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American computer scientist
Timothy Avelin Roughgarden (born July 20, 1975) is an American computer scientist whose research spans theoretical computer science, algorithmic game
Tim_Roughgarden
Surname list
Roughgarden is a surname. Notable people with the surname include: Joan Roughgarden (born 1946), American ecologist and evolutionary biologist Tim Roughgarden
Roughgarden
Study of algorithms in strategic environments
8836, doi:10.1145/380752.380883, ISBN 978-1581133493, S2CID 207594967 Tim Roughgarden (2005). Selfish routing and the price of anarchy. MIT Press. ISBN 0-262-18243-2
Algorithmic_game_theory
American ecologist (born 1946)
Joan Roughgarden (born 13 March 1946) is an American ecologist and evolutionary biologist. She has engaged in theory and observation of coevolution and
Joan_Roughgarden
Computer science award
Computer Science Review. 3 (2): 65–69. doi:10.1016/j.cosrev.2009.04.003. Roughgarden, Tim; Tardos, Éva (2002). "How bad is selfish routing?". Journal of the
Gödel_Prize
Computer science award
Omer Reingold 2006 Dan Klein 2007 Vern Paxson 2008 Dawson Engler 2009 Tim Roughgarden 2010 Craig Gentry 2011 Luis von Ahn 2012 Martin Casado and Dina Katabi
Grace_Murray_Hopper_Award
Hungarian mathematician
2007 textbook Algorithmic Game Theory, working alongside Noam Nisan, Tim Roughgarden, and Vijay V. Vazirani. Tardos has been elected to the National Academy
Éva_Tardos
Annual award by Association for Computing Machinery
Retrieved 2021-01-23. "Tim Roughgarden". Awards Home. Association for Computing Machinery. Retrieved 2021-01-23. "Tim Roughgarden". Awards Home. Association
ACM Doctoral Dissertation Award
ACM_Doctoral_Dissertation_Award
Hee Oh Gigliola Staffilani Medicine and Health Aydoğan Özcan [tr] Tim Roughgarden Teresa K. Woodruff Molecular and Cellular Biology Ehab Abouheif Organismic
List of Guggenheim Fellowships awarded in 2017
List_of_Guggenheim_Fellowships_awarded_in_2017
Concept in economics and game theory
Tim Roughgarden and Eva Tardos, "Introduction to the Inefficiency of Equilibria". Chapter 17 in Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos
Price_of_anarchy
ratio is between 3 and 16, depending on the setting. Monopoly pricing Tim Roughgarden (2013). "Revenue-Maximizing Auctions" (PDF). Retrieved 19 July 2016
Bayesian-optimal_pricing
Roscoe Jonathan Rosenberg Azriel Rosenfeld Gian-Carlo Rota Klaus Roth Tim Roughgarden Bimal Kumar Roy Marie-Françoise Roy Gordon Royle Grzegorz Rozenberg
List of people by Erdős number
List_of_people_by_Erdős_number
Igor Rodnianski Mikael Rørdam Antonio Ros Linda Preiss Rothschild Tim Roughgarden Raphaël Rouquier Ronitt Rubinfeld Imre Z. Ruzsa Francisco Santos Mark
List of International Congresses of Mathematicians Plenary and Invited Speakers
List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
Păsăreanu Massoud Pedram Anand Raghunathan Benjamin Raphael Dana Ron Tim Roughgarden David Sankoff Stefan Saroiu Albrecht Schmidt Björn Schuller Phoebe
List of fellows of the Association for Computing Machinery
List_of_fellows_of_the_Association_for_Computing_Machinery
political economist 2013 2015 Marshall N. Rosenbluth physicist 1967 1982 Tim Roughgarden mathematician 2026 current Peter Sarnak mathematician 2007 current
List of faculty members at the Institute for Advanced Study
List_of_faculty_members_at_the_Institute_for_Advanced_Study
Algorithm in mathematical optimization
graph" = rGraph)) print(list("Maximum flow" = mxFlow)) Lecture Notes Tim Roughgarden, A Second Course in Algorithms (CS261, winter 2016), Columbia University
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Industrial Organization, 2006, doi:10.1016/j.ijindorg.2006.10.002 . Roughgarden, Tim (2015). "Intrinsic Robustness of the Price of Anarchy". Journal of
Kalai_Prize
Ronald Rivest, former faculty, Turing Award-winning computer scientist Tim Roughgarden, faculty in CS, winner of Grace Murray Hopper Award Arthur Samuel,
List of Stanford University faculty and staff
List_of_Stanford_University_faculty_and_staff
