291:-sponsored workshop in Santa Monica, California. It is here that Edmonds first presented his findings on defining a class of algorithms that could run more efficiently. Most combinatorics scholars, during this time, were not focused on algorithms. However Edmonds was drawn to them and these initial investigations were key developments for his later work between matroids and optimization. He spent the years from 1961 to 1965 on the subject of NP versus P and in 1966 originated the conjectures NP â P and NP â© coNP = P.
279:, graduating in 1952; and has talked about the influence this school had on his career (for instance at his 2014 NIST Gallery induction ). Edmonds attended Duke University before completing his undergraduate degree at George Washington University in 1957. He thereafter received a master's degree in 1960 at the University of Maryland under Bruce L. Reinhart with a thesis on the problem of embedding graphs into surfaces. From 1959 to 1969 he worked at the
31:
317:. It sealed in the importance of there being proofs, or "witnesses", that the answer for an instance is yes and there being proofs, or "witnesses", that the answer for an instance is no. In this blossom algorithm paper, Edmonds also characterizes feasible problems as those solvable in polynomial time; this is one of the origins of the
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where his research encompassed combinatorial optimization problems and associated polyhedra. He supervised the doctoral work of a dozen students in this time. He gave courses or spent research leaves at Duke
University, George Washington University, the University of Maryland, Stanford, Princeton,
350:
Edmonds's paper âMaximum
Matching and a Polyhedron with 0-1 Verticesâ along with his previous work gave astonishing polynomial-time algorithms for the construction of maximum matchings. Most notably, these papers demonstrated how a good characterization of the polyhedron associated with a
426:
From 1991 to 1993, he was involved in a dispute ("the
Edmonds affair") with the University of Waterloo, wherein the university claimed that a letter submitted constituted a letter of resignation, which Edmonds denied. The conflict was resolved in 1993, and he returned to the university.
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Edmonds's 1965 paper âPaths, Trees and
Flowersâ was a preeminent paper in initially suggesting the possibility of establishing a mathematical theory of efficient combinatorial algorithms. One of his earliest and notable contributions is the
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on graphs, discovered in 1961 and published in 1965. This was the first polynomial-time algorithm for maximum matching in graphs. Its generalization to weighted graphs was a conceptual breakthrough in the use of
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Cornell, as well as universities in China, Leuven (Belgium), Copenhagen, Southern
Denmark (Odense), Paris, Marseille, Grenoble (France), as well as Bonn and Cologne (Germany).
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combinatorial optimization problem could lead, via the duality theory of linear programming, to the construction of an efficient algorithm for the solution of that problem.
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of a graph, and more generally for all independent sets of a matroid. Building on this, as a novel application of linear programming to discrete mathematics, he proved the
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Edmonds, Jack; Giles, Richard (1977), P.L. Hammer; E.L. Johnson; B.H. Korte; G.L. Nemhauser (eds.), "A min-max relation for submodular functions on graphs",
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406:. A recurring theme in his work is to seek algorithms whose time complexity is polynomially bounded by their input size and bit-complexity.
988:, in: Kenneth Westhues, ed., Workplace Mobbing in Academe: Reports from Twenty Universities, Lewiston: NY: The Edwin Mellen Press, 2004
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theorem, a very general combinatorial min-max theorem which, in modern terms, showed that the matroid intersection problem lay in both
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From 1969 on, with the exception of 1991â1993, he held a faculty position at the
Department of Combinatorics and Optimization at the
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In 2014 he was honored as a
Distinguished Scientist and inducted into the National Institute of Standards and Technology's Gallery.
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Edmonds, Jack (1970). "Submodular functions, matroids, and certain polyhedra". In R. Guy; H. Hanam; N. Sauer; J. Schonheim (eds.).
