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Type of computational problem
In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another
Covering_problems
such a way as to cover the unit disk? More unsolved problems in mathematics The disk covering problem asks for the smallest real number r ( n ) {\displaystyle
Disk_covering_problem
Set of primitive shapes whose union equals a polygon
many different polygon covering problems, depending on the type of polygon being covered. An example polygon covering problem is: given a rectilinear
Polygon_covering
Area of discrete mathematics
Museum guard problem Covering problems in graphs may refer to various set cover problems on subsets of vertices/subgraphs. Dominating set problem is the special
Graph_theory
Problems which attempt to find the most efficient way to pack objects into containers
of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks
Packing_problems
Operations research problem of packing items into the largest number of bins
In the bin covering problem, items of different sizes must be packed into a finite number of bins or containers, each of which must contain at least a
Bin_covering_problem
overlap? More unsolved problems in mathematics The covering problem of Rado is an unsolved problem in geometry concerning covering planar sets by squares
Covering_problem_of_Rado
Subset of a graph's vertices, including at least one endpoint of every edge
cover problem can be formulated as the following integer linear program (ILP). This ILP belongs to the more general class of ILPs for covering problems. The
Vertex_cover
Graph related to another graph by a covering map
a graph C is a covering graph of another graph G if there is a covering map from the vertex set of C to the vertex set of G. A covering map f is a surjection
Covering_graph
Classical problem in combinatorics
fewest sets. The decision version of set covering is NP-complete. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. The optimization/search
Set_cover_problem
Unsolved geometry problem
Lebesgue's universal covering problem is an unsolved problem in geometry that asks for the convex shape of smallest area that can cover every planar set
Lebesgue's universal covering problem
Lebesgue's_universal_covering_problem
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Collection of subsets covering all t-element subsets
In combinatorial design theory, a covering design, or a (v, k, t)-covering design, is a collection of k-element subsets, called blocks, chosen from a v-element
Covering_design
Subset of a graph's edges
cover problem is the problem of finding an edge cover of minimum size. It is an optimization problem that belongs to the class of covering problems and
Edge_cover
Set of edges without common vertices
optimization problems are known to be NP-hard; the decision versions of these problems are classical examples of NP-complete problems. Both problems can be
Matching_(graph_theory)
Mathematical and computational problem
on non-trivial problems with 100 items, and outperforms the BCP (branch-and-cut-and-price) algorithm by Belov and Scheithauer on problems that have fewer
Bin_packing_problem
Method to solve optimization problems
algorithms for other types of optimization problems work by solving linear programming problems as sub-problems. Historically, ideas from linear programming
Linear_programming
Unrelated vertices in graphs
the theory of NP-completeness to problems related to independent sets. The independent set problem and the clique problem are complementary: a clique in
Independent set (graph theory)
Independent_set_(graph_theory)
Collection of residue classes
modulus on a covering system. Unsolved problem in mathematics Does there exist a covering system with odd distinct moduli? More unsolved problems in mathematics
Covering_system
Set of "near" codewords in coding theory
In coding theory, a covering code is a set of elements (called codewords) in a space, with the property that every element of the space is within a fixed
Covering_code
American mathematician and biomedical engineer
biomedical engineer who has worked on DNA sequencing theory, covering and matching problems in probability, theoretical fluid mechanics, and co-wrote Phred
Michael_Christopher_Wendl
Type of continuous map in topology
In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies
Covering_space
Size of biclique cover of a graph
subgraphs), needed to cover all edges in E. A collection of bicliques covering all edges in G is called a biclique edge cover, or sometimes biclique cover
Bipartite_dimension
Mathematical problem
their surroundings. Other domains, where this problem is applied, are in image editing, lighting problems of a stage or installation of infrastructures
Art_gallery_problem
In mathematics, a covering set for a sequence of integers refers to a set of prime numbers such that every term in the sequence is divisible by at least
Covering_set
Canadian mathematician