Indian computer scientist
postdoctoral studies at Stanford University under the mentorship of Tim Roughgarden, and at Microsoft Research, Silicon Valley, she joined the Wisconsin
Shuchi_Chawla
IEEE conference for theoretical computer science
Chrobak (Local Chair), Neal Yong (Local Chair), Palm Springs " 2012 Tim Roughgarden (PC Chair), Rebecca Wright (Local Chair), Lisa Zhang (Local Chair)
Symposium on Foundations of Computer Science
Symposium_on_Foundations_of_Computer_Science
Award for American scientists and engineers
Ramamoorthi, Columbia University Purnima Ratilal, Northeastern University Tim Roughgarden, Stanford University Rachel A. Segalman, University of California,
Presidential Early Career Award for Scientists and Engineers
Presidential_Early_Career_Award_for_Scientists_and_Engineers
valuation of other bidders, and even the value of the item to the seller. Tim Roughgarden (2014). "Approximately optimal mechanism design: Motivation, examples
Regular distribution (economics)
Regular_distribution_(economics)
Israeli computer scientist (born 1965)
Gödel Prize, along with Elias Koutsoupias, Christos Papadimitriou, Tim Roughgarden, Noam Nisan, and Eva Tardos, for initiating and developing a new field
Amir_Ronen
Hashing technique
Tim (2025). This is for Everyone: the unfinished story of the World Wide Web. Farrar, Straus and Giroux. p. 156. ISBN 978-0-374-61246-7. Roughgarden &
Consistent_hashing
Award
Cornuéjols 2016 Not awarded 2017 Not awarded 2018 Not awarded 2019 Tim Roughgarden, Omar Besbes, Yonatan Gur, N. Bora Keskin and Assaf Zeevi 2020: Peyman
Frederick_W._Lanchester_Prize
Award
his PhD thesis. Other Finalists: Kamal Jain and Fabian Chudak 2003: Tim Roughgarden for "Selfish Routing". Other Finalists: Pablo Parrilo and Jiming Peng
Tucker_Prize
(2014) Jason Rohrer (B.S. 2000) – independent video game designer Tim Roughgarden (Ph.D. 2002) – computer scientist at Stanford University; recipient
List of Cornell University alumni (natural sciences)
List_of_Cornell_University_alumni_(natural_sciences)
Professional special interest group on genetic and evolutionary computation
speakers at FOGA conferences Year Keynote speakers 2021 Adi Livnat & Tim Roughgarden 2023 Carola Doerr & José A. Lozano 2025 Joshua D. Knowles, Vedran Dunjko
ACM_SIGEVO
was outlined by then-Stanford computer science researchers including Tim Roughgarden in 2014 that same year. Japanese auction Vickrey–Clarke–Groves (VCG)
Deferred-acceptance_auction
Term used in biology
Social selection is a term used with varying meanings in biology. Joan Roughgarden proposed a hypothesis called social selection as an alternative to sexual
Social_selection
Game in algorithmic game theory
succinct games as a computational problem, is given by Papadimitriou & Roughgarden 2008). Graphical games are games in which the utilities of each player
Succinct_game
1137/090748986. ISSN 0097-5397. Bhawalkar, Kshipra; Gairing, Martin; Roughgarden, Tim (2014-10-28). "Weighted Congestion Games: The Price of Anarchy, Universal
Price of anarchy in congestion games
Price_of_anarchy_in_congestion_games
"Live from Lincoln Center" broadcast Danny Elfman's Music from the Films of Tim Burton, for which Elfman won Outstanding Music Direction at the 68th Primetime
List of compositions by Danny Elfman
List_of_compositions_by_Danny_Elfman
German computer scientist
"Learning, regret minimization, and equilibria", in Nisan, Noam; Roughgarden, Tim; Tardos, Éva; Vazirani, Vijay V. (eds.), Algorithmic Game Theory, Cambridge
Manfred_K._Warmuth
Concept in game theory
Preference revelation Strategyproofness Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Incentive_compatibility
Notion in supervised machine learning
Theoretical Foundations. ISBN 9780521118620. Morgenstern, Jamie H.; Roughgarden, Tim (2015). On the Pseudo-Dimension of Nearly Optimal Auctions. NIPS. arXiv:1506
Vapnik–Chervonenkis_dimension
Sanitizing and hiding of undesirable qualities
2307/40201538. Accessed 2 Oct. 2024. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Whitewashing_(communications)
