Geir Dahl                     (For norsk tekst: klikk her)

    Position : Professor of mathematics
    Affiliation: Dept. of Mathematics, and Dept. of Informatics,
    Center of Mathematics for Applications CMA, University of Oslo.
    Address : CMA c/o Dept of Mathematics, P.O. Box 1053 Blindern, NO-0316 Oslo, NORWAY.
    Office : Room 1029 in Mathematics building (NHA hus)
    Phone : (+47) 22 85 58 35
    Fax : (+47) 22 85 43 49
    Email : geird@math.uio.no

    My CV can be found here: CV

    Two polyhedra and GD

Presentation

Dr. Philos. (Ph.D.), 1992, University of Oslo (Norway): mathematical optimization. Master of Science, 1983, University of Oslo: mathematical statistics. Master of Business and Adm., 1982, BI, Oslo.

Teaching

I teach courses in optimization and linear algebra. Here are our courses in these areas: Lecture notes:

Research

Mathematical optimization, in particular integer and linear optimization and relations to convex polyhedra. Linear algebra, in particular majorization and combinatorial matrix theory. More specifically, a main activity has been in applied polyhedral combinatorics, i.e., the study of polyhedra related to combinatorial optimization problems arising in graphs and networks using techninques from linear algebra, linear programming and convexity. Some of these problems are motivated by network design problems in telecommunications. Furthermore, algorithms are developed, in particular, cutting plane algorithms. In linear algebra a main interest is majorization and doubly stochastic matrices.

Publications:

Some recent papers/preprints are listed next. Paper copies are (usually) available.

  • G. Dahl, ``A matrix-based ranking method with application to tennis'', Linear Algebra and its Appl., 437 (2012), 26--36.

  • R.A.Brualdi, G.Dahl, ``Majorization classes of integral matrices'', Linear Algebra and its Appl., 436 (2012), 802--813.

  • G.Dahl, ``Polytopes related to interval vectors and incidence matrices'', Linear Algebra and Its Appl., Vol. 435 (11), p.~2955--2960, 2011. ,

  • G.Dahl, ``Majorization permutahedra and (0,1)-matrices''. Linear Algebra and its Appl., Volume 432, Issue 12, 1, July 2010, Pages 3265-3271.

  • G.Dahl, H.Minken, ``A note on permutations and rank aggregation'', Mathematical and computer modelling , 2010 ;Volum 52.(1-2) p. 380-385

  • G.Dahl, "Disjoint congruence classes and a timetabling application." Discrete Applied Mathematics, 2009 ;Volume 157. s. 1702-1710.

  • G.Dahl, "Permutation matrices related to Sudoku". Linear Algebra and its Appl., Volume 430, Issues 8-9, 15 April 2009, Pages 2457-2463.

  • M.O. Ball, G. Dahl, and T. Vossen, "Matchings in Connection with Ground Delay Program Planning". Networks, 2009 ;Volum 53.(3) p. 293-307.

  • G.Dahl, "Transportation matrices with staircase patterns and majorization", Linear Algebra and its Applications, Volume 429, Issue 7, 1 October 2008, Pages 1840-1850.

  • G. Dahl and T. Flatberg, ``Reconstructing (0,1)-matrices from projections using integer programming''. Computational Optimization and Applications, (2009) 42: 141--154.

  • G. Dahl, "Combinatorial properties of Fourier-Motzkin elimination", Electronic Journal of Linear Algebra, 16 (2007), 334--346.

  • G. Dahl and T. Flatberg, "An Integer Programming Approach to Image Segmentation and Reconstruction Problems". In Geometric Modelling, Numerical Simulation, and Optimization: Applied Mathematics at SINTEF: Springer Publishing Company 2007, p.461-481.
  • G. Dahl, ``Majorization and distances in trees''. Networks, Vol. 50 (Issue 4) 2007, 251--257.

  • G. Dahl, ``A note on a parameter relating traffic equilibria and system optimal routing'', Applied Mathematics and Computation, 191 (2007) 445-450.

  • R.A. Brualdi and G. Dahl, ``The Bruhat shadow of a permutation matrix''. In ``Mathematical papers in honour of Eduardo Marques de Sa'', Universidade de Coimbra, Textos de Matematica, Departamento de Matematica, 2006. ISBN 978-972-8564-43-8.

  • G. Dahl and H. Minken, "Methods based on discrete optimization for finding road network rehabilitation strategies", 2006, To appear in Computers and Operations Research.

  • G. Dahl, J.M. Leinaas, J. Myrheim, E. Ovrum, "A tensor product matrix approximation problem in quantum physics". Linear Algebra and Its Applications Vol. 420 (2007) 711-725. (Technical report, Dept.of Math./CMA,University of Oslo, Pure Mathematics No. 3, ISSN 0806--2439 February 2006.)

  • G. Dahl and N. Foldnes, ``LP based heuristics for the multiple knapsack problem with assignment restrictions''. Annals of Operations Research, Volume 146, Number 1 (September), 2006, p. 91--104.

  • R.A. Brualdi and G. Dahl, ``Constructing (0,1)-matrices with given line sums and certain fixed zeros''. In Advances in Discrete Tomography and Its Applications, Eds.: Herman, G.T., Kuba, A., Birkhauser, Boston (2007).

  • R.A. Brualdi and G. Dahl, ``Matrices of zeros and ones with given line sums and a zero block'', Electronic Notes in Discrete Mathematics, Vol. 20 (2005), 83--97.

  • G. Dahl and T. Flatberg, ``A remark concerning graphical sequences'', Discrete Mathematics, Volume 304, Issues 1-3, 28 November 2005, Pages 62-64.
  • G. Dahl and T. Flatberg, ``Optimization and Reconstruction of hv-convex (0,1)-matrices'', Discrete Applied Mathematics, 151 (2005), 93-105. (Prelim. version published in Electronic Notes in Discrete Mathematics, Volume 12, March 2003).