topics such as Littlewood problems on polynomials, probability and geometry of polynomials, arithmetic Ramsey theory, Erdős covering systems, random matrices
Julian_Sahasrabudhe
William; Pach, János (2005). "3.3 Levi–Hadwiger Covering Problem and Illumination". Research Problems in Discrete Geometry. Springer-Verlag. pp. 136–142
Hadwiger conjecture (combinatorial geometry)
Hadwiger_conjecture_(combinatorial_geometry)
On short connecting nets with added points
the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization
Steiner_tree_problem
monotone dualization is a computational problem of constructing the dual of a monotone Boolean function. Equivalent problems can also be formulated as constructing
Monotone_dualization
Academic journal
Cancer Nursing is a bi-monthly peer-reviewed nursing journal covering problems arising in the care and support of cancer patients from prevention and
Cancer_Nursing
Unsolved geometry problem about planar regions
Unsolved problem in mathematics What is the minimum area of a shape that can cover every unit-length curve? More unsolved problems in mathematics Moser's
Moser's_worm_problem
Arrangement of spheres within a space
However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in
Sphere_packing
Number in combinatorial design
Turán problems typically have n {\displaystyle n} large relative to ℓ {\displaystyle \ell } and r {\displaystyle r} , while covering problems typically
Turán_number
Two-dimensional packing problem
smaller number > 1. (Higher density records all have rattles.) Disk covering problem Square packing in a circle Friedman, Erich, "Circles in Circles", Erich's
Circle_packing_in_a_circle
Biological theory
important paper examining the covering problem from the standpoint of gaps. Although they focused on the so-called mapping problem, the abstraction to sequencing
DNA_sequencing_theory
Disease of horses and other Equidae
Covering sickness, or dourine (French, from the Arabic darina, meaning mangy (said of a female camel), feminine of darin, meaning dirty), is a disease
Covering_sickness
Mathematical problem
In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite
Zero-sum_problem
Combinatorics problem proposed by Thomas Penyngton Kirkman
357 The corresponding Sylvester problem asks for 7 different S(2,3,9) systems of 12 triples each, together covering all ( 9 3 ) = 84 {\textstyle {9 \choose
Kirkman's_schoolgirl_problem
One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the traveling salesman problem (TSP), whereby it is required to find
Set_TSP_problem
Problems in mathematics concerning chessboard or the sport chess
A mathematical chess problem is a mathematical problem which is formulated using a chessboard and chess pieces. These problems belong to recreational
Mathematical_chess_problem
Geometric construct
MR 0684591 Erickson, Alejandro; Ruskey, Frank (2013), "Domino tatami covering is NP-complete", in Lecroq, Thierry; Mouchard, Laurent (eds.), Combinatorial
Domino_tiling
Covering of the main river of Brussels, Belgium
The covering of the Senne (French: Voûtement de la Senne; Dutch: Overwelving van de Zenne) was the covering and later diverting of the main river of Brussels
Covering_of_the_Senne
Problem in computer science
classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has a finite
Set_packing
Wig or half-wig worn by some married Orthodox Jewish women
presence of men other than their husband or close family members. Such covering is common practice among Orthodox Jewish women. This is called kisui rosh
Head covering for Jewish women
Head_covering_for_Jewish_women
NP-hard problem in combinatorial optimization
with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as
Travelling_salesman_problem
American mathematician and statistician
research in mathematics included work on the bin covering problem (a discrete optimization problem), while her later work in statistics and biostatistics
Susan_Assmann
About polynomials in several variables
Jacobian conjecture is number 16 in Stephen Smale's 1998 list of Mathematical Problems for the Next Century. According to Alexander Borisov, the conjecture in
Jacobian_conjecture
Polygon in which all angles are right
rectangles or squares. There are several types of decomposition problems: In covering problems, the goal is to find a smallest set of units (squares or rectangles)
Rectilinear_polygon
Set of computational problems stated by Richard Karp (1973)
NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility Among Combinatorial Problems", Richard
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Problem in historical fiction
deliver messages from one end of the empire to the other in under a week, covering a distance of nearly 3,200 km (2,000 mi).[citation needed] Due to the recency
Tiffany_problem
Practice of female head covering in Christianity
Christian head covering, also known as Christian veiling, is the traditional practice of women covering their head in a variety of Christian denominations
Head covering for Christian women
