Fulkerson Prize

Fulkerson Prize
Fulkerson Prize
Awarded for	Outstanding papers in the area of discrete mathematics
Country	United States
Presented by	Mathematical Optimization Society; American Mathematical Society;
Reward(s)	$1,500
First awarded	1979
Website	http://www.ams.org/profession/prizes-awards/ams-prizes/fulkerson-prize

The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. 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.

Winners

1979:
- Richard M. Karp for classifying many important NP-complete problems.^[1]
- Kenneth Appel and Wolfgang Haken for the four color theorem.^[2]
- Paul Seymour for generalizing the max-flow min-cut theorem to matroids.^[3]
1982:
- D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the ellipsoid method in linear programming and combinatorial optimization.^[4]^[5]^[6]^[7]
- G. P. Egorychev and D. I. Falikman for proving van der Waerden's conjecture that the matrix with all entries equal has the smallest permanent of any doubly stochastic matrix.^[8]^[9]
1985:
- Jozsef Beck for tight bounds on the discrepancy of arithmetic progressions.^[10]
- H. W. Lenstra Jr. for using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.^[11]
- Eugene M. Luks for a polynomial time graph isomorphism algorithm for graphs of bounded maximum degree.^[12]^[13]
1988:
- Éva Tardos for finding minimum cost circulations in strongly polynomial time.^[14]
- Narendra Karmarkar for Karmarkar's algorithm for linear programming.^[15]
1991:
- Martin E. Dyer, Alan M. Frieze and Ravindran Kannan for random-walk-based approximation algorithms for the volume of convex bodies.^[16]
- Alfred Lehman for 0,1-matrix analogues of the theory of perfect graphs.^[17]
- Nikolai E. Mnev for Mnev's universality theorem, that every semialgebraic set is equivalent to the space of realizations of an oriented matroid.^[18]
1994:
- Louis Billera for finding bases of piecewise-polynomial function spaces over triangulations of space.^[19]
- Gil Kalai for making progress on the Hirsch conjecture by proving subexponential bounds on the diameter of d-dimensional polytopes with n facets.^[20]
- Neil Robertson, Paul Seymour and Robin Thomas for the six-color case of Hadwiger's conjecture.^[21]
1997:
- Jeong Han Kim for finding the asymptotic growth rate of the Ramsey numbers R(3,t).^[22]
2000:
- Michel X. Goemans and David P. Williamson for approximation algorithms based on semidefinite programming.^[23]
- Michele Conforti, Gérard Cornuéjols, and M. R. Rao for recognizing balanced 0-1 matrices in polynomial time.^[24]^[25]
2003:
- J. F. Geelen, A. M. H. Gerards and A. Kapoor for the GF(4) case of Rota's conjecture on matroid minors.^[26]^[27]
- Bertrand Guenin for a forbidden minor characterization of the weakly bipartite graphs (graphs whose bipartite subgraph polytope is 0-1).^[28]^[27]
- Satoru Iwata, Lisa Fleischer, Satoru Fujishige, and Alexander Schrijver for showing submodular minimization to be strongly polynomial.^[29]^[30]^[27]
2006:
- Manindra Agrawal, Neeraj Kayal and Nitin Saxena, for the AKS primality test.^[31]^[32]^[33]
- Mark Jerrum, Alistair Sinclair and Eric Vigoda, for approximating the permanent.^[34]^[33]
- Neil Robertson and Paul Seymour, for the Robertson–Seymour theorem showing that graph minors form a well-quasi-ordering.^[35]^[33]
2009:
- Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas, for the strong perfect graph theorem.^[36]^[37]
- Daniel A. Spielman and Shang-Hua Teng, for smoothed analysis of linear programming algorithms.^[38]^[37]
- Thomas C. Hales and Samuel P. Ferguson, for proving the Kepler conjecture on the densest possible sphere packings.^[39]^[40]^[37]
2012:
- Sanjeev Arora, Satish Rao, and Umesh Vazirani for improving the approximation ratio for graph separators and related problems from $O(\log n)$ to $O({\sqrt {\log n}})$ .^[41]
- 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.^[42]
- László Lovász and Balázs Szegedy for characterizing subgraph multiplicity in sequences of dense graphs.^[43]
2015:
- Francisco Santos Leal for a counter-example of the Hirsch conjecture.^[44]^[45]
2018:
- Robert Morris, Yoshiharu Kohayakawa, Simon Griffiths, Peter Allen, and Julia Böttcher for The chromatic thresholds of graphs
- Thomas Rothvoss for his work on the extension complexity of the matching polytope.^[46]
2021:
- Béla Csaba, Daniela Kühn, Allan Lo, Deryk Osthus, and Andrew Treglown for Proof of the 1-factorization and Hamilton decomposition conjectures
- Jin-Yi Cai and Xi Chen for Complexity of Counting CSP with Complex Weights
- Ken-Ichi Kawarabayashi and Mikkel Thorup for Deterministic Edge Connectivity in Near-Linear Time