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287:âs newly created Operations Research Section in 1961. Goldman proved to be a crucial influence by enabling Edmonds to work in a
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578:"The Traveling Salesman Problem and P vs. NP: Some 1960s Theoretical Work at NIST On the Complexity of Mathematical Algorithms"
563:"The Traveling Salesman Problem and P vs. NP: Some 1960s Theoretical Work at NIST on the Complexity of Mathematical Algorithms"
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who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of
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Edmonds, Jack (1991), "A glimpse of heaven", in J.K. Lenstra; A.H.G. Rinnooy Kan; A. Schrijver (eds.),
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in their celebratory edition of A Century of
Excellence in Measurements Standards and Technology
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In 2001 his paper, "Paths, Trees and
Flowers" was honoured as an Outstanding Publication by the
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Studies in
Integer Programming | Proceedings Workshop on Integer Programming, Bonn, 1975
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University of Waterloo Daily Bulletin, March 5 2001: Conference honours Jack Edmonds
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or intractable problem). Today, problems solvable in polynomial time are called the
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if it can be solved in polynomial time (as stated for the first time in Edmonds ).
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In 2006 the Queen of Denmark presented Edmonds with an Honorary Doctorate from the
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Combinatorial structures and their applications (Proc. 1969 Calgary Conference)
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Fellows of the Institute for Operations Research and the Management Sciences
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History of Mathematical Programming â A Collection of Personal Reminiscences
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describes finite graphs from the point of view of matchings. He introduced
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from the Institute for Operations Research and the Management Sciences
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Workshop on Combinatorial Optimization in 2001 was dedicated to him.
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Combinatorial Algorithms |Courant Computer Science Symposium 9, 1972
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Edmonds, Jack (1973), R. Rustin (ed.), "Edge-disjoint branchings",
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JĂŒnger, Michael; Reinelt, Gerhard; Rinaldi, Giovanni, eds. (2003),
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A Century of Excellence in Measurements, Standards, and Technology
874:, Monterey, California, 1972: Algorithmics Press, New York: 91â96
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Journal of Research of the National Bureau of Standards Section B
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Journal of Research of the National Bureau of Standards Section B
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UW Gazette, October 7, 1992: CAUT called in on Jack Edmonds case
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A combinatorial representation for oriented polyhedral surfaces
493:, and his wife Kathie Cameron is a professor of mathematics at
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30:
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and the theory of computing. He was the recipient of the 1985
1016:
Institute for Operations Research and the Management Sciences
826:, Lecture Notes in Computer Science, vol. 2570, Springer
660:, CWI, Amsterdam and North-Holland, Amsterdam, pp. 32â54
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Institute for Operations Research and the Management Sciences
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35:
Edmonds with his NP rock outside his home in Ontario, Canada
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Edmonds, Jack (1971). "Matroids and the greedy algorithm".
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Edmonds retired from the University of Waterloo in 1999.
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Christoph Witzgall (2001), "Paths, Trees, and Flowers",
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Math. Programming (Princeton Symposium Math. Prog. 1967)
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and packing edge-disjoint branchings and his work with
354:
Additional landmark work of Edmonds is in the area of
243:(born April 5, 1934) is an American-born and educated
16:
American/Canadian mathematician and computer scientist
714:"Maximum matching and a polyhedron with 0,1-vertices"
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824:Combinatorial Optimization â Eureka, You Shrink!
798:
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807:. Gordon and Breach, New York. pp. 69â87.
447:National Institute of Standards and Technology
281:National Institute of Standards and Technology
190:National Institute of Standards and Technology
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374:. Edmonds is well known for his theorems on
358:. He found a polyhedral description for all
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438:Edmonds was the 1985 recipient of the
1611:John von Neumann Theory Prize winners
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907:, North-Holland, Amsterdam: 185â204,
512:List of University of Waterloo people
1616:20th-century Canadian mathematicians
452:He was elected to the 2002 class of
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388:EdmondsâGallai decomposition theorem
113:EdmondsâGallai decomposition theorem
13:
903:, Annals of Discrete Mathematics,
576:Edmonds, Jack (October 10, 2014).
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619:Edmonds Jr., John Robert (1960).