Head_covering_for_Christian_women
Exterior layer of a building
In construction, covering is the exterior layer of a building's roof. The covering ensures waterproofing by directing and collecting rainwater. It also
Covering_(construction)
Phylogenetic method
both heuristics for NP-hard optimization problems and polynomial-time distance-based methods. Disk-covering methods are a meta-technique in that they
Disk-covering_method
Location Problems on Trees and in the Rectilinear Plane. PhD thesis, Universiteit van Amsterdam, 1982. Kolen, Antoon WJ, and Arie Tamir. Covering problems. Econometric
Antoon_Kolen
Part of the mathematical subject of group theory
these two constructions, Bass–Serre theory uses the geometric language of covering theory and fundamental groups. Graphs of groups, which are the basic objects
Bass–Serre_theory
Topologically invariant definition of the dimension of a space
In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension
Lebesgue_covering_dimension
Computer bugs related to the year 2000
their own problems and were prepared for problems with others. While some commentators and experts argued that the coverage of the problem largely amounted
Year_2000_problem
Fewest cliques covering a graph's edges
The problem of computing the intersection number has been called the intersection number problem, the intersection graph basis problem, covering by cliques
Intersection number (graph theory)
Intersection_number_(graph_theory)
Academic journal
Problems of Post-Communism is a bimonthly peer-reviewed academic journal covering economic, political, security, and international developments in post-communist
Problems_of_Post-Communism
The phrase "covering of eyes" is found in Genesis 20:16. It is translated literally in Young's Literal Translation. The King James Version inserts the
Covering_of_the_eyes
Optimization problem in computer science
lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central
Lattice_problem
Puzzle based on chess
are divided into orthodox and heterodox types, both covering a variety of genres. Orthodox problems employ the standard rules of chess and involve positions
Chess_puzzle
1998 book by Fan Chung
Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It
Erdős_on_Graphs
Mathematical puzzle
Martin (1967). "536 Puzzles And Curious Problems". p. 376. Klamkin, M. S. (1955-02-01). "Polygonal Path Covering a Square Lattice (E1123)". The American
Nine_dots_puzzle
Finding the smallest circle that contains all given points
smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is
Smallest-circle_problem
Covering of furniture with padding, springs, webbing, and fabric or leather
Traditional upholstery is a craft that evolved over centuries for padding and covering chairs, seats, and sofas before the development of sewing machines, synthetic
Upholstery
Well-spaced set of points in a metric space
In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after
Delone_set
Mathematical problem about tiling the plane with stripes
^{-1}/2} . Affine plank problem, on covering a constant body by stripes of small total relative width Tarski's plank problem, on covering bounded sets by stripes
Pyjama_problem
Chordal graph where all cycles of even length have odd chords
ISBN 0-89871-432-X. Chang, G. J. (1982), K-domination and Graph Covering Problems, Ph.D. thesis, Cornell University. Dahlhaus, E.; Manuel, P. D.; Miller
Strongly_chordal_graph
Danish biologist and writer
published in English as The Arc of the Swallow, another thriller covering problems resulting from the commercial interests of Danish immunology research
Sissel-Jo_Gazan
Prime Minister of the United Kingdom since 2026
trade magazine Tank Container World (later Bulk Distributor), a magazine covering tanker and intermodal transportation. From 1994 until the 1997 general
Andy_Burnham
dominated convergence theorem Lebesgue's number lemma Lebesgue's universal covering problem Riemann–Lebesgue lemma Walsh–Lebesgue theorem Dovgoshey, O.; Martio
List of things named after Henri Lebesgue
List_of_things_named_after_Henri_Lebesgue
Odd number with specific properties
covering set. Unsolved problem in mathematics Is 78,557 the smallest Sierpiński number? More unsolved problems in mathematics The Sierpiński problem asks
Sierpiński_number
Partition into subsets from a given family
satisfaction problem Dancing Links Difference map algorithm Karp's 21 NP-complete problems Knuth's Algorithm X List of NP-complete problems Partition of
Exact_cover
2021 essay collection by Black Nerd Problems
Black Nerd Problems (2021) is a collection of essays written by Black Nerd Problems, primarily Omar Holmon and William Evans. It was named a 2021 Goodreads
Black_Nerd_Problems:_Essays
Subdivision into few independent sets
those for matroid partitioning. The fractional set packing and set covering problems associated with a matroid (that is, assign a weight to each independent
Matroid_partitioning
from space; development of the project concept of military reform, covering problems converting all defense structures of the state; study of the peculiarities
