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Problem in computer science
Set packing is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose
Set_packing
Problems which attempt to find the most efficient way to pack objects into containers
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to
Packing_problems
Classical problem in combinatorics
Commons has media related to Set cover problem. Benchmarks with Hidden Optimum Solutions for Set Covering, Set Packing and Winner Determination Archived
Set_cover_problem
Unrelated vertices in graphs
independent sets, only one need be output. This problem is sometimes referred to as "vertex packing". In the maximum-weight independent set problem, the
Independent set (graph theory)
Independent_set_(graph_theory)
Mathematical and computational problem
The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each
Bin_packing_problem
Problem of grouping into triples
most 3 sets, i.e., when we want a perfect matching in a 3-regular hypergraph. In this case, a 3-dimensional matching is not only a set packing, but also
3-dimensional_matching
Method to solve optimization problems
relaxations of the set packing problem, the independent set problem, and the matching problem are packing LPs. The LP relaxations of the set cover problem
Linear_programming
Set of edges without common vertices
discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In other words, a subset
Matching_(graph_theory)
Optimization problem in mathematics
Rectangle packing is a packing problem where the objective is to determine whether a given set of small rectangles can be placed inside a given large polygon
Rectangle_packing
Subset of a graph's vertices, including at least one endpoint of every edge
In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph
Vertex_cover
Type of computational problem
are called packing problems. The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem,
Covering_problems
In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges
Packing_in_a_hypergraph
Independent set which is not a subset of any other independent set
by an N C 1 {\displaystyle NC^{1}} reduction from either the maximum set packing or the maximal matching problem or by an N C 2 {\displaystyle NC^{2}}
Maximal_independent_set
Sets with no element in common
for disjoint convex sets Mutually exclusive events Relatively prime, numbers with disjoint sets of prime divisors Separoid Set packing, the problem of finding
Disjoint_sets
Arrangement of spheres within a space
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical
Sphere_packing
Cycle graph with all opposite nodes linked
computer science, as part of integer programming approaches to problems of set packing and linear ordering. Certain configurations within these problems can
Möbius_ladder
Two-dimensional packing problem
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. If
Circle_packing_in_a_circle
Subset of a graph's edges
edge cover of a graph is a set of edges such that every vertex of the graph is an endpoint of at least one edge of the set. In computer science, the minimum
Edge_cover
Shape containing unit line segments in all directions
In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance
Kakeya_set
Three-dimensional packing problem
Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It
Sphere_packing_in_a_sphere
Fraction of a space filled by objects packed into that space
A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In simplest
Packing_density
optimal allocation. The combinatorial auction problem can be modeled as a set packing problem. Therefore, many algorithms have been proposed to find approximated
Combinatorial_auction
Set of hyperedges where every pair is disjoint
intersect) is a perfect graph. The problem of set packing is equivalent to hypergraph matching. A vertex-packing in a (simple) graph is a subset P of its vertices
Matching_in_hypergraphs
On tangency patterns of circles
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping
Circle_packing_theorem
Set of computational problems stated by Richard Karp (1973)
optimization) Clique (see also independent set problem) Set packing Vertex cover Set covering Feedback node set Feedback arc set Directed Hamilton circuit (Karp's
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Well-spaced set of points in a metric space
theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several
Delone_set
Fractal sets in complex dynamics of mathematics
the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function
Julia_set
Set cover (also called "minimum cover" problem). This is equivalent, by transposing the incidence matrix, to the hitting set problem. Set packing Set
List_of_NP-complete_problems
Subdivision into few independent sets
partitioning. The fractional set packing and set covering problems associated with a matroid (that is, assign a weight to each independent set in such a way that
Matroid_partitioning
given cube? More unsolved problems in mathematics In combinatorics, tripod packing is a problem of finding many disjoint tripods in a three-dimensional grid
Tripod_packing
Artificial intelligence method for mathematical discovery
the cap set problem in extremal combinatorics and to the online bin packing problem, where it found new mathematical constructions and new packing heuristics
FunSearch
Problem on triangles in graph theory
{\displaystyle G} have a triangle-hitting set whose size is at most twice the number of triangles in an optimal packing? More unsolved problems in mathematics
Tuza's_conjecture
