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Accelerated greedy algorithms for maximizing submodular set functions

Integer Programming, Networks

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS,volume 7)


Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E maximizing f over P(E). Many combinatorial optimization problems can be formulated in these terms. Here, a family of approximate solution methods is studied : the greedy algorithms.

After having described the standard greedy algorithm (SG) it is shown that, under certain assumptions (namely : submodularity of f) the computational complexity of (SG) can often be significantly reduced, thus leading to an accelerated greedy algorithm (AG). This allows treatment of large scale combinatorial problems of the (P) type. The accelerated greedy algorithm is shown to be optimal (interms of computational complexity) over a wide class of algorithms, and the submodularity assumption is used to derive bounds on the difference between the greedy solution and the optimum solution.


  • Greedy Algorithm
  • Minimum Span Tree
  • Combinatorial Optimization Problem
  • Fixed Charge
  • Span Tree Problem

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  1. MINOUX (M.) "Multiflots de coût minimum avec fonctions de coût concaves". Annales des télécommunications, 31, no 3–4, (1976)

    Google Scholar 

  2. MINOUX (M.) "Algorithmes gloutons et algorithmes glotons accélérés pour la résolution des grands problèmes combinatoires". Bulletin de la Direction des Etudes et Recherches — EDF (France) Série C No 1 (1977) pp.41–58

    Google Scholar 

  3. LAURIERE (J.L.) "Un langage et un programme pour énoncer et résoudre des problèmes combinatoires" — Thèse, doc.ès sciences. Université PARIS VI — Mai 1976

    Google Scholar 

  4. KRUSKAL (J.B.) "On the shortest spanning subtree of a graph and the travelling salesman problem" — Proc. Am. Math. Soc. 2 (1956) pp. 48–50

    Google Scholar 

  5. EDMONDS (J.) "Matroids and the greedy algorithm" — Mathematical programming 1, (1971), pp. 127–136.

    Google Scholar 

  6. GONDRAN (M.) "L'algorithme glouton dans les algèbres de chemins" Bulletin Dir. Et. Rech. EDF Série C No 1 (1975) pp.25–32

    Google Scholar 

  7. BILLHEIMER (J.W.) GRAY (P.) "Network design with fixed and variable cost elements". Transp. Science 7, no 1 (1973) pp. 49–74

    Google Scholar 

  8. LEGROS (J.F.) MINOUX (M.) OUSSET (A.) "Local networks optimization" Proc. ISSLS Conference London (May 1976)

    Google Scholar 

  9. COOPER (L.) "The transportation location problem" Ops. Res. 20, no 1 (1972) pp. 94–108

    Google Scholar 

  10. KUENNE (R.E.) SOLAND (R.M.) "Exact and approximate solutions to the multisource weber problem". Mathematical programming 3 (1972) pp. 193–209.

    Google Scholar 

  11. STEINBERG (D.I.) "The fixed charge problem" — Nav. Res. Log. Quart. 17 (1970) pp. 217–236.

    Google Scholar 

  12. BALINSKY (M.L.) "Fixed Cost Transportation Problems" — Nav. Res. Log. Quart. 8 (1961) pp. 41–54

    Google Scholar 

  13. MALEK-ZAVARET (M.), FRISCH (I.T.) "On the fixed cost flow problem" Intern.Journal Control 16, no 5, (1972), pp. 897–902

    Google Scholar 

  14. EDMONDS (J.) "Submodular functions, matroids, and certain polyhedra" in: Combinatorial structures and their applications, R. Guy ed. pp.69–87 Gordon and Breach 1971.

    Google Scholar 

  15. FISCHER (M.L.) NEMHAUSER (G.L.) WOLSEY (L.A.) "An analysis of approximations for maximizing submodular set functions" IX Internat. Symp. on Mathematical Programming BUDAPEST Hungary (1976).

    Google Scholar 

  16. SAVAGE (S.L.) "Some theoretical implications of local optimization" Mathematical Programming 10 (1976) pp. 354–366.

    Google Scholar 

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© 1978 Springer-Verlag

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Minoux, M. (1978). Accelerated greedy algorithms for maximizing submodular set functions. In: Stoer, J. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 7. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-540-08708-3

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