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| The '''Fulkerson Prize''' for outstanding papers in the area of [[discrete mathematics]] is sponsored jointly by the [[Mathematical Programming Society]] (MPS) and the [[American Mathematical Society]] (AMS). Up to three awards of $1500 each are presented at each (triennial) International Symposium of the MPS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late [[Delbert Ray Fulkerson]] to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.
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| ==Winners==
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| * 1979:
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| ** [[Richard M. Karp]] for classifying many important [[NP-complete]] problems.<ref>[[Richard M. Karp]], "On the computational complexity of combinatorial problems", ''Networks'' 5: 45–68, 1975.</ref>
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| ** [[Kenneth Appel]] and [[Wolfgang Haken]] for the [[four color theorem]].<ref>[[Kenneth Appel]] and [[Wolfgang Haken]], "Every planar map is four colorable, Part I: Discharging," ''Illinois Journal of Mathematics'' 21: 429–490, 1977.</ref>
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| ** [[Paul Seymour (mathematician)|Paul Seymour]] for generalizing the [[max-flow min-cut theorem]] to [[matroid]]s.<ref>[[Paul Seymour (mathematician)|Paul Seymour]] , "The matroids with the max-flow min-cut property," ''[[Journal of Combinatorial Theory]]'', Series B, 23: 189–222, 1977.</ref>
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| * 1982:
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| ** D.B. Judin, [[Arkadi Nemirovski]], [[Leonid Khachiyan]], Martin Grötschel, [[László Lovász]] and [[Alexander Schrijver]] for the [[ellipsoid method]] in [[linear programming]] and [[combinatorial optimization]].<ref>D.B. Judin and [[Arkadi Nemirovski]], "Informational complexity and effective methods of solution for convex extremal problems," ''Ekonomika i Matematicheskie Metody'' 12: 357–369, 1976.</ref><ref>[[Leonid Khachiyan]], "A polynomial algorithm in linear programming," ''Akademiia Nauk SSSR. Doklady'' 244: 1093–1096, 1979.</ref><ref>{{citation|newspaper=[[Boston Globe]]|url=http://www.boston.com/news/globe/obituaries/articles/2005/05/05/leonid_khachiyan_professor_leading_computer_scientist/|date=May 5, 2005|title=Leonid Khachiyan, professor, leading computer scientist}}.</ref><ref>Martin Grötschel, [[László Lovász]] and [[Alexander Schrijver]], "The ellipsoid method and its consequences in combinatorial optimization," ''[[Combinatorica]]'' 1: 169–197, 1981.</ref>
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| **G. P. Egorychev and D. I. Falikman for proving [[Bartel Leendert van der Waerden|van der Waerden]]'s conjecture that the matrix with all entries equal has the smallest [[permanent]] of any [[doubly stochastic matrix]].<ref>G. P. Egorychev, "The solution of van der Waerden's problem for permanents," ''Akademiia Nauk SSSR. Doklady'' 258: 1041–1044, 1981.</ref><ref>D. I. Falikman, "A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix," ''Matematicheskie Zametki'' 29: 931–938, 1981.</ref>
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| **
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| * 1985:
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| ** [[Jozsef Beck]] for tight bounds on the [[discrepancy theory|discrepancy]] of [[arithmetic progression]]s.<ref>[[Jozsef Beck]], "Roth's estimate of the discrepancy of integer sequences is nearly sharp," ''[[Combinatorica]]'' 1 (4): 319–325, 1981.</ref>
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| ** [[Hendrik Lenstra|H. W. Lenstra, Jr.]] for using the [[geometry of numbers]] to solve [[integer program]]s with few variables in time polynomial in the number of constraints.<ref>[[Hendrik Lenstra|H. W. Lenstra, Jr.]], "Integer programming with a fixed number of variables," ''Mathematics of Operations Research'' 8 (4): 538–548, 1983.</ref>
