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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
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
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
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
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
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
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
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
Geometrical structure
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
Several sets of circles associated with Apollonius of Perga
fields of mathematics; for example, it is the limit set of Kleinian groups; see also Circle packing theorem. The circles of Apollonius may also denote
Circles_of_Apollonius
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
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
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
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
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
Synthetic polymer
Polytetrafluoroethylene (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene, and has numerous applications because it is chemically inert. The commonly
Polytetrafluoroethylene
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
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
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
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)
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
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
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
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
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
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
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.
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
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
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)
American baseball player and manager (1941–2026)
(October 10, 2005). "After 18 Innings and Almost 6 Hours, Astros Send Braves Packing Again". The New York Times. ISSN 0362-4331. Retrieved May 10, 2026. "2006
Bobby_Cox
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
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
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
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)
2026 American television series
rating of 71% based on 24 reviews. The website's critics consensus reads, "Packing big performances by Banks and Macfadyen, The Miniature Wife's premise risks
The_Miniature_Wife
Japanese art of paper folding
allocations is referred to as the 'circle-packing' or 'polygon-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial
Origami
American professional basketball player (born 1988)
RPI Rankings". Cbssports.com. Retrieved April 9, 2013. "Davidson sent packing by College of Charleston in Southern semis". USA Today. March 9, 2009.
Stephen_Curry
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
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
Upcoming video game
"Naughty Dog's next game kicks off a new 'franchise' with a sci-fi PS5 romp packing the studio's 'wildest, most creative story' and 'deepest gameplay' yet"
Intergalactic: The Heretic Prophet
Intergalactic:_The_Heretic_Prophet
2025 American crime drama television series
Dominates BAFTA Television Awards Nominations, With 'A Thousand Blows' Also Packing a Punch". Deadline Hollywood. Retrieved March 25, 2026. Dalton, Ben (January
Task_(TV_series)
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)
American social media personality in Utah
pigs, and other livestock. Cattle and pigs are part of the farm's meat packing operations, where the packaged meat is sold on her online store. The Ballerina
Hannah_Neeleman
2026 Indian film
dialogue writing does something most recent Tamil films fail to do. [...] Packing a twist a minute in the last hour, everything feels rushed, and without
Kaalidas_2
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
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!
lowest maximum packing density of all centrally-symmetric convex plane sets Sphere packing problems, including the density of the densest packing in dimensions
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
American multinational technology conglomerate
computer recorded locations to make up an individual shipment; sorting and packing orders; and shipping. A computer that records the location of goods and
Amazon_(company)
Problem in combinatorial optimization
to the Bin Packing Problem. It differs from the Bin Packing Problem in that a subset of items can be selected, whereas, in the Bin Packing Problem, all
Knapsack_problem
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
Accountant, Board of Customs and Excise. Harry Allen, Director, Lloyds Packing Warehouses Ltd. Albert Henry Edward Allingham, Senior Staff Officer, Admiralty
1946_New_Year_Honours_(MBE)
American comedy series
(season 3), Jimmy's father Lisa Gilroy as Kimmy (season 3), a nurse Liz sets Jimmy up with Candice Bergen as Constance (season 3), Derek's mother Matt
Shrinking_(TV_series)
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 singer-songwriter (born 1989)
"Five Stars for Taylor Swift's Sparkling New Album: Basking in Romance, Packing in Pot-Shots". The Irish Times. Archived from the original on October 3
Taylor_Swift
2010 film by Edward Zwick
arrives and reveals Jamie has been promoted to the Chicago office. While packing, Jamie finds the videotape recorder with a video of himself and Maggie
Love_&_Other_Drugs
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
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
2023 direct-to-video animated movie
its sequels, but his career eventually falls apart. Cage is later seen packing his car and preparing to shoot his new film on a remote island. Joel McHale
Mortal Kombat Legends: Cage Match
Mortal_Kombat_Legends:_Cage_Match
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
American politician and activist (born 1989)
original on July 6, 2022. Schultz, Marisa; Phares, Kelly. "AOC backs court-packing push: 'We should be expanding the court'". Fox News. Archived from the
Alexandria_Ocasio-Cortez
AI that generates content
used to discover new mathematical constructions in the cap set problem and the bin packing problem. In 2023, Google DeepMind introduced AlphaDev, which
Generative_AI
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
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
Graph-theoretic description of polyhedra
system and lifting the result into three dimensions, or by using the circle packing theorem. Several extensions of the theorem are known, in which the polyhedron
Steinitz's_theorem
2019 American independent film
characters had come to town expecting to spend no more than a few days packing up April's house at first and would likely find themselves forced to share
Driveways_(film)
2024 studio album by Gracie Abrams
first time as a surprise song. The performance, part of the show's acoustic set, featured Abrams on piano and Swift on guitar. On July 15, Abrams announced
The_Secret_of_Us
American comedy series
way before you, prepping. A lot of times, actors come to the set like, "Why is this set up this way?" There's all these reasons." In June 2026, Netflix
The_Four_Seasons_(TV_series)
1906 novel by Upton Sinclair
In 1904, Sinclair spent seven weeks gathering information in the meat packing district of the Union Stock Yards in Chicago for the socialist newspaper
The_Jungle
Chinese meat processing company
majority owned by Hong Kong based WH Group. Founded in 1936 as the Smithfield Packing Company by Joseph W. Luter and his son, the company is the largest pig
Smithfield_Foods
2021 musical by Jeanine Tesori and David Lindsay-Abaire
her parents that they can finally go on their road trip, and to start packing. She then goes into her room, and sees that they have replaced her bed
Kimberly_Akimbo_(musical)
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
SET PACKING
SET PACKING
Male
English
Short form of English Stephen, STE means "crown."