Source: Mathematical Optimization Society official website.^[47]

2024:
- Ben Cousins and Santosh Vempala for Gaussian cooling and $O^{*}(n^{3})$ algorithms for volume and Gaussian volume
- Zilin Jiang, Jonathan Tidor, Yuan Yao, Shengtong Zhang, and Yufei Zhao for Equiangular lines with a fixed angle
- Nathan Keller and Noam Lifshitz for The junta method for hypergraphs and the Erdős–Chvátal simplex conjecture

Source: American Mathematical Society official website.^[48]

References

^ Karp, Richard M. (1975). "On the computational complexity of combinatorial problems". Networks. 5: 45–68. doi:10.1002/net.1975.5.1.45.
^ Appel, Kenneth; Haken, Wolfgang (1977). "Every planar map is four colorable, Part I: Discharging". Illinois Journal of Mathematics. 21: 429–490.
^ Seymour, Paul (1977). "The matroids with the max-flow min-cut property". Journal of Combinatorial Theory. 23 (2–3): 189–222. doi:10.1016/0095-8956(77)90031-4.
^ Judin, D.B.; Nemirovski, Arkadi (1976). "Informational complexity and effective methods of solution for convex extremal problems". Ekonomika I Matematicheskie Metody. 12: 357–369.
^ Khachiyan, Leonid (1979). "A polynomial algorithm in linear programming". Akademiia Nauk SSSR. Doklady. 244: 1093–1096.
^ "Leonid Khachiyan, professor, leading computer scientist". Boston Globe. May 5, 2005..
^ Grötschel, Martin; Lovász, László; Schrijver, Alexander (1981). "The ellipsoid method and its consequences in combinatorial optimization". Combinatorica. 1 (2): 169–197. doi:10.1007/bf02579273.
^ Egorychev, G. P. (1981). "The solution of van der Waerden's problem for permanents". Akademiia Nauk SSSR. Doklady. 258: 1041–1044.
^ Falikman, D. I. (1981). "A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix". Matematicheskie Zametki. 29: 931–938.
^ Beck, Jozsef (1981). "Roth's estimate of the discrepancy of integer sequences is nearly sharp". Combinatorica. 1 (4): 319–325. doi:10.1007/bf02579452.
^ Lenstra, H. W. Jr. (1983). "Integer programming with a fixed number of variables". Mathematics of Operations Research. 8 (4): 538–548. CiteSeerX 10.1.1.431.5444. doi:10.1287/moor.8.4.538.
^ Luks, Eugene M. (1982). "Isomorphism of graphs of bounded valence can be tested in polynomial time". Journal of Computer and System Sciences. 25 (1): 42–65. doi:10.1016/0022-0000(82)90009-5.
^ "U of O Computer Chief Gets Top Award". Eugene Register-Guard. August 10, 1985..
^ Tardos, Éva (1985). "A strongly polynomial minimum cost circulation algorithm". Combinatorica. 5 (3): 247–256. doi:10.1007/bf02579369.
^ Karmarkar, Narendra (1984). "A new polynomial-time algorithm for linear programming". Combinatorica. 4 (4): 373–395. doi:10.1007/bf02579150.
^ Dyer, Martin E.; Frieze, Alan M.; Kannan, Ravindran (1991). "A random polynomial time algorithm for approximating the volume of convex bodies". Journal of the ACM. 38 (1): 1–17. CiteSeerX 10.1.1.145.4600. doi:10.1145/102782.102783.
^ 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.
^ 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.
^ Billera, Louis (1988). "Homology of smooth splines: Generic triangulations and a conjecture of Strang". Transactions of the American Mathematical Society. 310 (1): 325–340. doi:10.2307/2001125. JSTOR 2001125.
^ Kalai, Gil (1992). "Upper bounds for the diameter and height of graphs of the convex polyhedra". Discrete and Computational Geometry. 8 (4): 363–372. doi:10.1007/bf02293053.
^ Robertson, Neil; Seymour, Paul; Thomas, Robin (1993). "Hadwiger's conjecture for K_6-free graphs". Combinatorica. 13 (3): 279–361. doi:10.1007/bf01202354.