  • G. Dahl, D. Huygens, A.R. Mahjoub and P. Pesneau, "On the k edge-disjoint 2-hop-constrained paths polytope" Oper. Res. Letters, 2006;34(5):577-582.

  • G. Dahl, ``A method for approximating symmetrically reciprocal matrices by transitive matrices'', Linear Algebra and Its Applications, Vol. 403 (2005), 207--215.

  • G. Dahl, L. Gouveia and C. Requejo, ``On formulations and methods for the hop-constrained spanning tree problem'', In Handbook of Optimization in Telecommunications, Eds. P.M. Pardalos and M.G.C. Resende. Springer, 2006

  • G. Dahl, ``Tridiagonal doubly stochastic matrices'', Linear Algebra and Its Applications, Vol. 390 (2004), 197-208.

  • G. Dahl, N. Foldnes and L. Gouveia, ``A note on hop-constrained walk polytopes''. To appear in Operations Research Letters.

  • G. Dahl, ``A note on linear discrepancy'', 2003. Electronic Journ. of Linear Algebra, Vol. 10 (2003), 77--80.

  • R.A. Brualdi and G. Dahl, ``Matrices of zeros and ones with given line sums and a zero block'', Linear Algebra and Its Applications, Vol. 371 (2003), 191--207.
  • G. Dahl, ``The doubly graded matrix cone and Ferrers matrices'', Linear Algebra and Its Applications 368 (2003), 171--190.

  • G. Dahl and N. Foldnes, ``Complete description of a class of knapsack polytopes'', (To appear in Operations Research Letters), 2002.

  • G. Dahl and T. Flatberg, ``Some constrained partitioning problems and majorization'', (To appear in European Journ. of Operational Research), 2002.

  • G. Dahl and B. Johannessen, ``The 2-path network problem'', Networks 43, No.3, 190-199 (2004).

  • G. Dahl and L. Gouveia, ``On the directed hop-constrained shortest path problem'', Operations Research Letters) 32 (2004) 15-22.

  • R.A. Brualdi and G. Dahl, ``Majorization-Constrained Doubly Stochastic Matrices'', Linear Algebra and Its Applications, Vol.361, 75--97, 2003.

  • G. Dahl, "Principal majorization ideals and optimization". Nov. 2000. (Linear Algebra and Its Applications, Vol.331, 113--130, 2001.)

  • G. Dahl, "Majorization polytopes", Linear Algebra and Its Applications Vol. 297, 157--175, 1999.

  • G. Dahl, "A note on diagonally dominant matrices". (To appear in Linear Algebra and Its Applications)

  • G. Dahl, "Matrix majorization". ( Linear Algebra and Its Applications, Vol. 288, 53--73, 1999.)

  • G. Dahl, G. Storvik and A. Fadnes, "Large-scale integer programs in image analysis". Operations Research, Vol.50 (2002), No.3, 490--500.

  • G. Dahl, "Notes on polyhedra associated with hop-constrained paths". ( Operations Research Letters Vol.25 (1999) 97--101.)

  • G. Dahl, "The 2-hop spanning tree problem". ( Operations Research Letters, Vol.23 (1998) 21--26.)

  • G. Dahl, "Stable set polytopes for a class of circulant graphs". ( SIAM Journal on Optimization , Vol.9, No.2, 493--503.)

  • G. Dahl, "Majorization, polyhedra and statistical testing problems". ( Linear Algebra and Its Applications, Vol. 272, 205--225, 1998.)

  • G. Dahl, "Polytopes related to some polyhedral norms". ( Operations Research Letters, Vol.22 (1998) 49--54.)
  • G. Storvik and G. Dahl, "Lagrangian based methods for finding MAP solutions for MRF models". November, 96. (To appear in IEEE Transactions on Image Processing )

  • G. Dahl and B. Realfsen, "The cardinality-constrained shortest path problem in 2-graphs". (Networks Vol. 36 (1), 1--8 (2000).)

  • G. Dahl and M. Stoer, "A cutting plane algorithm for multicommodity survivable network design problems". (INFORMS Journal on Computing, 10(1), Winter 1998, 1--11.)

  • G. Dahl, A. Martin and M. Stoer, "Routing through virtual paths in layered telecommunication networks". Oct, 95. (Operations Research, Vol. 47, No. 5, 1999, pp 693--702).

  • G. Dahl and F. Margot, "Weak k-majorization and polyhedra". ( Mathematical Programming, Vol.81 (1998), No.1, 37--53.).

  • G. Dahl, "Polyhedra and optimization in connection with a weak majorization ordering". Dec, 94. ( Lecture Notes in Computer Science, Vol. 920, Integer programming and combinatorial optimization, (Ed. Balas and Clausen), Springer, 1995.)

    Recent talks:

    "DahlINOC09",

    "Disjoint congruence classes and an optimization problem". Nordic Optimization Symp., Stockholm, March 2009",

    "Minimum cuts: theory and algorithms". Workshop on Image analysis. Bergen, Jan. 2008",

    "Nash....", 2007

    "Constructing (0,1)-matrices with given line sums and certain fixed zeros", ILAS 2006, Amsterdam, July.

    "A tensor product matrix approximation problem in quantum physics", CMA: Trends in Mathematics for Applications, June 2006.

    "Matrices of zeros and ones with given line sums and a zero block", Workshop in Discrete Tomography and its Applications, New York, June, 2005.

    "Dahl_1"

    "Dahl_2"

    Updated Jan. 2007, GD.