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| ** [[Eugene M. Luks]] for a [[polynomial time]] [[graph isomorphism problem|graph isomorphism algorithm]] for graphs of bounded [[degree (graph theory)|maximum degree]].<ref>Eugene M. Luks, "Isomorphism of graphs of bounded valence can be tested in polynomial time," ''Journal of Computer and System Sciences'' 25 (1): 42–65, 1982.</ref><ref>{{citation|url=http://news.google.com/newspapers?id=w_hVAAAAIBAJ&sjid=huEDAAAAIBAJ&pg=6539,2351404&dq=fulkerson-prize&hl=en|newspaper=[[The Register-Guard|Eugene Register-Guard]]|title=U of O Computer Chief Gets Top Award|date=August 10, 1985}}.</ref>
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| * 1988:
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| ** [[Éva Tardos]] for finding [[circulation problem|minimum cost circulations]] in [[Time complexity|strongly polynomial time]].<ref>[[Éva Tardos]], "A strongly polynomial minimum cost circulation algorithm," ''[[Combinatorica]]'' 5: 247-256, 1985.</ref>
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| ** [[Narendra Karmarkar]] for [[Karmarkar's algorithm]] for [[linear programming]].<ref>[[Narendra Karmarkar]], "A new polynomial-time algorithm for linear programming," ''[[Combinatorica]]'' 4:373–395, 1984.</ref>
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| * 1991:
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| ** [[Martin Dyer|Martin E. Dyer]], [[Alan M. Frieze]] and [[Ravindran Kannan]] for [[random walk|random-walk]]-based [[approximation algorithm]]s for the volume of convex bodies.<ref>[[Martin Dyer|Martin E. Dyer]], [[Alan M. Frieze]] and [[Ravindran Kannan]], "A random polynomial time algorithm for approximating the volume of convex bodies", ''[[Journal of the Association for Computing Machinery]]'' 38 (1): 1–17, 1991.</ref>
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| ** Alfred Lehman for [[Logical matrix|0,1-matrix]] analogues of the theory of [[perfect graph]]s.<ref>Alfred Lehman, "The width-length inequality and degenerate projective planes," W. Cook and P. D. Seymour (eds.), Polyhedral Combinatorics, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, volume 1, (American Mathematical Society, 1990) pp. 101-105.</ref>
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| ** Nikolai E. Mnev for [[Mnev's universality theorem]], that every semialgebraic set is equivalent to the space of realizations of an [[oriented matroid]].<ref>Nikolai E. Mnev, "The universality theorems on the classification problem of configuration varieties and convex polytope varieties," O. Ya. Viro (ed.), Topology and Geometry-Rohlin Seminar, Lecture Notes in Mathematics 1346 (Springer-Verlag, Berlin, 1988) pp. 527-544.</ref>
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| * 1994:
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| ** Louis Billera for finding bases of piecewise-polynomial function spaces over triangulations of space.<ref>Louis Billera, "Homology of smooth splines: Generic triangulations and a conjecture of Strang", ''[[Transactions of the AMS]]'' 310: 325–340, 1988.</ref>
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| ** [[Gil Kalai]] for making progress on the [[Hirsch conjecture]] by proving subexponential bounds on the diameter of ''d''-dimensional polytopes with ''n'' facets.<ref>[[Gil Kalai]], "Upper bounds for the diameter and height of graphs of the convex polyhedra", ''[[Discrete and Computational Geometry]]'' 8: 363–372, 1992.</ref>
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| ** [[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]] and [[Robin Thomas (mathematician)|Robin Thomas]] for the six-color case of [[Hadwiger conjecture (graph theory)|Hadwiger's conjecture]].<ref>[[Neil Robertson (mathematician)|Neil Robertson]], [[Paul Seymour (mathematician)|Paul Seymour]] and [[Robin Thomas (mathematician)|Robin Thomas]], "Hadwiger's conjecture for K_6-free graphs," ''[[Combinatorica]]'' 13: 279–361, 1993.</ref>
