Mathematical Programming

, Volume 1, Issue 1, pp 127–136 | Cite as

Matroids and the greedy algorithm

  • Jack Edmonds


Linear-algebra rank is the solution to an especially tractable optimization problem. This tractability is viewed abstractly, and extended to certain more general optimization problems which are linear programs relative to certain derived polyhedra.


Mathematical Method Greedy Algorithm General Optimization Tractable Optimization General Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Jack Edmonds, “Maximum matching and a polyhedron with {0, 1}-vertices,”Journal of Research of the National Bureau of Standards 69B (1965) 125–130.Google Scholar
  2. [2]
    Jack Edmonds, “Matroid partition, Math. of the Decision Sciences,”American Mathematical Society Lectures in Applied Mathematics 11 (1968) pp. 335–345.Google Scholar
  3. [3]
    Jack Edmonds, “Optimum branchings,”Journal of Research of the National Bureau of Standards 71B (1967) 233–240; reprinted with [2], pp. 346–361.Google Scholar
  4. [4]
    Jack Edmonds, “Systems of distinct representatives and linear algebra,”Journal of Research National Bureau of Standards 71B (1967) 241–245.Google Scholar
  5. [5]
    J.B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem,Proceedings American Mathematical Society 7 (1956) 48–50.Google Scholar
  6. [6]
    P. Rosenstiehl, “L'arbre minimum d'un graphe,”Proc. Int'l. Symp. on the Theory of Graphs in Rome 1966 (Dunod/Gordon-Breach, 1967).Google Scholar
  7. [7]
    R. Rado, “Note on independence functions,”Proceedings London Mathematical Society 7 (1957) 300–320.Google Scholar
  8. [8]
    H. Whitney, “On the abstract properties of linear dependence,”American Journal of Mathematics 57 (1935) 509–533.Google Scholar

Copyright information

© North-Holland Publishing Company 1971

Authors and Affiliations

  • Jack Edmonds
    • 1
    • 2
  1. 1.National Bureau of StandardsWashington, D.C.USA
  2. 2.University of WaterlooOntarioCanada

Personalised recommendations