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1089:John von Neumann Theory Prize
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440:John von Neumann Theory Prize
265:John von Neumann Theory Prize
173:Computer Science, Mathematics
156:John von Neumann Theory Prize
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402:and blocker in the study of
82:George Washington University
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673:"Paths, trees, and flowers"
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315:combinatorial optimization
253:combinatorial optimization
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884:: CS1 maint: location (
765:A problem is said to be
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257:polyhedral combinatorics
211:Gilberto Calvillo Vives
1578:Christos Papadimitriou
1418:Arthur F. Veinott, Jr.
1323:R. Tyrrell Rockafellar
837:Edmonds, Jack (1967).
712:Edmonds, Jack (1965).
690:10.4153/CJM-1965-045-4
671:Edmonds, Jack (1965).
420:Faculty of Mathematics
416:University of Waterloo
384:faster flow algorithms
324:A breakthrough of the
221:William R. Pulleyblank
185:University of Waterloo
108:EdmondsâKarp algorithm
77:University of Maryland
1498:Jean Bernard Lasserre
979:Editor's introduction
856:10.6028/jres.071B.032
731:10.6028/jres.069B.013
326:CobhamâEdmonds thesis
319:CobhamâEdmonds thesis
839:"Optimum Branchings"
749:. Elsevier. p.
724:(1 and 2): 125â130.
364:matroid intersection
261:discrete mathematics
138:Matroid intersection
1410:Alexander Schrijver
1386:J. Michael Harrison
551:. October 10, 2014.
45:John Robert Edmonds
1582:Mihalis Yannakakis
1542:Dimitris Bertsimas
1362:Donald L. Iglehart
1346:Manfred W. Padberg
984:2010-10-27 at the
532:"Tech_alumni_pp48"
495:Laurier University
311:linear programming
245:computer scientist
1606:Combinatorialists
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306:maximum matchings
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249:mathematician
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57:(age 90)
55:April 5, 1934
43:
39:
32:
27:
20:
1554:Adrian Lewis
1366:Cyrus Derman
1335:2000âpresent
1283:Lajos Takacs
1267:Philip Wolfe
1243:Richard Karp
1203:Jack Edmonds
1202:
1195:Ralph Gomory
1127:John F. Nash
1043:Jack Edmonds
1024:, retrieved
1020:the original
1010:
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993:
974:
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946:the original
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677:Can. J. Math
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634:. Retrieved
621:
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602:. Retrieved
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487:Jeff Edmonds
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392:polymatroids
380:Richard Karp
353:
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341:, or simply
336:
323:
298:
285:Alan Goldman
274:
271:Early career
240:
239:
226:Peyton Young
216:Komei Fukuda
178:Institutions
163:
23:Jack Edmonds
1626:1934 births
1426:Frank Kelly
683:: 449â467.
485:Jack's son
404:hypergraphs
133:Polymatroid
1600:Categories
1354:Ward Whitt
1291:Egon Balas
1147:David Gale
1026:2019-10-09
955:2011-08-11
789:: 127â136.
631:1903/24820
518:References
473:The fifth
396:submodular
51:1934-04-05
1096:1975â1999
699:247198603
313:ideas in
1438:Yinyu Ye
982:Archived
880:citation
767:feasible
501:See also
356:matroids
295:Research
1045:at the
636:23 June
604:23 June
475:Aussois
456:of the
454:Fellows
400:clutter
1585:(2023)
1573:(2022)
1565:(2021)
1557:(2020)
1549:(2019)
1537:(2018)
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1214:(1986)
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1166:(1981)
1158:(1980)
1142:(1979)
1134:(1978)
1122:(1977)
1114:(1976)
1106:(1975)
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410:Career
386:. The
170:Fields
158:(1985)
152:Awards
64:, U.S.
949:(PDF)
942:(PDF)
695:S2CID
581:(PDF)
549:(PDF)
372:co-NP
338:PTIME
917:ISBN
886:link
755:ISBN
751:p. 4
638:2022
606:2022
370:and
247:and
41:Born
909:doi
851:doi
847:71B
726:doi
685:doi
627:hdl
418:'s
382:on
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