7473. doi:10.1006/game.1999.0790. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Algorithmic_mechanism_design
Longest distance between two vertices
algorithms for the diameter and radius of sparse graphs", in Boneh, Dan; Roughgarden, Tim; Feigenbaum, Joan (eds.), Symposium on Theory of Computing Conference
Diameter_(graph_theory)
Paradox related to increasing roadway capacity
the best to make things better, 16 January 2014 by Justin Mullins Roughgarden, Tim; Tardos, Éva. "How Bad is Selfish Routing?" (PDF). Journal of the ACM
Braess's_paradox
1137/090772988. ISSN 0097-5397. Dütting, Paul; Gkatzelis, Vasilis; Roughgarden, Tim (2014-06-01). "The performance of deferred-acceptance auctions". Proceedings
Knapsack_auction
Writing principle of using few words
(2007). "The Complexity of Finding Nash Equilibria". In Nisan, Noam; Roughgarden, Tim; Tardos, Éva; et al. (eds.). Algorithmic Game Theory. Cambridge University
Concision
Method of making choices that maximises utility
Incentive compatibility Quadratic voting Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Vickrey–Clarke–Groves mechanism
Vickrey–Clarke–Groves_mechanism
Branch of mathematics
Kearns (2007) "Graphical Games". In Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Graphical_game_theory
Unsolved problem in parallel algorithms
arXiv:1401.0042, doi:10.1145/2591796.2591805, ISBN 978-1-4503-2710-7 Roughgarden, Tim; Vassilvitskii, Sergei; Wang, Joshua R. (2018), "Shuffles and circuits
1-vs-2_cycles_problem
approach to prior-free mechanism design. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Random-sampling_mechanism
Algorithm analysis method
ISBN 978-3-540-17096-9 Manthey, Bodo (2021). "Smoothed Analysis of Local Search". In Roughgarden, Tim (ed.). Beyond the Worst-Case Analysis of Algorithms. Cambridge: Cambridge
Smoothed_analysis
Pairing where no unchosen pair prefers each other over their choice
V. (2007). "Mechanism design without money" (PDF). In Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Vazirani, Vijay (eds.). Algorithmic Game Theory. pp. 255–262
Stable_matching_problem
Attribute of machine learning models
Learning: Theoretical Foundations. ISBN 9780521118620. Morgenstern, Jamie; Roughgarden, Tim (2015). On the Pseudo-Dimension of Nearly Optimal Auctions. NIPS. Curran
Sample_complexity
Auction where all participants concurrently submit undisclosed bids
2018-11-28, retrieved 2008-06-25 Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
First-price sealed-bid auction
First-price_sealed-bid_auction
Conference version appeared in FOCS 2004. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Price_of_stability
Economic equilibrium concept
"Combinatorial Auctions / Walrasian Equilibrium". In Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Vazirani, Vijay (eds.). Algorithmic Game Theory (PDF)
Competitive_equilibrium
prior-free mechanism should be used. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Bayesian-optimal_mechanism
Type of market maker
Makers". arXiv:2103.14769 [q-fin.MF]. Milionis, Jason; Moallemi, Ciamac; Roughgarden, Tim; Zhang, Anthony Lee (2022). "Automated market making and loss-versus-rebalancing"
Constant function market maker
Constant_function_market_maker
Techniques to preserve differential privacy when releasing computational results
265–284. doi:10.1007/11681878_14. ISBN 978-3-540-32731-8. Ghosh, Arpita; Roughgarden, Tim; Sundararajan, Mukund (2012). "Universally Utility-maximizing Privacy
Additive noise differential privacy mechanisms
Additive_noise_differential_privacy_mechanisms
worst-case. Market research Algorithmic pricing Dhangwatnotai, Peerapong; Roughgarden, Tim; Yan, Qiqi (2015). "Revenue maximization with a single sample". Games
Prior-independent_mechanism
Sexual behavior of non-human animals
Encyclopedia of Marine Mammals. Academic Press. ISBN 978-0-08-091993-5. Roughgarden, Joan (2013). Evolution's Rainbow: Diversity, Gender, and Sexuality in
Animal_sexual_behaviour
Computing the fixed point of a function
Mathematik. 43 (2): 225–240. doi:10.1007/BF01390124. S2CID 120937024. Roughgarden, Tim; Weinstein, Omri (2016). "On the Communication Complexity of Approximate
