Data Structures and Algorithms · Computer Science 2022-06-16 Justin Sybrandt , Ruslan Shaydulin , Ilya Safro

Recently, Hajirasouliha and Raphael (WABI 2014) proposed a model for deconvoluting mixed tumor samples measured from a collection of high-throughput sequencing reads. This is related to understanding tumor evolution and critical cancer…

Populations and Evolution · Quantitative Biology 2016-07-11 Ademir Hujdurović , Urša Kačar , Martin Milanič , Bernard Ries , Alexandru I. Tomescu

The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…

Information Theory · Computer Science 2016-08-31 Qi Cheng

Continuing results from JCDCGGG 2016 and 2017, we solve several new cases of the simple foldability problem -- deciding which crease patterns can be folded flat by a sequence of (some model of) simple folds. We give new efficient algorithms…

Computational Geometry · Computer Science 2023-06-02 Hugo Akitaya , Josh Brunner , Erik D. Demaine , Dylan Hendrickson , Victor Luo , Andy Tockman

A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…

Computational Geometry · Computer Science 2012-03-28 Sergio Cabello , Bojan Mohar

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to…

Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…

Statistical Mechanics · Physics 2024-12-24 Eduardo J. Aguilar , Valmir C. Barbosa , Raul Donangelo , Sergio R. Souza

We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Data Structures and Algorithms · Computer Science 2018-12-18 Michael J. Bannister , Sergio Cabello , David Eppstein

The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…

Numerical Analysis · Computer Science 2009-08-28 Alexandre Goldsztejn

By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…

Computational Complexity · Computer Science 2024-01-08 Yigit Oktar