Academy of Military Science (Russia)
Academy_of_Military_Science_(Russia)
Hungarian mathematician (1913–1996)
Erdős would offer payments for solutions to unresolved problems. These ranged from $25 for problems that he felt were just out of the reach of the current
Paul_Erdős
Peer-reviewed academic journal
Race and Social Problems is a quarterly peer-reviewed academic journal covering the sociology of race and ethnicity. It was established in 2009 and is
Race_and_Social_Problems
Shape in mathematics of domino tiling
tilings of the Aztec diamond involves the solution of the underlying set-covering problem. Let D = { d 1 , d 2 , … , d n } {\displaystyle D=\{d_{1},d_{2},\dots
Aztec_diamond
Medical condition caused by receiving too little or too many nutrients
when an organism gets too few or too many nutrients, resulting in health problems. Specifically, it is a deficiency, excess, or imbalance of energy, protein
Malnutrition
design of fixed-parameter-tractable algorithms for domination and covering problems on graphs. 2016: Andreas Björklund for his paper Determinant Sums
Nerode_Prize
2006 book by Kenji Yoshino
Covering: The Hidden Assault on Our Civil Rights, published in 2006 is an analysis on society's views on race and sexuality and a collection of autobiographical
Covering: The Hidden Assault on Our Civil Rights
Covering:_The_Hidden_Assault_on_Our_Civil_Rights
Unsolved problem in mathematics
Unsolved problem in mathematics Is there an algorithm to test whether a constant-recursive sequence has a zero? More unsolved problems in mathematics
Skolem_problem
Country in West Asia
singular is harrah), form one of Earth's largest alkali basalt regions, covering some 180,000 square kilometres (69,000 sq mi). Except for the southwestern
Saudi_Arabia
Odd number with specific properties
integer multiple of 11184810. The Riesel problem consists in determining the smallest Riesel number. Because no covering set has been found for any k less than
Riesel_number
Number of forests a graph's edges may be partitioned into
trees that can be drawn in a graph. It is the packing problem that is dual to the covering problem raised by the arboricity. The two parameters have been
Arboricity
French mathematician (1875–1941)
Lebesgue point Lebesgue space Lebesgue spine Lebesgue's universal covering problem Lebesgue–Rokhlin probability space Lebesgue–Stieltjes integration Lebesgue–Vitali
Henri_Lebesgue
2010 French act of parliament
The French ban on face covering is the result of an act of parliament passed in 2010 banning the wearing of face-covering headgear, including masks, helmets
French_ban_on_face_covering
Circle-packing on the surface of a sphere
problem in mathematics What is the optimal packing of circles on the surface of a sphere for every possible amount of circles? More unsolved problems
Tammes_problem
Subset of mathematical connundrums
Problems involving arithmetic progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied points
Problems involving arithmetic progressions
Problems_involving_arithmetic_progressions
Type of window covering
A window blind is a type of window covering (also known as blinds). There are many different kinds of window blinds which use a variety of control systems
Window_blind
Human male external reproductive organ
root, body, the epithelium, including the shaft skin, and the foreskin covering the glans. The body of the penis is made up of three columns of tissue:
Human_penis
Polish-American mathematician, Auburn U
particular on packing and covering problems. His first paper in this area (1982) showed that the ratio of packing density to covering density of any convex
Włodzimierz_Kuperberg
Open problem in convex geometry
planks covering a convex body must be at least 1. Unlike the original plank problem, which was solved by Bang himself, the affine plank problem remains
Affine_plank_problem
Kortsarz, Guy (2000), "Tree spanners for subgraphs and related tree covering problems", Graph-Theoretic Concepts in Computer Science: 26th International
Tree_spanner
Algorithm for the minimization of Boolean functions
methods.) (5 pages) Masek, William J. (1979). Some NP-complete set covering problems. unpublished. Czort, Sebastian Lukas Arne (1999). The complexity of
Quine–McCluskey_algorithm
the approximation ratios for these problems can be much better than the general set cover/hitting set problems. Moreover, these approximate solutions
Geometric_set_cover_problem
Fair division class using unique allocation methods
scheduling, often called machine covering. Tan and Wu present optimal algorithms for three semi-online machine covering problems. They prove that: If either
Online_fair_division
Hungarian mathematician (1895–1965)
System Technical Journal 41/1962 scan Computer studies of Turing machine problems, Journal of the ACM 12/1965 Radó's theorem (Riemann surfaces) Radó's theorem
Tibor_Radó
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