Fixed-point_computation
Principle in economics and game theory
result. Econometrica 41, 587–601. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Revelation_principle
Computer Science. 9 (1): 127–136. doi:10.46298/dmtcs.387. Fox, Jacob; Roughgarden, Tim; Seshadhri, C.; Wei, Fan; Wein, Nicole (2020). "Finding Cliques in
Graphs_with_few_cliques
bit dated, but a classic survey. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Combinatorial_auction
Graph with almost the max amount of edges
(4th ed.), Cambridge, Massachusetts: The MIT Press, ISBN 978-0262046305 Roughgarden, Tim (2018), Algorithms Illuminated, Part 2: Graph Algorithms and Data Structures
Dense_graph
Impossibility result for ranked-choice voting systems
1016/S0165-1765(00)00362-1. ISSN 0165-1765. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Gibbard–Satterthwaite_theorem
1468-0262.2006.00695.x. S2CID 6210226. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Monotonicity (mechanism design)
Monotonicity_(mechanism_design)
British biologist
Norman; Naeem, Shahid; Paavola, Jouni; Rayment, Matthew; Rosendo, Sergio; Roughgarden, Joan; Trumper, Kate; Turner, R. Kerry (August 2002). "Economic Reasons
Andrew_Balmford
Theorem in political science
Rakesh V. (2013). "Mechanism Design Without Money". In Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Vazirani, Vijay (eds.). Algorithmic Game Theory. New
Median_voter_theorem
Concept in mechanism design
strategy-proofness in voting systems. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Strategyproofness
Field of economics and game theory
October 15, 2007. Retrieved 2008-08-15. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Mechanism_design
Mathematical models of strategic interactions
Behavior. 35 (1–2): 166–196. doi:10.1006/game.1999.0790. Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Vazirani, Vijay V., eds. (2007). Algorithmic Game Theory
Game_theory
Economical computational problem
00153. hdl:10230/525. ISSN 1468-0262. Papadimitriou, Christos H.; Roughgarden, Tim (2008-08-06). "Computing correlated equilibria in multi-player games"
Nash_equilibrium_computation
Fairness notion in fair item allocation
1137/1.9781611975031.165. ISBN 978-1-61197-503-1. Plaut, Benjamin; Roughgarden, Tim (January 2020). "Almost Envy-Freeness with General Valuations". SIAM
Envy-freeness_up_to_any_item
Process of buying and selling goods
"Introduction to Mechanism Design for Computer Scientists". In Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Vazirani, Vijay (eds.). Algorithmic Game Theory. pp. 230–231
Double_auction
Increasing value with increasing participation
1109/TVT.2018.2822843. ISSN 0018-9545. S2CID 52003270. Lin, Henry; Roughgarden, Tim; Tardos, Éva; Walkover, Asher. "Stronger Bounds on Braess's Paradox
Network_effect
Competitive game
"Network Formation Games". Chapter 19 in Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Facility location (competitive game)
Facility_location_(competitive_game)
Public research university in Boston, Massachusetts, US
Richard A. Horsley, chemist John Warner, evolutionary biologist Joan Roughgarden, feminist writers Beverly Smith and Christina Hoff Sommers, politician
University of Massachusetts Boston
University_of_Massachusetts_Boston
Concept in auction theory
information from the bids of other players. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Revenue_equivalence
Theorem in mechanism design
doi:10.1007/s00199-006-0080-z. 1 Gopalan, Parikshit; Nisan, Noam; Roughgarden, Tim (2015). "Public projects, Boolean functions and the borders of Border's
Border's_theorem
Game theory solution
2307/1911154. JSTOR 1911154. S2CID 18649722. Papadimitriou, Christos H.; Roughgarden, Tim (2008). "Computing correlated equilibria in multi-player games". J
Correlated_equilibrium
doi:10.1016/j.tcs.2020.07.008. S2CID 220546580. Plaut, Benjamin; Roughgarden, Tim (January 2020). "Almost Envy-Freeness with General Valuations". SIAM
Fair_division_among_groups
Fair item allocation problem