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| * 1997:
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| **[[Jeong Han Kim]] for finding the [[asymptotic analysis|asymptotic growth rate]] of the [[Ramsey number]]s ''R''(3,''t'').<ref>[[Jeong Han Kim]], "The Ramsey Number R(3,t) Has Order of Magnitude t^2/log t," ''Random Structures and Algorithms'' 7 (3): 173–207, 1995.</ref>
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| * 2000:
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| ** [[Michel Goemans|Michel X. Goemans]] and David P. Williamson for [[approximation algorithm]]s based on [[semidefinite programming]].<ref>Michel X. Goemans and David P. Williamson, "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming", ''[[Journal of the Association for Computing Machinery]]'' 42 (6): 1115–1145, 1995.</ref>
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| ** Michele Conforti and Gérard Cornuéjols and [[Mendu Rammohan Rao|M. R. Rao]] for recognizing [[Balanced matrix|balanced 0-1 matrices]] in [[polynomial time]].<ref>Michele Conforti, Gérard Cornuéjols, and [[Mendu Rammohan Rao|M. R. Rao]], "Decomposition of balanced matrices", ''[[Journal of Combinatorial Theory]]'', Series B, 77 (2): 292–406, 1999.</ref><ref>{{citation|title=MR Rao New Dean Of ISB|newspaper=[[The Financial Express (India)|Financial Express]]|date=July 2, 2004|url=http://www.financialexpress.com/news/mr-rao-new-dean-of-isb/109506/}}.</ref>
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| * 2003:
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| ** [[Jim Geelen|J. F. Geelen]], A. M. H. Gerards and A. Kapoor for the [[finite field|GF(4)]] case of [[Rota's conjecture]] on [[matroid minor]]s.<ref>[[Jim Geelen|J. F. Geelen]], A. M. H. Gerards and A. Kapoor, "The Excluded Minors for GF(4)-Representable Matroids," ''[[Journal of Combinatorial Theory]]'', Series B, 79 (2): 247–2999, 2000.</ref><ref name="fpc03">[http://www.mathopt.org/?nav=fulkerson_2003 2003 Fulkerson Prize citation], retrieved 2012-08-18.</ref>
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| ** Bertrand Guenin for a [[forbidden graph characterization|forbidden minor characterization]] of the weakly bipartite graphs (graphs whose bipartite subgraph polytope is 0-1).<ref>Bertrand Guenin, "A characterization of weakly bipartite graphs," ''[[Journal of Combinatorial Theory]]'', Series B, 83 (1): 112–168, 2001.</ref><ref name="fpc03"/>
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| ** Satoru Iwata, Lisa Fleischer, Satoru Fujishige, and [[Alexander Schrijver]] for showing [[Submodular set function#Optimization problems|submodular minimization]] to be strongly polynomial.<ref>Satoru Iwata, Lisa Fleischer, Satoru Fujishige, "A combinatorial strongly polynomial algorithm for minimizing submodular functions," ''[[Journal of the ACM]]'', 48 (4): 761–777, 2001.</ref><ref>[[Alexander Schrijver]], "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," ''[[Journal of Combinatorial Theory]]'', Series B 80 (2): 346–355, 2000.</ref><ref name="fpc03"/>
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| * 2006:
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| ** [[Manindra Agrawal]], [[Neeraj Kayal]] and [[Nitin Saxena]], for the [[AKS primality test]].<ref>[[Manindra Agrawal]], [[Neeraj Kayal]] and [[Nitin Saxena]], "PRIMES is in P," ''[[Annals of Mathematics]]'', 160 (2): 781–793, 2004.</ref><ref>{{citation|newspaper=[[The Hindu]]|date=June 11, 2009|first=M. S.|last=Raghunathan|title=India as a player in Mathematics|url=http://www.hindu.com/2009/06/11/stories/2009061155161000.htm}}.</ref><ref name="fpc06">[http://www.mathopt.org/?nav=fulkerson_2006 2006 Fulkerson Prize citation], retrieved 2012-08-19.</ref>
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| ** [[Mark Jerrum]], [[Alistair Sinclair]] and Eric Vigoda, for [[Computing the permanent#Approximate computation|approximating the permanent]].<ref>[[Mark Jerrum]], [[Alistair Sinclair]] and [[Eric Vigoda]], "A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries," ''[[Journal of the ACM]]'', 51 (4): 671–697, 2004.</ref><ref name="fpc06"/>