Fractal composed of tangent circles
mathematics, an Apollonian gasket, Apollonian net, or Apollonian circle packing is a fractal generated by starting with a triple of circles, each tangent
Apollonian_gasket
2D geometric minimization problem
The strip packing problem is a 2-dimensional geometric minimization problem. Given a set of axis-aligned rectangles and a strip of bounded width and infinite
Strip_packing_problem
Mathematical theory
packings. This article primarily discusses free packings. In general, a packing refers to any arrangement of a set of spatially-connected, possibly differently-sized
Finite_sphere_packing
Branch of geometry that studies combinatorial properties and constructive methods
polytopes Ehrhart polynomials Pick's theorem Hirsch conjecture Opaque set Packings, coverings, and tilings are all ways of arranging uniform objects (typically
Discrete_geometry
Dimension of a subset of a metric space
mathematics, the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension is
Packing_dimension
Shape with seven sides
optimal double lattice packing density of any convex set, and more generally for the optimal packing density of any convex set. Some 1000-kwacha coins
Heptagon
21: "Maximum clique (and therefore also maximum independent set and maximum set packing) cannot be approximated to within O ( n 1 − ϵ ) {\displaystyle
Welfare_maximization
Three-dimensional packing problem
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder
Sphere_packing_in_a_cylinder
Operations research problem of packing items into the largest number of bins
of the bin packing problem: in bin covering, the bin sizes are bounded from below and the goal is to maximize their number; in bin packing, the bin sizes
Bin_covering_problem
United States historic place
The Portland Packing Company Factory is an historic factory building at 14–26 York Street in Portland, Maine. It was added to the National Register of
Portland Packing Company Factory
Portland_Packing_Company_Factory
Method of determining fractal dimension
the centers of the open balls lie in the set S. The packing number N packing ( ε ) {\textstyle N_{\text{packing}}(\varepsilon )} is the maximal number of
Minkowski–Bouligand_dimension
Math theorem about sphere packing
and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of
Kepler_conjecture
1991 British television series
Packet of Three, re-titled as Packing Them In for the second series, is a comedy series broadcast by Channel 4 between 2 August 1991 and 4 November 1992
Packet_of_Three_(TV_series)
Proposed U.S. legislative initiative
Judicial Procedures Reform Bill of 1937, frequently called the "court-packing plan", was a failed legislative initiative proposed by U.S. President Franklin
Judicial Procedures Reform Bill of 1937
Judicial_Procedures_Reform_Bill_of_1937
Geometric concept
spheres it touches. For a lattice packing, the kissing number is the same for every sphere; but for an arbitrary sphere packing, the kissing number may vary
Kissing_number
Written acknowledgment that a person has received money or property in payment
A receipt (also known as a packing list, packing slip, packaging slip, (delivery) docket, shipping list, delivery list, bill of the parcel, manifest,
Receipt
Synthetic polymer
Polytetrafluoroethylene (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene, and has numerous applications because it is chemically inert. The commonly
Polytetrafluoroethylene
1969 United States Supreme Court case
NLRB v. Gissel Packing Co., Inc., 395 U.S. 575 (1969) was a unanimous United States Supreme Court case clarifying the application of the National Labor
NLRB_v._Gissel_Packing_Co.
2022 novel by Freida McFadden
is made to leave, Millie prepares to settle in, only to discover, while packing, that Andrew has locked her in the attic room. From Nina's perspective
The_Housemaid_(novel)
Limit on the parameters of a block code
code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the
Hamming_bound
2026 concert tour by Kanye West
Kelsey (July 5, 2026). "Ye fans 'forgive' controversial hip-hop star, packing Alamodome for July Fourth show". Express News. Archived from the original
Ye_Live_Concert_Tour
Data encoding standard
by the Motion Imagery Standards Board. In a binary stream of data, a KLV set is broken down in the following fashion, with all integer interpretation
KLV
Condition for fractals in math
computation of the packing measure. An equivalent statement of the open set condition is to require that the s-dimensional Hausdorff measure of the set is greater
Open_set_condition
Computer science algorithm
First-fit-decreasing (FFD) is an algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins
First-fit-decreasing bin packing
First-fit-decreasing_bin_packing
Graph coloring variant in graph theory
In graph theory, a packing coloring (also called a broadcast coloring) is a type of graph coloring where vertices are assigned colors (represented by
Packing_coloring
Subpermutation of a longer permutation
≥ k, and so the limit exists. When β is monotone, its packing density is clearly 1, and packing densities are invariant under the group of symmetries
Permutation_pattern
Season of television series
Brother' Season 28, Week 3 Eviction: A Unanimous Vote Sent Another Houseguest Packing". Deadline. Retrieved July 31, 2026. "Big Brother season 28 cast revealed
Big Brother 28 (American season)
Big_Brother_28_(American_season)
Continuous function that is not absolutely continuous
and every point not in the Cantor set is in one of these intervals, so its derivative is 0 outside of the Cantor set. On the other hand, it has no derivative