^ Kim, Jeong Han (1995). "The Ramsey number R(3,t) has order of magnitude t²/log t". Random Structures & Algorithms. 7 (3): 173–207. doi:10.1002/rsa.3240070302. MR 1369063..
^ Goemans, Michel X.; Williamson, David P. (1995). "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming". Journal of the ACM. 42 (6): 1115–1145. doi:10.1145/227683.227684.
^ Michele Conforti, Gérard Cornuéjols, and M. R. Rao, "Decomposition of balanced matrices", Journal of Combinatorial Theory, Series B, 77 (2): 292–406, 1999.
^ "MR Rao New Dean Of ISB". Financial Express. July 2, 2004..
^ 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.
^ ^a ^b ^c 2003 Fulkerson Prize citation, retrieved 2012-08-18.
^ Bertrand Guenin, "A characterization of weakly bipartite graphs," Journal of Combinatorial Theory, Series B, 83 (1): 112–168, 2001.
^ Satoru Iwata, Lisa Fleischer, Satoru Fujishige, "A combinatorial strongly polynomial algorithm for minimizing submodular functions," Journal of the ACM, 48 (4): 761–777, 2001.
^ Alexander Schrijver, "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," Journal of Combinatorial Theory, Series B 80 (2): 346–355, 2000.
^ Manindra Agrawal, Neeraj Kayal and Nitin Saxena, "PRIMES is in P," Annals of Mathematics, 160 (2): 781–793, 2004.
^ Raghunathan, M. S. (June 11, 2009). "India as a player in Mathematics". The Hindu. Archived from the original on June 14, 2009..
^ ^a ^b ^c 2006 Fulkerson Prize citation, retrieved 2012-08-19.
^ 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.
^ Neil Robertson and Paul Seymour, "Graph Minors. XX. Wagner's conjecture," Journal of Combinatorial Theory, Series B, 92 (2): 325–357, 2004.
^ Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006). "The strong perfect graph theorem". Annals of Mathematics. 164: 51–229. arXiv:math/0212070. doi:10.4007/annals.2006.164.51.
^ ^a ^b ^c 2009 Fulkerson Prize citation, retrieved 2012-08-19.
^ Spielman, Daniel A.; Teng, Shang-Hua (2004). "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time". Journal of the ACM. 51: 385–463. arXiv:math/0212413. doi:10.1145/990308.990310.
^ Hales, Thomas C. (2005). "A proof of the Kepler conjecture". Annals of Mathematics. 162 (3): 1063–1183. doi:10.4007/annals.2005.162.1065.
^ Ferguson, Samuel P. (2006). "Sphere Packings, V. Pentahedral Prisms". Discrete and Computational Geometry. 36: 167–204. doi:10.1007/s00454-005-1214-y.
^ Arora, Sanjeev; Rao, Satish; Vazirani, Umesh (2009). "Expander flows, geometric embeddings and graph partitioning". Journal of the ACM. 56 (2): 1–37. CiteSeerX 10.1.1.310.2258. doi:10.1145/1502793.1502794.
^ Johansson, Anders; Kahn, Jeff; Vu, Van H. (2008). "Factors in random graphs". Random Structures and Algorithms. 33: 1–28. doi:10.1002/rsa.20224.
^ Lovász, László; Szegedy, Balázs (2006). "Limits of dense graph sequences". Journal of Combinatorial Theory. 96 (6): 933–957. arXiv:math/0408173. doi:10.1016/j.jctb.2006.05.002.
^ Santos, Francisco (2011). "A counterexample to the Hirsch conjecture". Annals of Mathematics. 176 (1): 383–412. arXiv:1006.2814. doi:10.4007/annals.2012.176.1.7. MR 2925387.
^ 2015 Fulkerson Prize citation, retrieved 2015-07-18.
^ Rothvoß, Thomas (2017). "The matching polytope has exponential extension complexity". Journal of the ACM. 64 (6): A41:1–A41:19. arXiv:1311.2369. doi:10.1145/3127497. MR 3713797.
^ "The Fulkerson Prize". MOS Prizes. Mathematical Optimization Society. Retrieved 2024-07-25.
^ "2024 Delbert Ray Fulkerson Prize Awarded". News from the AMS. American Mathematical Society. July 23, 2024. Retrieved 2024-07-25.

