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provide popularized explanations of the Rental Harmony protocol. and provide on-line implementations. See Rental harmony for more solutions to this problem
Simmons–Su_protocols
Problem of fair division
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously. The housemates
Rental_harmony
constant, which represents the total apartment rent. This is known as the Rental Harmony problem. In general, in the economics literature, it is common to assume
Fair allocation of items and money
Fair_allocation_of_items_and_money
allowed; the variant in which monetary transfers are allowed is known as rental harmony. There are n people (also called: agents), and m objects (also called:
House_allocation_problem
Fair division class using unique allocation methods
always exists an envy-free allocation of rooms and rent (also called rental harmony) when there is a single secretive agent. The result holds for very general
Online_fair_division
Theorem on triangulation graph colorings
113–120. doi:10.1007/BF01587081. S2CID 5325605. Su, F. E. (1999). "Rental Harmony: Sperner's Lemma in Fair Division". The American Mathematical Monthly
Sperner's_lemma
Matching where no person wants to switch their thing with someone else's
another bundle with the same prices. An example of this setting is the rental harmony problem - matching tenants (the agents) to rooms (the items) while setting
Envy-free_matching
Type of optimization problem
work by those nations. Another use for chore division would be in the Rental harmony problem. Gardner, Martin (1978). aha! Insight. New York: W. F. Freeman
Chore_division
Criterion for fair division
the less valuable items. This solution is used, for example, in the rental harmony problem, and in envy-free pricing. Sharing a small number of items.
Envy-freeness
Kind of fair item allocation
envy-free item allocation, monetary payments are not allowed. In the rental harmony problem, monetary payments are allowed, and the agents are quasilinear
Envy-free_pricing
Problem of sharing resources
heterogeneous bad. Combinations and special cases are also common: Rental harmony (aka the housemates problem) – dividing a set of indivisible heterogeneous
Fair_division
Scientific tests related to game theory
procedure for settling the dispute, and present its (hypothetic) outcome. Rental harmony is the problem of simultaneously allocating rooms in an apartment and
Fair_division_experiments
Fair division problem for discrete items
some case-studies and lab experiments related to fair item assignment. Rental harmony - a fair division problem where indivisible items and a fixed total
Fair_item_allocation
possible. Envy-free item allocation - without the requirement of PE. Rental harmony - with an additional restriction that each agent must get a single item
Efficient approximately fair item allocation
Efficient_approximately_fair_item_allocation
find a 1/3-democratic 1-out-of-best-k allocation. In the context of rental harmony (envy-free division of rooms and rent), the following results are known
Fair_division_among_groups
Fair division problem
priorities are uncertain. Duddy studies egalitarian random assignment. Rental harmony is a variant of the assignment problem in which fairness is attained
Fair_random_assignment
auditions and dance rehearsals. Kadokawa released several region 2 DVDs for rental as the series was airing. After the show's end, the episodes were collected
List of Idol × Warrior Miracle Tunes! episodes
List_of_Idol_×_Warrior_Miracle_Tunes!_episodes
Place in California, United States
and the rental vacancy rate was 16.7%. The CDP is in Escondido Union Elementary School District and Escondido Union High School District. "Harmony Grove
Harmony_Grove,_California
2026 Indian film by Sunil Pandey
whose notes are not particularly profound. But they suggest an enduring harmony between the location and the heart. And if all fails — and that’s not the
Ek_Din
H Single Tower, Twin Tower Single I, Double I, Triple I Harmony 1, 1A, 2, 3,Rural,New Harmony 1,3 Linear 1, 3, L, B Trident 1, 2, 3, 4 Mark I, II, III
Public_housing_in_Hong_Kong
Period in Argentine cinema history
grounding, embodies Peronism's emphasis on social reconciliation by portraying harmony between rich and poor, aligning with the movement's ideological rhetoric
Golden Age of Argentine cinema
Golden_Age_of_Argentine_cinema
2007 American film
the United States on March 24, 2009. It debuted at number 17 on the DVD rental charts of March 23–30, 2009. Stan Minton is a wealthy real estate con artist
Big_Stan
Element of Japanese language
and prevail as she did over the gods and demons who disturbed the cosmic harmony. Her sword has those magical powers." Lakshmi prayed that Bhavani and Chandi
Japanese conjugation (mizenkei base)
Japanese_conjugation_(mizenkei_base)
Canadian real estate company
3 to 4 bedrooms The Heights of Harmony Located at 2561 Harmony Road near Highway 407 in Oshawa, The Heights of Harmony offers back-to-back and rear land
Minto_Group
1995 single by The Rentals
American rock band The Rentals. It was first released in 1995 as the lead single for the band's debut studio album Return of the Rentals, released on October
Friends_of_P.
