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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
2000 paper "Graph Structure in the Web" at the WWW conference. "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
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
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
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
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
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
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
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
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
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
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 with a 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
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
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
and such an implementation is computable in polynomial time by the randomized rounding scheme of Aziz, Lev, Mattei, Rosenschein and Walsh; consequently
Fractional multiwinner approval voting
Fractional_multiwinner_approval_voting
Basketball player selection
rounds resulting in a new random rounding order and subsequent even-numbered rounds resulting in the reversal of that previous round's ordering in question
1967_ABA_draft
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
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
Discrete probability distribution
overflow on computers: λk and k!. The fraction of λk to k! can also produce a rounding error that is very large compared to e−λ, and therefore give an erroneous
Poisson_distribution
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
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
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
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
2011 American television series
So Random! is an American sketch comedy television series created by Steve Marmel and developed by Michael Feldman that aired on Disney Channel from June
So_Random!
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
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
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
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
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
English explorer (born 1944)
2015. Cool, Kenton (2015). One Man's Everest. London: Preface (Penguin Random House). pp. 143–162. ISBN 9781848094482. "Fiennes climbs to Everest summit"
Ranulph_Fiennes
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
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
Digit necessary to represent a quantity
This is the default rounding method implied in many disciplines[citation needed] if the required rounding method is not specified. Round half to even, which
Significant_figures
English association football league
Kick-Off". Glory, Goals and Greed: Twenty Years of the Premier League. Random House. ISBN 978-1-78057-144-7. "Premiership 1992/93". Soccerbase. Archived
Premier_League
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
Soccer tournament in Canada, Mexico, and the United States
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
2024 game show hosted by Rob Lowe
(randomized or choosing to play on)/Defender (chosen by challenger). Winners of individual duels are shown in boldface shown as Challenger (randomized
The Floor (American game show)
The_Floor_(American_game_show)
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
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
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
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
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
NFL team 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
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
Psychedelic drug
(February 2023). "Ketanserin Reverses the Acute Response to LSD in a Randomized, Double-Blind, Placebo-Controlled, Crossover Study in Healthy Participants"
LSD
Calculate the maximum revenue in the entire population; apply a certain random rounding process that guarantees that the calculation is truthful with-high-probability
Profit_extraction_mechanism
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
American former basketball player and sports 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
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
American actress (1946–2025)
As writer Then Again, New York: Random House, 2011, ISBN 9781400068784 Let's Just Say It Wasn't Pretty, New York: Random House, 2014, ISBN 9780812994261
Diane_Keaton
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
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)
Randomized algorithm
Reservoir sampling is a family of randomized online algorithms for choosing a simple random sample, without replacement, of k items from a population
Reservoir_sampling
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)
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
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
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
satellite links. Instant worldwide reaction and debate were made possible by round-the-clock television news organizations and by the Internet. As a result
Timeline for the day of the September 11 attacks
Timeline_for_the_day_of_the_September_11_attacks
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
English computer scientist (1912–1954)
original on 17 February 2019. Retrieved 18 March 2019. Turing, A.M. (1948). "Rounding-Off Errors in Matrix Processes". The Quarterly Journal of Mechanics and
Alan_Turing
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
2015 video game