External links

Official web page (MOS)
Official site with award details (AMS website)
AMS archive of past prize winners

[1] Karp, Richard M. (1975). "On the computational complexity of combinatorial problems". Networks. 5: 45–68. doi:10.1002/net.1975.5.1.45.

[2] Appel, Kenneth; Haken, Wolfgang (1977). "Every planar map is four colorable, Part I: Discharging". Illinois Journal of Mathematics. 21: 429–490.

[3] Seymour, Paul (1977). "The matroids with the max-flow min-cut property". Journal of Combinatorial Theory. 23 (2–3): 189–222. doi:10.1016/0095-8956(77)90031-4.

[4] Judin, D.B.; Nemirovski, Arkadi (1976). "Informational complexity and effective methods of solution for convex extremal problems". Ekonomika I Matematicheskie Metody. 12: 357–369.

[5] Khachiyan, Leonid (1979). "A polynomial algorithm in linear programming". Akademiia Nauk SSSR. Doklady. 244: 1093–1096.

[6] "Leonid Khachiyan, professor, leading computer scientist". Boston Globe. May 5, 2005..

[7] Grötschel, Martin; Lovász, László; Schrijver, Alexander (1981). "The ellipsoid method and its consequences in combinatorial optimization". Combinatorica. 1 (2): 169–197. doi:10.1007/bf02579273.

[8] Egorychev, G. P. (1981). "The solution of van der Waerden's problem for permanents". Akademiia Nauk SSSR. Doklady. 258: 1041–1044.

[9] Falikman, D. I. (1981). "A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix". Matematicheskie Zametki. 29: 931–938.

[10] Beck, Jozsef (1981). "Roth's estimate of the discrepancy of integer sequences is nearly sharp". Combinatorica. 1 (4): 319–325. doi:10.1007/bf02579452.

[11] Lenstra, H. W. Jr. (1983). "Integer programming with a fixed number of variables". Mathematics of Operations Research. 8 (4): 538–548. CiteSeerX 10.1.1.431.5444. doi:10.1287/moor.8.4.538.

[12] Luks, Eugene M. (1982). "Isomorphism of graphs of bounded valence can be tested in polynomial time". Journal of Computer and System Sciences. 25 (1): 42–65. doi:10.1016/0022-0000(82)90009-5.

[13] "U of O Computer Chief Gets Top Award". Eugene Register-Guard. August 10, 1985..

[14] Tardos, Éva (1985). "A strongly polynomial minimum cost circulation algorithm". Combinatorica. 5 (3): 247–256. doi:10.1007/bf02579369.

[15] Karmarkar, Narendra (1984). "A new polynomial-time algorithm for linear programming". Combinatorica. 4 (4): 373–395. doi:10.1007/bf02579150.

[16] Dyer, Martin E.; Frieze, Alan M.; Kannan, Ravindran (1991). "A random polynomial time algorithm for approximating the volume of convex bodies". Journal of the ACM. 38 (1): 1–17. CiteSeerX 10.1.1.145.4600. doi:10.1145/102782.102783.

[17] 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.

[18] 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.

[19] Billera, Louis (1988). "Homology of smooth splines: Generic triangulations and a conjecture of Strang". Transactions of the American Mathematical Society. 310 (1): 325–340. doi:10.2307/2001125. JSTOR 2001125.

[20] Kalai, Gil (1992). "Upper bounds for the diameter and height of graphs of the convex polyhedra". Discrete and Computational Geometry. 8 (4): 363–372. doi:10.1007/bf02293053.

[21] Robertson, Neil; Seymour, Paul; Thomas, Robin (1993). "Hadwiger's conjecture for K_6-free graphs". Combinatorica. 13 (3): 279–361. doi:10.1007/bf01202354.

[22] Kim, Jeong Han (1995). "The Ramsey number R(3,t) has order of magnitude t²/log t". Random Structures & Algorithms. 7 (3): 173–207. doi:10.1002/rsa.3240070302. MR 1369063..