"The Christmas Story" (Season 1, Episode 12) (December 4, 1955) Perfect Harmony "Merry Jaxmas" (December 12, 2019) (Season 1, Episode 10) Perfect Strangers
List of United States Christmas television episodes
List_of_United_States_Christmas_television_episodes
Retrieved February 12, 2025. Pierce, Barry (March 18, 2025). "The trailer for Harmony Korine's Baby Invasion is here". Hero. Retrieved March 18, 2025. T, Amber
List of American films of 2025
List_of_American_films_of_2025
Residence for humans to live in
internal loggias, while Venetian villas by Palladio emphasized proportion, harmony, and integration with landscaped gardens. Advances in glassmaking allowed
Home
2007 video game
(Region 2) -- the full movie of Part II with the original English dub, using Harmony Gold voice actors, complete with the intro of Part I's alternate (non-canonical)
Megazone_23:_Aoi_Garland
2020 film by Nisha Ganatra
audiences seeking some comfort viewing should find themselves solidly in harmony with this well-acted genre entry." On Metacritic, the film has a weighted
The_High_Note
City in Georgia, United States
called "Harmony Grove", found in an 1830 book called The Virginia Harmony. This tune is popular today as the melody to "Amazing Grace". The Harmony Grove
Commerce,_Georgia
1996 (1996-05-03) "I eat Hokkaido!" (Japanese: 北海道を食べちゃうゾ) "A broken-down rental car!" (Japanese: レンタカーがこわれたゾ) Hiroshi and his family plan a trip to Hokkaido
List of Crayon Shin-chan episodes (1992–2001)
List_of_Crayon_Shin-chan_episodes_(1992–2001)
American television series
censors deleted several comedy sequences that poked fun at the Hertz car-rental TV commercials, which ran on TV throughout the early 1960s. See Segrave
CBS_Thursday_Night_Movie
1995 studio album by Jawbreaker
of the members of Earth, Wind & Fire. Schwarzenbach recorded a lot of harmony vocal tracks for all of the songs, many of which Bauermeister and Pfahler
Dear_You
Residential skyscraper in Manhattan, New York
21, 2020. Retrieved May 25, 2022. Finn, Robin (August 29, 2014). "Where Harmony Resided". The New York Times. ISSN 0362-4331. Archived from the original
The_Beresford
Public housing in Tseung Kwan O, Hong Kong
between 1993 and 1994, the estate comprises 6 blocks of Harmony I style, providing more than 4,000 rental flats. Hin Ming Court (Chinese: 顯明苑) is a HOS estate
Public housing estates in Tseung Kwan O
Public_housing_estates_in_Tseung_Kwan_O
Games for the Sony PlayStation / PS1 / PSone
Unreleased Unreleased Iwatobi Penguin Rocky & Hopper F2 Company Nippon Rental April 25, 1997 Unreleased Unreleased Iwatobi Penguin Rocky & Hopper 2 –
List of PlayStation (console) games (A–L)
List_of_PlayStation_(console)_games_(A–L)
Canadian actor
television series on SyFy. In 2019, he starred in the NBC comedy Perfect Harmony as Reverend Jax, a missionary who runs a church. The show, which starred
Rizwan_Manji
traveling inflatable theater. Motion (Canada 1967) – Superpanorama 70 Harmony: Nature and Man (1969) – Dimension 150. Shown in the Washington State Pavilion
List_of_70_mm_films
American guitarist (1970–2026)
Jelsoft Enterprises. Retrieved April 2, 2010. "I like Cake's guitar sound". Harmony Central. April 2, 2010.{{cite web}}: CS1 maint: deprecated archival service
Greg_Brown_(rock_musician)
platform for a determined strategic urban planning action, with a perfect harmony between social and economic agents, which led to a new projection of the
Urban_planning_of_Barcelona
Barraclough, Leo (February 7, 2017). "Matthew McConaughey to Star in Harmony Korine's 'The Beach Bum'". Variety. Retrieved November 2, 2017. Lee, Benjamin
Matthew McConaughey filmography
Matthew_McConaughey_filmography
Car rental company
Avis Rent a Car South Africa, better known as Avis, is a South African car rental company headquartered in Kempton Park, Gauteng, South Africa. Avis Rent
Avis_Southern_Africa
Urban decay of Detroit from 1950s to 2010s