Cantor_function
British mathematician (1925–2015)
on the large sieve, on the Heilbronn triangle problem, and on square packing in a square. He was a coauthor of the book Sequences on integer sequences
Klaus_Roth
Optimization algorithm
(FF) is an online algorithm for bin packing. Its input is a list of items of different sizes. Its output is a packing - a partition of the items into bins
First-fit_bin_packing
American operations manager
Mathematics. pp. 119–148. Balas, E.; E. Zemel (1977). Graph Substitution and Set Packing Polytopes. Vol. 7. Networks. pp. 267–284. Balas, E.; E. Zemel (1984)
Eitan_Zemel
British TV sitcom (1984–1986)
break. Another recurring character is the hotel waiter Carlos. Although set in Spain, the show was recorded entirely in the Leeds Studios – only for
Duty_Free_(TV_series)
2007 studio album by Stereophonics
artwork, commenting, "And that's not to mention the distasteful artwork of two sets of psychedelic glossed-up lips pulling a grenade pin." The band's newsletter
Pull_the_Pin
1999 American film
suggests to them that he recognizes the work. Later, Banning finds Crown packing his belongings with Anna. He promises Banning his interest lies with her
The Thomas Crown Affair (1999 film)
The_Thomas_Crown_Affair_(1999_film)
5, 2016. "BRIA 24 1 b Upton Sinclairs The Jungle: Muckraking the Meat-Packing Industry - Constitutional Rights Foundation". Crf-usa.org. June 30, 1906
List of fiction set in Chicago
List_of_fiction_set_in_Chicago
Season of television series
2026 (2026-01-19) As the battle in the Sapporo brewery continues, Ostrong sets packing straw alight as a distraction and then catches Asirpa. Ostrong believes
Golden_Kamuy_season_5
Heavy duty container used for shipping
time and effort and helps prevent delayed flights. Each ULD has its own packing list, manifest, or tracking identification to improve control and tracking
Shipping_container
British actress
co-directed. In 2003, a portrait of Ward by artist Jan Williamson won the Packing Room Prize at the Archibald Prize competition. In 2005, Ward was made a
Rachel_Ward
American sci-fi horror television series
Hawley. It is the first television series in the Alien franchise and is set two years before the events of the 1979 film Alien. The series stars Sydney
Alien:_Earth
October 31, 1933 354 6378 Code of Fair Competition for the Canning and Packing Machinery Industry October 31, 1933 355 6379 Code of Fair Competition for
List of executive actions by Franklin D. Roosevelt
List_of_executive_actions_by_Franklin_D._Roosevelt
Technology hub in California, United States
the tech industry, the region had been the largest fruit-producing and packing region in the world up through the 1960s, with 39 fruit canneries. The
Silicon_Valley
Geometric shape formed from nine squares
= 9,910 fixed nonominoes. 37 nonominoes have holes. Therefore a complete set cannot be packed into a rectangle and not all nonominoes have tilings. Of
Nonomino
Audio file format
Meridian Lossless Packing, also known as Packed PCM (PPCM),[citation needed] is a lossless compression technique for PCM audio data developed by Meridian
Meridian_Lossless_Packing
2026 Spanish film
friends, and Hasley tearfully attend his funeral. The movie ends with Hasley packing her bags and visiting her and Luke's secret place one last time. Mikel
Boulevard_(2026_film)
applicable to workers in the American meat packing industry. According to scholars of the American meat packing industry, despite federal regulation through
Labor rights in American meatpacking industry
Labor_rights_in_American_meatpacking_industry
Form of political manipulation
voting power of the opposing party's supporters across many districts) or "packing" (concentrating the opposing party's voting power in one district to reduce
Gerrymandering
with rational reciprocal series. A conjecture with Norman Oler on circle packing in an equilateral triangle with a number of circles one less than a triangular
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Indigenous Canadian miner (c. 1855 – 1916)
Káa Goox (Dawson Charlie) they formed a partnership and spent two years packing on the Chilkoot Pass. Carmack later started a family with Keish's sister
Keish
Enclosure or protection of products for distribution, storage, and sale
sealing machines Box, case erecting, tray forming, and carrier forming, packing, unpacking, closing, and sealing machines Cartoning machines Cleaning,
Packaging
2023 Canadian drama film
has to work, then she asks to see his chickens. Later on, as Waverly is packing for Toronto, her aunt Rachel asks her if she really needs to do the Toronto
Float_(2023_film)
Mathematics award
proof that the E 8 {\displaystyle E_{8}} lattice provides the densest packing of identical spheres in 8 dimensions, and further contributions to related
Fields_Medal
Netflix political thriller by Debora Cahn
Dominates BAFTA Television Awards Nominations, With 'A Thousand Blows' Also Packing A Punch". Deadline Hollywood. Archived from the original on March 25, 2026
The Diplomat (American TV series)
The_Diplomat_(American_TV_series)
Geometric shape formed from two squares
from a chessboard makes it impossible to tile with dominoes. Dominoes, a set of domino-shaped gaming pieces Tatami, Japanese domino-shaped floor mats
Domino_(mathematics)
2004 Serbia and Montenegro film
Packing the Monkeys, Again! (Serbian: Opet pakujemo majmune) is a 2004 Montenegrin drama film directed by Marija Perović. Packing the Monkeys, Again!