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Female
Egyptian
, the wife of the usurper Sipthah.
Female
Egyptian
, a sister of Sekherta.
Female
Egyptian
, an uncertain goddess.
Female
Egyptian
, the wife of Osirtesen.
Female
Hungarian
Hungarian form of Greek Elisabet, ERZSÉBET means "God is my oath."
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, a sister of Sekherta.
Surname or Lastname
English and German
English and German : topographic name for someone who lived by the sea-shore or beside a lake, from Middle English see ‘sea’, ‘lake’ (Old English sǣ), Middle High German sē. Alternatively, the English name may denote someone who lived by a watercourse, from an Old English sēoh ‘watercourse’, ‘drain’.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Female
Egyptian
, second wife of Antef.
Surname or Lastname
English
English : variant spelling of See.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Male
Egyptian
, the seven great spirits of the Ritual of the Dead.
Female
Egyptian
, a wife and daughter of Antef.
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
SET PACKING
SET PACKING
Boy/Male
Indian, Sanskrit
Pious
Boy/Male
Indian, Punjabi, Sikh
Love for Mind
Boy/Male
Irish
Surname.
Boy/Male
Tamil
Lord Vishnu
Girl/Female
Hindu, Indian
Beautiful
Girl/Female
Native American
Star dancer.
Boy/Male
Arabic, Australian, German, Muslim
Peace; Peaceful; Peach
Girl/Female
Hindu, Indian
Beloved of Shiva
Boy/Male
Australian, French, German, Italian, Latin
Italian Form of Maurice; Dark-skinned; Moorish
Boy/Male
Hindu, Indian, Traditional
Moon
SET PACKING
SET PACKING
SET PACKING
SET PACKING
SET PACKING
v. t.
To put in order in a particular manner; to prepare; as, to set (that is, to hone) a razor; to set a saw.
a.
Established; prescribed; as, set forms of prayer.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
n.
Direction or course; as, the set of the wind, or of a current.
n.
A series of as many games as may be necessary to enable one side to win six. If at the end of the tenth game the score is a tie, the set is usually called a deuce set, and decided by an application of the rules for playing off deuce in a game. See Deuce.
imp. & p. p.
of Set
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
v. t.
To establish as a rule; to furnish; to prescribe; to assign; as, to set an example; to set lessons to be learned.
v. t.
To determine; to appoint; to assign; to fix; as, to set a time for a meeting; to set a price on a horse.
v. t.
To make to agree with some standard; as, to set a watch or a clock.
v. t.
To extend and bring into position; to spread; as, to set the sails of a ship.
n.
A young plant for growth; as, a set of white thorn.
n.
That which is set, placed, or fixed.
a.
Firm; unchanging; obstinate; as, set opinions or prejudices.
v. i.
To fit or suit one; to sit; as, the coat sets well.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
n.
See Set, n., 2 (e) and 3.
v. t.
To reduce from a dislocated or fractured state; to replace; as, to set a broken bone.
v. i.
To be fixed for growth; to strike root; to begin to germinate or form; as, cuttings set well; the fruit has set well (i. e., not blasted in the blossom).