institutions—by constructing a public space that creates a sense of inclusion and harmony with the rest of the city. Public transportation within the Downtown area
Decline_of_Detroit
Terrorist attack in Sydney, Australia
violence in all its forms and affirming our shared commitment to social harmony and the safety of all Australians". They issued a statement saying the
2025_Bondi_Beach_shooting
English musician (born 1967)
by suicide in October 1996. After Lush split, Berenyi appeared on The Rentals' album Seven More Minutes (1999). She also contributed vocals to a remix
Miki_Berenyi
Rob Reiner Oliver Stone Dennis Hopper Shane Carruth Anthony Minghella Harmony Korine Richard Linklater Robert Altman William Friedkin James Cameron Damien
List of American independent films
List_of_American_independent_films
December 31, 2018 The channel's top 10 moments of the year. Cinemassacre Rental Reviews – Kazaam Review (1996) 23:39 April 19, 2019 The CGI genie from the
List of Angry Video Game Nerd episodes
List_of_Angry_Video_Game_Nerd_episodes
Notable people from Montclair, New Jersey, United States
jazz trumpeter Robert DeLeo (born 1966), bass player, songwriter, and harmony vocalist for the Stone Temple Pilots Tommy DeVito (1928–2020), guitarist
List of people from Montclair, New Jersey
List_of_people_from_Montclair,_New_Jersey
Hang Tsui Court 杏翠苑 HOS 1997 2 674 Harmony Garden 富欣花園 PSPS 1997 8 2,340 Healthy Village 健康村 Flat-for-Scheme/Rental 1965,1993,1997 14 2,237 HK Housing
List of Home Ownership Scheme Courts in Hong Kong
List_of_Home_Ownership_Scheme_Courts_in_Hong_Kong
Country in East Asia
Japanese society traditionally places a strong emphasis on collective harmony and conformity, which has led to the suppression of individual rights.
Japan
American actress (born 1998)
well. There challenge was balancing those two characters and finding that harmony and their differences because they're very different. Daly, Helen. "Margo's
Elle_Fanning
November 9, 2021. "Kite Realty Group Trust Set to Join S&P MidCap 400; Harmony Biosciences Holdings & LendingTree to Join S&P SmallCap 600" (PDF). S&P
List_of_S&P_400_companies
hometown, Providence Oaks. Angie Eastman Lesbian Angie is the owner of a VHS rental shop, who is romantically interested in Meredith Weiss, the protagonist
List of video games with LGBTQ characters: 2020s
List_of_video_games_with_LGBTQ_characters:_2020s
Full-size ultra-luxury sedan
and metallic finishes. Maextro says it follows 'Heaven, Earth, and Human Harmony' design philosophy, and uses the 'Starry Sky' design language, including
Maextro_S800
secretary general Ban Ki-moon is awarded the inaugural King Charles III Harmony Award during a ceremony held at St James's Palace. Two animal rights protestors
2024_in_the_United_Kingdom
Philippine laws
Cerilles State College 2001-09-29 9160 Anti-Money Laundering Act of 2001 2001-12-22 9161 Rental Reform Act of 2002 2001-12-22 9162 Appropriations Act of 2002
List_of_Philippine_laws
American actor and filmmaker (born 1930)
(January 31, 2019). "Is photo of Clint Eastwood's 8 children 'blended family harmony' or cruel abandonment?". Ladies Want More. Archived from the original on
Clint_Eastwood
PGI Panagra Airways PANAGRA United States RSL Panama Aircraft Rental and Sales PANAMA RENTAL Panama 2014 PEI Panamedia PANAMEDIA Spain PVI Panavia Panama
List_of_airline_codes
Russian billionaire businessman
Magomedov's company was siphoning money from NCSP. Despite the external harmony of this undoubtedly tactical alliance, the first shareholder conflict between
Ziyavudin_Magomedov
British-Australian-American businessman (born 1971)
in the Indian Premier League cricket team Rajasthan Royals, online DVD rental company Quickflix, toy marketer Funtastic and digital media company Destra
Lachlan_Murdoch
2021 animated Disney film by Don Hall & Carlos López Estrada