difference was the inclusion of friendly fire on the harder one. Arcade: Random limited time events which modify elements of existing modes and is on a
Tom Clancy's Rainbow Six Siege
Tom_Clancy's_Rainbow_Six_Siege
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
Counterintuitive result in probability
infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will almost surely
Infinite_monkey_theorem
American actress (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
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
South Korean television series (2021–2025)
said, "The game was selected because the scene filled with so many people randomly moving and stopping could be viewed as a ridiculous but a sad group dance
Squid_Game
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
Distribution procedure
Random priority (RP), also called random serial dictatorship (RSD), is a procedure for fair random assignment - dividing indivisible items fairly among
Random priority item allocation
Random_priority_item_allocation
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, loses his limp
The_Usual_Suspects
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
1851 novel by Herman Melville
before crossing to the Indian Ocean via the Cape of Good Hope rather than rounding Cape Horn. En route, Tashtego sights a sperm whale, and the shadowy figures
Moby-Dick
American singer and YouTuber (1994–2016)
special musical guest performing her hit song "Advice" on Disney Channel's So Random!, which premiered on December 11. In January 2012, Grimmie moved to Los
Christina_Grimmie
Standard example in game theory
behavior in the iterated version of the game can differ from that in a single-round version. This insight anticipated a key result in game theory: cooperation
Prisoner's_dilemma
American aviator, aerospace engineer and business magnate (1905–1976)
Forge: How American Business Produced Victory in World War II. New York: Random House, 2012. ISBN 978-1-4000-6964-4. Higham, Charles. Howard Hughes: The
Howard_Hughes
Seed-bearing part of a flowering plant
plants. During meiosis homologous chromosomes replicate, recombine and randomly segregate, and then undergo segregation of sister chromatids to produce
Fruit
Canadian singer-songwriter (1938–2023)
Lightfoot the greatest songwriter in the world. That same year, Penguin Random House Canada published the Gordon Lightfoot biography, Lightfoot, written
Gordon_Lightfoot
1956 British film by Herbert Wilcox
Stephen Watts (21 August 1955). "Neagle-Wilcox on Youth – Profits – Random Round-Up of New Ventures". New York Times. p. 101. "London". Variety. 13 July
My_Teenage_Daughter
American singer, actor and producer (born 1978)
voting every week from the Wild Card week to the finale, when the possibly-random voting result gave Studdard the win. Rolling Stone featured Aiken on the
Clay_Aiken
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
Network that allows computers to share resources and communicate with each other
themselves, such as the technical exploitation of clients, poor quality random number generators, or key escrow. E2EE also does not address traffic analysis
Computer_network
2012 film by Christopher McQuarrie
the nearby Fort Duquesne Bridge, with the Sun at his back. An apparently random bar fight helps Reacher realize that someone wants him to drop his investigation
Jack_Reacher_(film)
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
Home video game console
chosen as the format. The team designed the system with 2,000 bytes of random-access memory (RAM). The console's hardware was largely based on arcade
Nintendo_Entertainment_System
NFL team in Los Angeles, 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
2002 studio album by Beck
session, Hansen began strumming his 1995 single "It's All in Your Mind" randomly before beginning a new song, and Godrich became ecstatic, remarking "We
Sea_Change_(album)
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 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
Australian rules football competition
the percentage earned in such matches, with a final tie-breaker being a random drawing of lots. Several teams also play against each other at set times
Australian_Football_League
Indian independence activist (1869–1948)
ˈkəɾəmtʃənd ˈɡɑndʱi] "Gandhi". Archived 14 January 2015 at the Wayback Machine Random House Webster's Unabridged Dictionary. B. R. Nanda (2019). "Mahatma Gandhi"
Mahatma_Gandhi
American aviation pioneer (1897–disappeared 1937)
2012, at the Wayback Machine at Great Circle Mapper "Amelia Lost". Penguin Random House Library Marketing. Jacobson, Randall S., PhD. "The Final Flight. Part
Amelia_Earhart
Italian explorer and navigator (1454–1512)
Felipe (2007). Amerigo: The Man Who Gave His Name to America. New York: Random House. Formisano, Luciano (1992). Letters from a New World: Amerigo Vespucci's
Amerigo_Vespucci
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
Cuban baseball player (born 1964)
(February 5, 2021). "Former MLB star Jose Canseco TKO'd in boxing match by some random intern". Bloody Elbow. Archived from the original on February 6, 2021. Retrieved
Jose_Canseco
2003 video game
the game offline without AI partners. Each scenario also has invisible, randomly generated "SP" items hidden throughout the level. There are twenty scenario
Resident_Evil_Outbreak
Thirty-fourth national census of New Zealand
807,000 and 4,944,000. Data uses fixed random rounding to protect confidentiality; each data point is rounded either to the nearest multiple of 3 (2⁄3
2018_New_Zealand_census
travel, tourism, insurance
RANDOMIZED ROUNDING
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RANDOMIZED ROUNDING
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RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
RANDOMIZED ROUNDING
travel, tourism, insurance