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In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many
Randomized_rounding
Replacing a number with a simpler value
Rounding or rounding off is the process of adjusting a number to an approximate, more convenient value, often with a shorter or simpler representation
Rounding
American computer scientist
subsequent focus on ad revenue in the prioritization of search results. "Randomized Rounding And Discrete Ham-Sandwich Theorems: Provably Good Algorithms for
Prabhakar_Raghavan
Concept in integral mathematics
is the rounding ratio). If there is an instance with integrality gap IG, then every rounding strategy will return, on that instance, a rounded solution
Linear_programming_relaxation
below 1. The method is particularly relevant in the context of randomized rounding (which uses the probabilistic method to design approximation algorithms)
Method of conditional probabilities
Method_of_conditional_probabilities
Nonconstructive method for mathematical proofs
algebra, and real analysis, as well as in computer science (e.g. randomized rounding) and information theory. If every object in a collection of objects
Probabilistic_method
American mathematician
using a new rounding technique on a carefully designed bipartite graph. We now state the LP formulation and briefly describe the rounding technique. We
David_Shmoys
Optimization problem in computer science and operations research
Schulz and Skutella present a (3/2+ε)-approximation algorithm using randomized rounding. Their algorithm is a (2+ε)-approximation for the problem with job
Unrelated-machines_scheduling
Classical problem in combinatorics
{\displaystyle f} is the maximum number of sets that any element belongs to. Randomized rounding is an approximation technique for the weighted set cover problem
Set_cover_problem
Problem in graph theory
derived from the first level of the sum of squares hierarchy) and randomized rounding. It achieves an approximation ratio α ≈ 0.878 , {\displaystyle \alpha
Maximum_cut
Algorithmic technique
Raghavan's method of pessimistic estimators for derandomization of randomized rounding algorithms; Klivans and Servedio linked boosting algorithms in learning
Multiplicative weight update method
Multiplicative_weight_update_method
Creating sequence of numbers that cannot be predicted
cryptography. Random number generators have applications in gambling, statistical sampling, computer simulation, cryptography, completely randomized design,
Random_number_generation
Tree-based ensemble machine learning methods
The general method of random decision forests was first proposed by Salzberg and Heath in 1993, with a method that used a randomized decision tree algorithm
Random_forest
Class of algorithms that find approximate solutions to optimization problems
an integer solution. Typical rounding techniques include simple threshold rounding, Randomized rounding, Iterative rounding, etc. Dual-fitting methods.
Approximation_algorithm
order of what the third round would become, and then subsequent odd-numbered rounds being done in a newly randomized rounding order and subsequent even-numbered
American Basketball Association draft
American_Basketball_Association_draft
Edges that hit all cycles in a graph
polynomial-time approximation scheme. Its main ideas are to apply randomized rounding to a linear programming relaxation of the problem, and to derandomize
Feedback_arc_set
Hungarian-French mathematician
2015-11-02. Shayan Oveis Gharan; Amin Saberi; Mohit Singh (2011). "A Randomized Rounding Approach to the Traveling Salesman Problem" (PDF). Proc. IEEE 52nd
András_Sebő
Chess variant with randomized starting position
position of the pieces on the players' home ranks is randomized, following certain rules. The random setup makes gaining an advantage through the memorization
Chess960
British military officer (1810–1857)
personally executed many prisoners of war. In one episode, he compelled randomly rounded up Brahmins from Cawnpore, who had nothing to do with the massacre
James_George_Smith_Neill
qualification third round, while the remaining teams qualified for the 2027 AFC Asian Cup qualification – play-off round. Second round: 36 teams (ranked
2026 FIFA World Cup qualification (AFC)
2026_FIFA_World_Cup_qualification_(AFC)
Topics referred to by the same term
the Korean War Roundup (police action), targeting random members of a group for mass arrest Rounding up, when a boat heads into the wind, the rudder having
Roundup
Association football tournament
A single round-robin format in which each team in a group played all other teams in their group once, with the venues either drawn at random or assigned
2026 FIFA World Cup qualification
2026_FIFA_World_Cup_qualification
Type of feedforward neural network
The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (Masters) (in Finnish). University
Multilayer_perceptron
2011 American television series
So Random! is an American sketch comedy series created by Steve Marmel and developed by Michael Feldman that aired on Disney Channel from June 5, 2011
So_Random!