Packing_the_Monkeys,_Again!
On lattices and sphere packing in Euclidean space
anisohedral tiling in three-dimensional Euclidean space, and the densest sphere packing in Kepler conjecture. Respectively, these questions were answered affirmatively
Hilbert's_eighteenth_problem
2018 (2018-11-09) "Aim for the Center!" (Japanese: センターをねらえ！だゾ) 982 "Help with Packing" (Japanese: 荷造りを手伝うゾ) November 16, 2018 (2018-11-16) "Suddenly Grandpa"
List of Crayon Shin-chan episodes (2012–2021)
List_of_Crayon_Shin-chan_episodes_(2012–2021)
2025 crime drama TV series
Dominates BAFTA Television Awards Nominations, With 'A Thousand Blows' Also Packing a Punch". Deadline Hollywood. Retrieved 25 March 2026. Ramachandran, Naman
Adolescence_(TV_series)
Number of balls of a given size needed to cover a given space
number quantifies the size of a set and can be applied to general metric spaces. Two related concepts are the packing number, the number of disjoint balls
Covering_number
Process of choosing jury members
myriad of other tools and techniques not directly related to juries. Jury packing is "illegally or corruptly influencing a jury by making available for jury
Jury_selection
2025 American comedy television series
Dominates BAFTA Television Awards Nominations, With 'A Thousand Blows' Also Packing A Punch". Deadline Hollywood. Archived from the original on March 25, 2026
The_Studio_(TV_series)
Former Yugoslavian mine
The mine is laid in the well, the safety element is taken off, safety is set at 1 or 4 minutes the starter is pressed (the fuze bar is fitted) and the
TMRP-6
Roll of fabric
production activity is managed by unique batches. When it comes to fabric, a set of bolts or rolls forms a batch, representing the production. The yarn is
Bolt_(cloth)
American vlogger and convicted child abuser (born 1982)
then-6-year-old daughter Eve at school, because Eve is responsible for packing her own lunch. Miller, Jordan (October 4, 2023). "Ruby Franke case: A timeline
Ruby_Franke
Combinatorics problem proposed by Thomas Penyngton Kirkman
partition of the lines into spreads is called a packing or parallelism. There are 56 spreads and 240 packings. When Hirschfeld considered the problem in his
Kirkman's_schoolgirl_problem
Character encoding
Seven-bit characters must be encoded into octets following one of three packing modes: CBS: using this encoding, it is possible to send up to 93 characters
GSM_03.38
2022 survival film by Scott Mann
signal. Shiloh sends a message for help to her Instagram followers by packing her phone in a shoe and dropping it outside the range of the interference
Fall_(2022_film)
Act of the Parliament of the United Kingdom
Section. 19 & 20 Vict. c. 114 Hay and Straw Act 1856 An Act to prevent false Packing and other Frauds in the Hay and Straw Trade. Section Five from "Provided
Statute_Law_Revision_Act_1875
2022 film by Chloe Okuno
outline of a severed head in his shopping bag. She returns home and begins packing but is interrupted by music playing in Irina's apartment. Inside, she finds
Watcher_(film)
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