[23] Goemans, Michel X.; Williamson, David P. (1995). "Improved approximation algorithms for the maximum cut and satisfiability probelsm using semi-definite programming". Journal of the ACM. 42 (6): 1115–1145. doi:10.1145/227683.227684.

[24] Michele Conforti, Gérard Cornuéjols, and M. R. Rao, "Decomposition of balanced matrices", Journal of Combinatorial Theory, Series B, 77 (2): 292–406, 1999.

[25] "MR Rao New Dean Of ISB". Financial Express. July 2, 2004..

[26] 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.

[fpc03-27] 2003 Fulkerson Prize citation, retrieved 2012-08-18.

[28] Bertrand Guenin, "A characterization of weakly bipartite graphs," Journal of Combinatorial Theory, Series B, 83 (1): 112–168, 2001.

[29] Satoru Iwata, Lisa Fleischer, Satoru Fujishige, "A combinatorial strongly polynomial algorithm for minimizing submodular functions," Journal of the ACM, 48 (4): 761–777, 2001.

[30] Alexander Schrijver, "A combinatorial algorithm minimizing submodular functions in strongly polynomial time," Journal of Combinatorial Theory, Series B 80 (2): 346–355, 2000.

[31] Manindra Agrawal, Neeraj Kayal and Nitin Saxena, "PRIMES is in P," Annals of Mathematics, 160 (2): 781–793, 2004.

[32] Raghunathan, M. S. (June 11, 2009). "India as a player in Mathematics". The Hindu. Archived from the original on June 14, 2009..

[fpc06-33] 2006 Fulkerson Prize citation, retrieved 2012-08-19.

[34] 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.

[35] Neil Robertson and Paul Seymour, "Graph Minors. XX. Wagner's conjecture," Journal of Combinatorial Theory, Series B, 92 (2): 325–357, 2004.

[36] Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006). "The strong perfect graph theorem". Annals of Mathematics. 164: 51–229. arXiv:math/0212070. doi:10.4007/annals.2006.164.51.

[fpc09-37] 2009 Fulkerson Prize citation, retrieved 2012-08-19.

[38] Spielman, Daniel A.; Teng, Shang-Hua (2004). "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time". Journal of the ACM. 51: 385–463. arXiv:math/0212413. doi:10.1145/990308.990310.

[39] Hales, Thomas C. (2005). "A proof of the Kepler conjecture". Annals of Mathematics. 162 (3): 1063–1183. doi:10.4007/annals.2005.162.1065.

[40] Ferguson, Samuel P. (2006). "Sphere Packings, V. Pentahedral Prisms". Discrete and Computational Geometry. 36: 167–204. doi:10.1007/s00454-005-1214-y.

[41] Arora, Sanjeev; Rao, Satish; Vazirani, Umesh (2009). "Expander flows, geometric embeddings and graph partitioning". Journal of the ACM. 56 (2): 1–37. CiteSeerX 10.1.1.310.2258. doi:10.1145/1502793.1502794.

[42] Johansson, Anders; Kahn, Jeff; Vu, Van H. (2008). "Factors in random graphs". Random Structures and Algorithms. 33: 1–28. doi:10.1002/rsa.20224.

[43] Lovász, László; Szegedy, Balázs (2006). "Limits of dense graph sequences". Journal of Combinatorial Theory. 96 (6): 933–957. arXiv:math/0408173. doi:10.1016/j.jctb.2006.05.002.

[44] Santos, Francisco (2011). "A counterexample to the Hirsch conjecture". Annals of Mathematics. 176 (1): 383–412. arXiv:1006.2814. doi:10.4007/annals.2012.176.1.7. MR 2925387.

[45] 2015 Fulkerson Prize citation, retrieved 2015-07-18.

[46] Rothvoß, Thomas (2017). "The matching polytope has exponential extension complexity". Journal of the ACM. 64 (6): A41:1–A41:19. arXiv:1311.2369. doi:10.1145/3127497. MR 3713797.

[47] "The Fulkerson Prize". MOS Prizes. Mathematical Optimization Society. Retrieved 2024-07-25.

[48] "2024 Delbert Ray Fulkerson Prize Awarded". News from the AMS. American Mathematical Society. July 23, 2024. Retrieved 2024-07-25.

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Fulkerson Prize

Winners

See also

References

External links

This information is adapted from Wikipedia which is publicly available.

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