International football competition
The second round of 2026 FIFA World Cup AFC qualification, which also served as the second round of 2027 AFC Asian Cup qualification, began on 16 November
2026 FIFA World Cup qualification – AFC second round
2026_FIFA_World_Cup_qualification_–_AFC_second_round
American basketball player (born 1988)
Double Banger in Oklahoma City". NBA.com. Retrieved May 26, 2025. "Sunday Randomness: Steph Curry's epic dagger in OKC revisited five years later". Associated
Stephen_Curry
Technique to reduce dimensionality of points in Euclidean space
(2016-08-16), Lecture Notes on Randomized Linear Algebra, arXiv:1608.04481 Achlioptas, Dimitris (2001). "Database-friendly random projections". Proceedings
Random_projection
Association football club in Spain
Lowe: Fear and loathing in La Liga.. Barcelona vs Real Madrid". p. 67. Random House. 26 September 2013 Aguilar, Paco (10 December 1998). "Barca – Much
FC_Barcelona
Association football club in Spain
"Sid Lowe: Fear and loathing in La Liga.. Barcelona vs Real Madrid" p. 67. Random House. 26 September 2013 Phil Ball (2001). Morbo: the story of Spanish football
Real_Madrid_CF
Football tournament
usually based on geographical criteria, and teams in each pot are drawn at random to the eight groups. Since 1998, constraints have been applied to the draw
FIFA_World_Cup
American basketball player and analyst (born 1972)
round of the playoffs. After defeating the Chicago Bulls in the first round, the Cavaliers went on to lose to the Boston Celtics in the second round.
Shaquille_O'Neal
King Arthur and order of chivalry in Arthurian romance
The Knights of the Round Table (French: Chevaliers de la Table Ronde) are the legendary knights of the fellowship of King Arthur that first appeared in
Knights_of_the_Round_Table
Cryptographic model of a random function
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every unique query with a (truly) random response chosen uniformly
Random_oracle
Association football tournament in Qatar
the draw are shown below. Notes H : Hosts The eight groups were formed randomly, selecting one team from each of the four pots. Two teams from the same
2022_FIFA_World_Cup
American entrepreneur and venture capitalist (born 1967)
around $20 million" (Bloomberg remarked that, "the investment amounts to a rounding error for Thiel's firm."). The company sold the majority of its crypto
Peter_Thiel
Queen of the United Kingdom from 1837 to 1901
Aubyn, pp. 546–548 MacMillan, Margaret (2013), The War That Ended Peace, Random House, p. 29, ISBN 978-0-8129-9470-4 Hibbert, pp. 457–458; Marshall, pp
Queen_Victoria
American mixed martial artist (born 1987)
my opinion is Jon Jones should be on a very short leash and should be random tested here until they sort out why he has these anomalies." This resulted
Jon_Jones
Irish mixed martial artist (born 1988)
Mayweather Jr. in a highly publicised bout, which he lost via TKO in the 10th round. He returned to MMA and challenged for the UFC Lightweight Championship
Conor_McGregor
European association football tournament
contested by top-division European clubs. The competition begins with a round robin league phase to qualify for the double-legged knockout rounds, and
UEFA_Champions_League
Type of artificial neural network
The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors (Masters) (in Finnish). University
Feedforward_neural_network
British singer-songwriter (born 1945)
History of Rock and Roll. Second edition; Jim Miller, editor. New York: Random House, 1980, ISBN 0-394-51322-3, p. 379. "every picture tells a story -
Rod_Stewart
American film franchise
J.W.; Laurent Bouzereau (2008). The Complete Making of Indiana Jones. Random House. ISBN 978-0-09-192661-8. Irwin, W. (2023). Kowalski D. (ed.). Indiana
Indiana_Jones
American politician and lawyer (1925–1968)
Tye, Larry (2017). Bobby Kennedy: The Making of a Liberal Icon. New York: Random House. ISBN 978-0-8129-8350-0. OCLC 935987185. "Robert Kennedy's Attorney
Robert_F._Kennedy
The randomized weighted majority algorithm is an algorithm in machine learning theory for aggregating expert predictions to a series of decision problems
Randomized weighted majority algorithm
Randomized_weighted_majority_algorithm
Psychedelic drug
(February 2023). "Ketanserin Reverses the Acute Response to LSD in a Randomized, Double-Blind, Placebo-Controlled, Crossover Study in Healthy Participants"