125. doi:10.1145/988772.988792. ISBN 1-58113-771-0. Plaut, Benjamin; Roughgarden, Tim (2020-01-01). "Communication Complexity of Discrete Fair Division"
Envy-free_item_allocation
Type of normal-form game
Behavior. 28 (2): 171–180. doi:10.1006/game.1998.0699. ISSN 0899-8256. Roughgarden, Tim; Tardos, Éva (2004-05-01). "Bounding the inefficiency of equilibria
Non-atomic_game
Marine invertebrates of the subphylum Anthozoa
Marshall, P.; Nystrom, M.; Palumbi, S.; Pandolfi, J.; Rosen, B.; and Roughgarden, J. (2003). "Climate change, human impacts, and the resilience of coral
Coral
Sexual reproduction involving a large, female gamete and a small, male gamete
(1): 74–101. Bibcode:1985ANat..125...74C. doi:10.1086/284329. Iyer, P.; Roughgarden, J. (2008). "Gametic conflict versus contact in the evolution of anisogamy"
Anisogamy
French mathematician (born 1950)
Theory (3 impr. ed.). Amsterdam: North-Holland. ISBN 978-0-444-89427-4. Roughgarden, Tim; Sundararajan, Mukund (1 June 2009). "Quantifying Inefficiency in Cost-sharing
Hervé_Moulin
Game class in game theory
and congestion games Section 19 in: Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Potential_game
4744. doi:10.1145/2465769.2465773. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Consensus_estimate
Class of games in game theory
Behavior. 28 (2): 171–180. doi:10.1006/game.1998.0699. ISSN 0899-8256. Roughgarden, Tim; Tardos, Éva (2004-05-01). "Bounding the inefficiency of equilibria
Congestion_game
Riccardo; Goldberg, Paul W.; Keijzer, Bart de; Leonardi, Stefano; Roughgarden, Tim; Turchetta, Stefano (2020-03-11). "Approximately Efficient Two-Sided
Budget-balanced_mechanism
Mahdian, "Cost Sharing". Chapter 15 in Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Facility location (cooperative game)
Facility_location_(cooperative_game)
soccer player (Teaneck) Philip Roth (1933–2018), author (Newark) Joan Roughgarden (born 1946), ecologist and evolutionary biologist (Paterson) Richard
List of people from New Jersey
List_of_people_from_New_Jersey
Consensus estimate for references. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Prior-free_mechanism
Mechanism Design". Chapter 13 in Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Profit_extraction_mechanism
Theory. Retrieved 15 March 2016. Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). "Chapter 5: Combinatorial Algorithms for Market
Fisher_market
Archived from the original on May 3, 2015. Retrieved June 3, 2022. Reid, Tim (January 26, 1996), Once Upon a Time... When We Were Colored (Drama, Romance)
Films and television shows produced in Wilmington, North Carolina
Films_and_television_shows_produced_in_Wilmington,_North_Carolina
Archived from the original on 25 April 2023. Retrieved 8 July 2017. Roughgarden, Joan (2013). Evolution's Rainbow: Diversity, Gender, and Sexuality in
Transgender people and religion
Transgender_people_and_religion
Auction in which every bidder pays
Press, 2004 Algorithmic Game Theory. Vazirani, Vijay V; Nisan, Noam; Roughgarden, Tim; Tardos, Eva; Cambridge, UK: Cambridge University Press, 2007. Complete
All-pay_auction
721.5346. doi:10.1145/2835172. S2CID 17082117. Bhawalkar, Kshipra; Roughgarden, Tim (2011). "Welfare Guarantees for Combinatorial Auctions with Item Bidding"
Price_of_anarchy_in_auctions
Fair item allocation problem
1007/978-3-031-15714-1_30. ISBN 978-3-031-15714-1. Plaut, Benjamin; Roughgarden, Tim (2020-01-01). "Almost Envy-Freeness with General Valuations". SIAM
Egalitarian_item_allocation
valuations. Single peaked preferences Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory (PDF). Cambridge, UK:
Single-parameter_utility
Risk of plant or animal species becoming extinct due to climate change
1704P. doi:10.1111/j.1365-2699.2006.01460.x. S2CID 611169. Buckley LB, Roughgarden J (July 2004). "Biodiversity conservation: effects of changes in climate
Extinction risk from climate change
Extinction_risk_from_climate_change
TIM ROUGHGARDEN
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TIM ROUGHGARDEN
TIM ROUGHGARDEN
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