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| ** [[Neil Robertson (mathematician)|Neil Robertson]] and [[Paul Seymour (mathematician)|Paul Seymour]], for the [[Robertson–Seymour theorem]] showing that [[graph minor]]s form a [[well-quasi-ordering]].<ref>[[Neil Robertson (mathematician)|Neil Robertson]] and [[Paul Seymour (mathematician)|Paul Seymour]], "Graph Minors. XX. Wagner's conjecture," ''[[Journal of Combinatorial Theory]]'', Series B, 92 (2): 325–357, 2004.</ref><ref name="fpc06"/>
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| * 2009:
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| ** [[Maria Chudnovsky]], Neil Robertson, Paul Seymour, and Robin Thomas, for the [[strong perfect graph theorem]].<ref>[[Maria Chudnovsky]], Neil Robertson, Paul Seymour, and Robin Thomas, "The strong perfect graph theorem", ''[[Annals of Mathematics]]'', 164: 51–229, 2006.</ref><ref name="fpc09">[http://www.mathopt.org/?nav=fulkerson_2009 2009 Fulkerson Prize citation], retrieved 2012-08-19.</ref>
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| ** [[Daniel A. Spielman]] and [[Shang-Hua Teng]], for [[smoothed analysis]] of [[linear programming]] algorithms.<ref>[[Daniel A. Spielman]] and [[Shang-Hua Teng]], "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time", ''[[Journal of the ACM]]'' 51: 385–463, 2004.</ref><ref name="fpc09"/>
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| ** [[Thomas Callister Hales|Thomas C. Hales]] and Samuel P. Ferguson, for proving the [[Kepler conjecture]] on the densest possible [[sphere packing]]s.<ref>[[Thomas Callister Hales|Thomas C. Hales]], "A proof of the [[Kepler conjecture]]", ''[[Annals of Mathematics]]'' 162: 1063–1183, 2005.</ref><ref>Samuel P. Ferguson, "Sphere Packings, V. Pentahedral Prisms", ''[[Discrete and Computational Geometry]]'' 36: 167–204, 2006.</ref><ref name="fpc09"/>
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| * 2012:
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| ** [[Sanjeev Arora]], Satish Rao, and [[Umesh Vazirani]] for improving the [[approximation ratio]] for [[Vertex separator|graph separators]] and related problems from <math>O(\log n)</math> to <math>O(\sqrt{\log n})</math>.<ref>[[Sanjeev Arora]], Satish Rao, and [[Umesh Vazirani]], "Expander flows, geometric embeddings and graph partitioning", ''[[Journal of the ACM]]'' 56: 1-37, 2009.</ref>
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| ** Anders Johansson, [[Jeff Kahn]], and [[Van H. Vu]] for determining the threshold of edge density above which a [[random graph]] can be covered by disjoint copies of a given smaller graph.<ref>Anders Johansson, [[Jeff Kahn]], and [[Van H. Vu]], "Factors in random graphs", ''Random Structures and Algorithms'' 33: 1-28, 2008.</ref>
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| ** [[László Lovász]] and Balázs Szegedy for characterizing subgraph multiplicity in sequences of [[dense graph]]s.<ref>[[László Lovász]] and Balázs Szegedy, "Limits of dense graph sequences", ''[[Journal of Combinatorial Theory]]'', Series B, 96: 933-957, 2006.</ref>
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| ==References==
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| {{reflist|colwidth=30em}}
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| ==External links==
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| * [http://www.ams.org/prizes/fulkerson-prize.html Official site with award details]
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| * [http://www.ams.org/profession/prizes-awards/pabrowse AMS archive of past prize winners]
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| [[Category:Computer science awards]]
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| [[Category:Awards of the American Mathematical Society]]
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