LSD
King of the United Kingdom from 1936 to 1952
ISBN 978-0-297-77031-2. Vickers, Hugo (2006). Elizabeth: The Queen Mother. Arrow Books/Random House. ISBN 978-0-09-947662-7. Wheeler-Bennett, Sir John (1958). King George
George_VI
Association football tournament in North America
draw and thus were automatically allocated to Pot 4. The 12 groups were randomly formed by selecting one team from each of the four pots. With the exception
2026_FIFA_World_Cup
Study of mental functions and behaviors
statistical hypothesis testing. Although the field makes abundant use of randomized and controlled experiments in laboratory settings, such research can only
Psychology
specific individuals, Statistics Canada applies random rounding to census data, where all figures are rounded (either up or down) to a multiple of 5 (or in
Kitasoo/Xaixais_First_Nation
Tournament format in which the loser of each match-up is immediately eliminated
eliminated from the tournament. Each winner will play another in the next round, until the final match-up, whose winner becomes the tournament champion(s)
Single-elimination_tournament
Association football tournament in Brazil
pots based on geographic considerations. Under the draw procedure, one randomly drawn team – Italy – was firstly relocated from Pot 4 to Pot 2 to create
2014_FIFA_World_Cup
Probability distribution
equivalent to sampling a real number from the standard normal distribution and rounding this to the nearest representable floating point number. There is also
Normal_distribution
World War II memorial in Umbria, Italy
While the Germans were preparing a withdrawal to the Gothic line, they randomly rounded citizens and despite the pleas by the local bishop, two days later
Mausoleum_of_the_40_Martyrs
Binary tree selected at random
data structure that behaves like a random binary search tree. Such a data structure is known as a treap or a randomized binary search tree. Variants of the
Random_binary_tree
Polish clergyman
formalities. While in a street outside, he was caught in a łapanka, a random rounding-up of Polish hostages in reprisal for what the Nazi propaganda portrayed
Stanisław_Wiórek
Electoral system with lottery among ballots
A random ballot, or random dictatorship, is a randomized electoral system where the election is decided on the basis of a single randomly selected ballot
Random_ballot
English writer and journalist (1812–1870)
Charles Dickens: An Introduction to His Novels. Random House Studies in Language and Literature. Random House. ASIN B0011BLL8W. Archived from the original
Charles_Dickens
American musician (born 1950)
Records. p. 3. Posner, Gerald (2003). Motown: Music, Money, Sex and Power. Random House. p. 254. ISBN 978-0-375-50062-6. Stubbs, David (2018). Future Sounds:
Stevie_Wonder
American mixed martial arts promotion company
drug tests. So in February 2015, UFC announced a more aggressive year round, random-testing approach for its competitors to begin in July 2015. UFC announced
Ultimate Fighting Championship
Ultimate_Fighting_Championship
Symbolic serpent with its tail in its mouth
Oxford University Press, 2012, ISBN 0199545561 "ouroboros". Dictionary.com. Random House. "uroboros". Lexico UK English Dictionary. Oxford University Press
Ouroboros
18th edition of UEFA European Championship
the time of the final draw. The remaining group head position(s) will be randomly assigned to Pot 1 team(s) in the final draw. The group head positions were
UEFA_Euro_2028
Italian navigator and explorer (1451–1506)
Asia was possible. Columbus's plans were complicated by Bartolomeu Dias's rounding of the Cape of Good Hope in 1488, which suggested the Cape Route around
Christopher_Columbus
European football tournament
position are superscripted. The second qualifying round, third qualifying round and play-off round were divided into Champions Path (CH) and League Path
2025–26_UEFA_Champions_League
Men's association football team
2019). Camisetas legendarias del fútbol argentino (in Spanish). Penguin Random House Grupo Editorial Argentina. ISBN 978-950-28-1319-6. OCLC 1112221401
Argentina national football team
Argentina_national_football_team
President of the United States from 1961 to 1963
1917–1956. Random House. pp. 50–51. ISBN 978-0-8129-9713-2. Logevall, Fredrik (2020). JFK Coming of Age in the American Century, 1917–1956. Random House.
