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Interview


Name: Dr. Alan J. Hoffman

Research Staff Member
IBM T.J. Watson Research Center
Yorktown Heights, New York 10598

HOFFA@watson.ibm.com

 

Credentials

AB1947Columbia University
PhD1950Columbia University

Principal employment

1943-46US Army
1950-51Member, Institute for Advanced Study, Princeton
1951-56Mathematician, National Bureau of Standards, Washington
1956-57Scientific Liason Officer, Office of Naval Research, London, UK
1957-61Consultant, Management Consultation Services, General Electric Company, New York
1961-presentResearch Staff Member, T. J. Watson Research Center, IBM, Yorktown Heights, New York

Visiting or adjunct professor

1965Technion, Israel Institute of Technology
1965-1976City University of New York
1975-1985 and 1991Yale University
1980-1991Stanford University
1990-1996Rutgers University
1992-93Georgia Institute of Technology

Editorial boards (Past and Present)

Linear Algebra and its Applications (founding editor)
Mathematics of Operations Research
Discrete Mathematics
Discrete Applied Mathematics
Naval Research Logistics Quarterly
Journal of Combinatorial Theory
Combinatorica
SIAM Journal of Discrete Mathematics
SIAM Journal of Applied Mathematics
Mathematics of Computation
International Computing Center Bulletin

Honors

Member, National Academy of Sciences
IBM Fellow
DSc (Honorary) Technion
Fellow, American Academy of Arts and Sciences
Fellow, New York Academy of Sciences
Phi Beta Kappa Lecturer, l989-90
Special issue of Linear Algebra and its Applications, l989, for 65th birthday
von Neumann Prize (Operations Research Society and Institute of Management Science), 1992
Founder's Award, Mathematical Programming Society, 2000

Principal Publications in Optimization

"On Approximate Solutions of Systems of Linear Inequalities," J. Research Natl. Bureau Stds., 49:263-265, 1952

"Computational Experience in Solving Linear Programs," Jour. Soc. Ind. Appl. Math., 1:17-34, 1953 (with M. Mannos, D. Sokolowsky and N. Wiegmann)

"Cycling in the Simplex Algorithm," Natl. Bureau Stds., Report 2974, 1953

"Integral Boundary Points of Convex Polyhedra," Annals of Mathematics Study, 38: 223-241, Princeton, 1956 (with J.Kruskal)

"Dilworth's Theorem on Partially Ordered Sets," Annals Of Mathematics Study, 38:207-214, Princeton, 1956 (with G. Dantzig).

"Some Recent Applications of the Theory of Linear Inequalities to Extremal Combinatorial Analysis," Proc. Symp. in Applied Mathematics, Amer. Math. Soc., 113-127, 1960

"On Simple Linear Programming Problems," Proc. Symposia in Pure Mathematics VII, Amer. Math. Soc., 317-327, 1963

"On Abstract Dual Linear Programs," Naval Research Logistics Quarterly, 10:369-373, 1964

"Linear Inequalities and Analysis," American Mathematical Monthly, 71:416-418, 1964 (with M. McAndrew)

"Some Properties of Graphs with Multiple Edges," Canadian Journal of Mathematics, 17:166-177, 1965 (with D. Fulkerson and M. McAndrew)v

"When Is a Team 'Mathematically' Eliminated?" Proc. Princeton Symposium On Math. Programming, 391-401, 1966; Princeton, 1970 (with T. Rivlin)

"On Finding All Shortest Distances in a Directed Network," IBM J. Res. And Dev., 16:412-414, 1972 (with S. Winograd)

"Lower Bounds for the Partitioning of Graphs," IBM J. Res. and Dev., 17:420-425, 1973 (with W. Donath

"A Generalization of Max Flow-Min Cut," Mathematical Programming, 6:352-359, 1974

"On Balanced Matrices," Mathematical Programming Study, 1:120-132, 1974 (with D. Fulkerson and R. Oppenheim)

"Local Unimodularity in the Matching Polytope," Annals of Discrete Mathematics, 2:201-209, 1978 (with R. Oppenheim)

"On Lattice Polyhedra," Proceedings 5th Hungarian Colloquium on Combinatorics, 593-598, 1978 (with D.E. Schwartz)

"On Lattice Polyhedra III: Blockers and Anti-blockers of Lattice Clutters," Mathematical Programming Study, 8:197-207, 1978

"Binding Constraints and Helly Numbers," Annals of the New York Academy of Sciences 319, 284-288, 1979

"Lattice Polyhedra II: Construction and Examples," Annals of Discrete Mathematics, 15:189-203, 1982 (with H. Groeflin)

"Two Remarks on the Mendelsohn-Dulmage Theorem," Annals of Discrete Mathematics, 15:171-177, 1982 (with D. Gale)

"A Fast Algorithm That Makes Matrices Optimally Sparse," Progress in Combinatorial Optimization, 185-196, Academic Press, 1984 (with S. McCormick)

"Totally Balanced and Greedy Matrices," SIAM Journal Algebraic and Discrete Methods, 721-730, l985 (with A. Kolen and M. Sakarovitch)

"Greedy Packing and Series-Parallel Graphs," J. Combinatorial Theory A47:6-15, 1988 (with A. Tucker)

"On Greedy Algorithms for Series Parallel Graphs," Mathematical Programming 40:197-204, 1988

"On Simple Combinatorial Optimization Problems," Discrete Mathematics 106/107, 285-289, 1992

"Series Parallel Composition of Greedy Linear Programming Problems," Mathematical Programming, B62:1-14, 1993 (with W.W. Bein and P. Brucker)

"A Nonlinear Allocation Problem," IBM Journal of R&D, 38:301-306, 1994 (with E.V. Denardo, T. Mackenzie, and W.R. Pulleyblank)

"On Computing Ax and piT A, When A Is Sparse," Annals of Numerical Mathematics, 4:359-368, 1996 (with W. Pulleyblank and J. Tomlin)

"Polyhedral Combinatorics and Totally Ordered Abelian Groups," to appear in Math Programming, Series A

"On the Submodular Matrix Representation of a Digraph," to appear in Theoretical Computer Science (with Heinz Groeflin, Arlette Gaillard, and W. R. Pulleyblank)


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