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The complexity of restricted minimum spanning tree problems

Extended abstract
  • Christos H. Papadimitriou
  • Mihalis Yannakakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)

Abstract

We examine the complexity of finding in a given finite metric the shortest spanning tree which satisfies a property P. Most problems discussed in the mathematical programming literature—including the minimum spanning tree problem, the matching problem matroid intersection, the travelling salesman problem, and many others—can be thus formulated. We study in particular isomonphism properties—those that are satisfied by at most one tree with a given number of nodes. We show that the complexity of these problems is captured by the rate of growth of a rather unexpected—and easy to calculate—parameter.

Keywords

Travel Salesman Problem Travel Salesman Problem Hamilton Path Minimum Span Tree Problem Positive Cycle 
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.

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References

  1. [Ed1]
    J. Edmonds "Paths, Trees, and Flowers," Canad. J. Math., 17, pp. 449–467, [65].Google Scholar
  2. [Ed2]
    J. Edmonds "Matroids and the Greedy Algorithm," Math. Programming, 1, pp. 127–136, [71].Google Scholar
  3. [GJ]
    M.R. Gar D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, 1979.Google Scholar
  4. [JL]
    D.S. Johnson, S. Lin, private communication, Feb. 1976.Google Scholar
  5. [Ka]
    R.M. Karp "Reducibility among Combinatorial Problems," in Complexity of Computer Computations, R.E. Miller and J.W. Thatcher (eds.), Plenum, NY, pp 85–103, 1972.Google Scholar
  6. [Kr]
    J.B. Kruskal "On the Shortest Spanning Subtree of the Graph and the Traveling Salesman Problem," Proc. Am. Math Soc. 2, pp. 48–50, [56].Google Scholar
  7. [La1]
    E.L. Lawler "Matroid Intersection Algorithms," Math. Programming, 9, pp. 31–56, [75].Google Scholar
  8. [La2]
    E.L. Lawler Combinatorial Optimization: Networks and Matroids, Holt-Rhinehart-Winston, 1977.Google Scholar
  9. [Li]
    Shen Lin, private communication, Feb. 1976.Google Scholar
  10. [Lo]
    L. Lovãsz "The Matroid Parity Problem", manuscript, University of Waterloo, 1979.Google Scholar
  11. [Pa]
    C.H. Papadimitriou "The Complexity of the Capacitated Tree Problem," Networks Aug. 1978.Google Scholar
  12. [Pr]
    R.C. Prim "Shortest Connection Networks and some Generalizations", BSTJ pp. 1389–1401, 1957.Google Scholar
  13. [PS]
    C.H. Papadimitriou, K. Steiglitz Combinatorial Optimization Algorithms, in preparation [79].Google Scholar
  14. [PY]
    C.H. Papadimitriou, M. Yannakakis, unpublished, [77].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Christos H. Papadimitriou
    • 1
  • Mihalis Yannakakis
    • 2
  1. 1.Laboratory for Computer ScienceM.I.T.CambridgeUSA
  2. 2.Bell LaboratoriesMurray HillUSA

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