John_F._Kennedy
Part of the female reproductive tract
changes that happen with aging and childbirth include mucosal redundancy, rounding of the posterior aspect of the vagina with shortening of the distance from
Vagina
American chess grandmaster (1943–2008)
invented Fischer random chess, also known as Chess960, a chess variant in which the initial positions of the pieces are randomized to one of 960 possible
Bobby_Fischer
American boxer and activist (1942–2016)
Muhammad; Durham, Richard (1975). The Greatest: My Own Story. New York: Random House. ISBN 978-0-394-46268-4. OCLC 1622063. Archived from the original
Muhammad_Ali
Football championship
co-hosting it. Portugal were the defending champions, but were eliminated in the round of 16 by Belgium. Italy won their second European Championship title by
UEFA_Euro_2020
English experimental composer
tuned percussion groups, as well as performing versions of Grainger's Random Round, Reich's Music for 18 Musicians and several works by Carla Bley. Other
Dave_Smith_(composer)
Family of hash functions
independent random variables, which is often a problem in the analysis of randomized algorithms. Therefore, a more common alternative to dealing with rounding issues
K-independent_hashing
Norwegian chess grandmaster (born 1990)
FIDE World Fischer Random Chess Championship. He was automatically seeded to the semi-final round, as the unofficial Fischer Random Chess champion. He
Magnus_Carlsen
Large, round non-stellar astronomical object
for hydrostatic equilibrium is universally relaxed to a requirement for rounding and compaction under self-gravity; Mercury is not actually in hydrostatic
Planet
Statistical Disclose Control measures: random rounding to base 5; as used by Statistics Canada; random rounding to base 3, as used by Statistics New Zealand;
Barnardisation
Top-level subdivisions of Canada
(2002). The Big Book of Canada: Exploring the Provinces and Territories. Random House Digital, Inc. ISBN 978-0-88776-457-8. Pross, A. Paul; Pross, Catherine
Provinces and territories of Canada
Provinces_and_territories_of_Canada
Prime Minister of India from 1947 to 1964
acknowledged the highly successful electoral attraction of Nehru. "Nehru". Random House Webster's Unabridged Dictionary. 2020. Archived 5 March 2016 at the
Jawaharlal_Nehru
Algorithm that estimates unknowns from a series of measurements over time
following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems
Kalman_filter
National Football League franchise in Inglewood, California
bitter fight for control of the division. Some divisional meetings saw random acts of violence on both sides. The teams have two Super Bowl wins and seven
Los_Angeles_Rams
Empress of Russia from 1762 to 1796
427. Rounding 2006, p. 499 Dixon 2009, p. 315 Rounding 2006, p. 502 Rounding 2006, p. 508 Rounding 2006, pp. 508–509 Dixon 2009, p. 314 Rounding 2006
Catherine_the_Great
Pokémon species
12, 2024. Retrieved August 27, 2024. Doolan, Liam (December 27, 2019). "Random: Why Pikachu Is No Longer As Chubby As It Once Was". Nintendo Life. Archived
Pikachu
External genitalia of the female mammal
"Preoperative hair removal and surgical site infections: network meta-analysis of randomized controlled trials". Journal of Hospital Infection. 91 (2): 100–108. doi:10
Vulva
International football competition
fourth round of 2010 FIFA World Cup qualification was decided by a random draw conducted in Kuala Lumpur, Malaysia on 27 June 2008. The round commenced
2010 FIFA World Cup qualification – AFC fourth round
2010_FIFA_World_Cup_qualification_–_AFC_fourth_round
Randomized mathematical sequence based upon the Fibonacci sequence
above using floating point arithmetic validated by an analysis of the rounding error. Mark Embree and Nick Trefethen showed in 1999 that the sequence
Random_Fibonacci_sequence
World Cup final, held in Brazil
Group G, with two wins and a draw, after which they defeated Algeria in the round of 16, France in the quarter-final and Brazil, by a score of 7–1, in the
2014_FIFA_World_Cup_final
1937–1938 mass murder in China
who fled at the approach of any Japanese soldiers risked being shot. The rounding-up and mass killings of male civilians and captured POWs were referred
Nanjing_Massacre
1995 film by Bryan Singer
entire story, improvising on the spot by piecing together details from random items in Rabin's cluttered office. Verbal walks outside, losing his limp
The_Usual_Suspects
American football player and sports analyst (born 1948)
Sunday, he hosts two semiregular features, Ten Yards with TB, where he fires random questions at an NFL professional, and The Terry Awards, an annual comedic
Terry_Bradshaw
National Football League franchise in Tampa, Florida
August 4, 2024. Payton, Mike (December 8, 2017). "Lions vs. Buccaneers: Random Stats". Pride Of Detroit. Retrieved September 6, 2022. Schalter, Ty (September