environmental harmony and is portrayed as an ideal and heavenly place where everything coexists in harmony. Benja strives to restore this environmental harmony after
Raya_and_the_Last_Dragon
Element of Japanese language
that sad note I named my knell, whilst I sit meditating On that celestial harmony I go to. ペーシェンスよ、始終傍(そば)にゐておくれ。‥‥もっと低くしとくれ。もう長いこと世話も掛けまい。‥‥グリフィスや、樂人ども
Japanese conjugation (ren'yōkei base)
Japanese_conjugation_(ren'yōkei_base)
Park in Annapolis, Maryland, United States
parks Catoctin Mountain Fort Foote Fort Washington Glen Echo Greenbelt Harmony Hall Oxon Cove and Oxon Hill Farm Piscataway National Parkways Baltimore-Washington
Quiet_Waters_Park_(Maryland)
Coach Barry before he is killed. Joss Whedon plays Douglas, a clueless car-rental salesman who inadvertently helps Veronica track down Abel Koontz' daughter
List of Veronica Mars characters
List_of_Veronica_Mars_characters
Eighteenth portion in the annual Jewish cycle of weekly Torah reading
is that of a servant to a master, and the forces of nature operate in harmony with the teaching of the Torah. Maimonides cited Exodus 23:25 to support
Mishpatim
New religious movement from China
fundamental part of Falun Gong practice. According to Li, humanity was once in harmony with these concepts (which are the fundamental characteristics of the universe)
Falun_Gong
Employees working from any location
work,[better source needed] though coworking spaces and short-term office rentals can help address this issue. In some countries, such as Romania, national
Remote_work
Cruise holding company headquartered in Miami, Florida
the Seas Independence of the Seas Oasis of the Seas Allure of the Seas Harmony of the Seas Symphony of the Seas Wonder of the Seas Utopia of the Seas
Royal_Caribbean_Group
becomes the new God, he tells the Winchesters that he and Amara exist in harmony. Death, portrayed by Julian Richings, is an immensely powerful entity also
List of Supernatural and The Winchesters characters
List_of_Supernatural_and_The_Winchesters_characters
(death announced on this date) 31 March – Tony Rivers, 85, English singer (Harmony Grass). 5 April – David Wiffen, 84, English–Canadian folk singer-songwriter
2026_in_England
American businesswoman and actress (born 1945)
three months, the cost proved unsustainable, prompting them to search for a rental property. They eventually moved into a spacious apartment in a "vintage
Priscilla_Presley
American educator
Ohio. After teaching in public and parochial schools, Nordyke founded Harmony Community School in 1998. He died in the school in 2003 over winter break
David_Nordyke
Hu, Kim (15 January 2026). "Rental Family (12A)". LondonNet. Ochiai, Jon (29 November 2025). "Know That We Exist in 'Rental Family'". The Good Men Project
List of feature films with lesbian characters
List_of_feature_films_with_lesbian_characters
EF4 tornado in Mississippi, US
fellowship hall and clinic being destroyed as well. The Mount Bethel Olive Harmony Branch Association building was destroyed at high-end EF3 strength, with
2014 Louisville, Mississippi tornado
2014_Louisville,_Mississippi_tornado
City in Wyoming, United States
of which 9.4% were vacant. The homeowner vacancy rate was 1.6% and the rental vacancy rate was 8.2%. As of the 2010 Census, there were 30,816 people,
Laramie,_Wyoming
1959 animated Disney film
30, 2023 – via Google Books. Paige, Earl (October 4, 1997). "Vids Bring Harmony To Music Retail". Billboard. Retrieved January 30, 2023 – via Google Books
Sleeping_Beauty_(1959_film)
2015 film by Pete Docter
relating to each other or to their own emotions but moments of personal harmony lead to positive interpersonal connections. According to USA Today's Jamie
Inside_Out
Greek professional basketball team
2018–19, 2020–2021 The trifolium is the emblem of the team, symbolizing harmony, unity, nature, and good luck. Since its foundation, the team's main colours
Panathinaikos_B.C.