Tampa_Bay_Buccaneers
Indian independence activist (1869–1948)
1888 and 1891 "Gandhi". Archived 14 January 2015 at the Wayback Machine Random House Webster's Unabridged Dictionary. B. R. Nanda (2019). "Mahatma Gandhi"
Mahatma_Gandhi
Techniques to train attention and awareness
Scheidegger, Milan (27 September 2024). "Meditating on psychedelics. A randomized placebo-controlled study of DMT and harmine in a mindfulness retreat"
Meditation
American basketball player (born 1988)
struggled with significant knee injuries throughout his career. In the first round of the 2012 NBA playoffs against the Philadelphia 76ers, Rose tore his ACL
Derrick_Rose
American singer-songwriter (1912–1967)
Jim (1997). Woody, Cisco and Me. Random House. ISBN 0-252-02276-9. Klein, Joe (1980). Woody Guthrie: A Life. Random House. ISBN 0-385-33385-4. Santelli
Woody_Guthrie
Games played in gambling facilities
casino game is one in which players gamble cash or chips on various possible random outcomes or combinations of outcomes, often in a casino environment. Such
Casino_game
American actress and director (born 1961)
Bomb. The recordings appeared on the soundtrack album and on singles. Rounding out film appearances in the late 1980s, Thompson starred in Some Kind of
Lea_Thompson
Gland of the male reproductive system
carcinoma with cyclophosphamide or 5-fluorouracil: results of first national randomized study". The Journal of Urology. 114 (6): 909–11. doi:10.1016/S0022-5347(17)67172-6
Prostate
roll In games that generate randomized loot, the "god roll" is loot that has the subjectively best selection of possible random attributes such as perks
Glossary_of_video_game_terms
American actress and author (born 1960)
That? and Freckleface Strawberry: Loose Tooth! were released as part of Random House's "Step Into Reading" program. They were followed by Freckleface Strawberry
Julianne_Moore
Bronze Age civilization on Crete and other Aegean Islands
the World Made the West: A 4,000 Year History (2025 Random House Trade Paperback ed.). London: Random House. p. 34. Watrous, L. Vance (2021). Minoan Crete:
Minoan_civilization
Two German multinational discount supermarket chains
has "Aldi Finds" aisles placed in the centre of their stores that feature random specialty items marked down in price, which has been nicknamed the "aisle
Aldi
European football tournament
qualifying round, will enter the third qualifying round. The labels in the parentheses show how each team qualified for the place of its starting round: TH:
2024–25_UEFA_Champions_League
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
Surname or Lastname
English
English : occupational name for an official who was responsible for rounding up stray animals and placing them in a pound, from an agent derivative of Middle English pind(en) ‘to shut up or enclose’. Black and MacLysaght quote Woulfe’s opinion that in Ireland this is often a reduced form of Prendergast.
Surname or Lastname
English
English : from Middle English p(o)und ‘enclosure (especially for confining animals)’; a topographic name for someone who lived near an enclosure in which animals were kept, or a metonymic occupational name for an official responsible for rounding up stray animals and placing them in a pound.Probably a translation of German Pfund or the North German cognate Pund.
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
Girl/Female
Hindu
Loving, Attractive & charming
Girl/Female
British, English, Hindu, Indian
Daughter; Radiance; Shadow
Girl/Female
Hebrew
Devoted to God.
Boy/Male
African, Arabic, German, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Pashtun, Sindhi, Swahili, Telugu
Best; Pure; Skilful; Another Name for the Prophet Muhammad; Pious; Name of a Surah in the Quran; Name of a Surah in Holy Quran
Girl/Female
Arabic, Muslim
Successor
Girl/Female
Gujarati, Hindu, Indian, Kannada, Traditional
Season
Biblical
house of grace
Boy/Male
Anglo Saxon
Name of a king.
Male
African
crown-ascending.
Boy/Male
Indian, Punjabi, Sikh
Fearless; Guided by Light
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
n.
The rounding, or rounded part, of the deck from a level line.
a.
Round or nearly round; becoming round; roundish.
n.
A wooden implement used by potters, crucible makers, etc., for forming, beating, and rounding their works. It is oval, round, and of other forms.
n.
The action of the elements on a rock in altering its color, texture, or composition, or in rounding off its edges.
n.
A tool for making creases or beads, as in sheet iron, or for rounding small tubes.
n.
Modifying a speech sound by contraction of the lip opening; labializing; labialization. See Guide to Pronunciation, / 11.
n.
Small rope, or strands of rope, or spun yarn, wound round a rope to keep it from chafing; -- called also service.
p. pr. & vb. n.
of Round