General election for the 54th Parliament of New Zealand
that 31% of voters regarded racial harmony as important; with 34% of Māori and 30% of Europeans regarding racial harmony as important. Several researchers
2023 New Zealand general election
2023_New_Zealand_general_election
Coral atoll in the Marshall Islands
island: No longer can I stay, it's true No longer can I live in peace and harmony No longer can I rest on my sleeping mat and pillow Because of my island
Bikini_Atoll
1964 film by Alfred Hitchcock
Marnie". The Guardian. "Big Rental Pictures of 1964", Variety, 6 January 1965, p. 39. Please note this figure is rentals accruing to distributors, not
Marnie_(film)
Byrne 17 October 1993 (1993-10-17) Bellamy finds himself in trouble when a rental storage linked to his address is found to be in possession of items stolen
List_of_Heartbeat_episodes
English rock band (1972–2006)
from airplay. At one point, Moulding and Gregory were working at a car rental service for additional income. Partridge was eventually left with "about
XTC
American rapper (1972–1997)
"Playa Hater" and adapted to the rapid-fire rhyme flow of Bone Thugs-n-Harmony on "Notorious Thugs". Wallace's lyrics explored a range of themes, including
The_Notorious_B.I.G.
City in Croatia
Vulić and it features modern passenger terminals with shops, cafés, car rental services, and public transportation links, including buses and taxis, and
Split,_Croatia
Indian composer and musician (born 1967)
keyboard. After his father's death when Rahman was nine years old, the rental of his father's musical equipment provided his family's income. Raised by
A._R._Rahman
American mass media company
October 17, 2022. Verrender, Ian (September 21, 2024). "Inside 'Project Harmony', Rupert Murdoch's desperate plan to keep control from beyond the grave"
Fox_Corporation
American actress (born 1985)
Universal Pictures released the film via video on-demand platforms as a digital rental on April 10, 2020. She starred in the Quibi comedy series Dummy, for which
Anna_Kendrick
Coleman "Harlem's Poppin'" by Noble Sissle* "Harlemania" by Duke Ellington "Harmony in Harlem" by Charlie Barnet* "Have You Forgotten?" by Darryl Worley "Have
List of songs about New York City
List_of_songs_about_New_York_City
1982 American fantasy film by John Milius
Sales and rental figures of the videocassette were high; from its launch, the title was listed in Billboard's Videocassette Top 40 (Sales and Rental categories)
Conan the Barbarian (1982 film)
Conan_the_Barbarian_(1982_film)
1930s programs of U.S. president Franklin D. Roosevelt
according to Lary May: [B]elieved that the prosperity and apparent class harmony of the post-World War II era reflected a return to the true Americanism
New_Deal
1940 animated film by Walt Disney
– via Newspapers.com. "Stokowski and Disney Sued in Tale of Scrambled Harmony". The Morning Post. April 8, 1939. p. 6. Retrieved July 23, 2023 – via
Fantasia_(1940_film)
2016 Russian film
producer Yuri Moskvin of Wizart Animation, the Chinese market is key for the rental of Sheep and Wolves, with the show expected to reach the widest audience
Sheep_and_Wolves
November 20, 2024 (2024-11-20) "Toony Video" is going to bring back the VHS rental business. Maybe. Featured cartoons : Cue Ball Cat (1950), Woolen Under Where
List of Toon In with Me episodes (2024)
List_of_Toon_In_with_Me_episodes_(2024)
2006 film by Michael Mann
also just laid the foundations for a new order of action films." Director Harmony Korine cited Miami Vice as a major influence on his 2012 film Spring Breakers
Miami_Vice_(film)
2007 film by David Silverman
software used for this film was animated using a combination of Toon Boom Harmony and Toon Boom Opus. For inspiration for the crowd scenes in the film, the
The_Simpsons_Movie
American singer-songwriter (1946–2023)
"Who Dat?" In 2019, Buffett had an extended cameo playing himself in the Harmony Korine film The Beach Bum. Buffett portrayed both himself and a con artist
Jimmy_Buffett
American guitarist (1942–1970)
the audience. The band narrowly escaped from the venue in the back of a rental truck, which was partly crushed by fans who had climbed on top of the vehicle
Jimi_Hendrix
Matt (August 24, 2022). "Larkin Poe Flip the Script with Latest Blood Harmony Track, "Georgia Off My Mind"". Guitar World. Retrieved November 2, 2022
List_of_2022_albums
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