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.
Research supported by NSF Grant MCS77-01193.
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References
J. Edmonds "Paths, Trees, and Flowers," Canad. J. Math., 17, pp. 449–467, [65].
J. Edmonds "Matroids and the Greedy Algorithm," Math. Programming, 1, pp. 127–136, [71].
M.R. Gar D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, 1979.
D.S. Johnson, S. Lin, private communication, Feb. 1976.
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.
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].
E.L. Lawler "Matroid Intersection Algorithms," Math. Programming, 9, pp. 31–56, [75].
E.L. Lawler Combinatorial Optimization: Networks and Matroids, Holt-Rhinehart-Winston, 1977.
Shen Lin, private communication, Feb. 1976.
L. Lovãsz "The Matroid Parity Problem", manuscript, University of Waterloo, 1979.
C.H. Papadimitriou "The Complexity of the Capacitated Tree Problem," Networks Aug. 1978.
R.C. Prim "Shortest Connection Networks and some Generalizations", BSTJ pp. 1389–1401, 1957.
C.H. Papadimitriou, K. Steiglitz Combinatorial Optimization Algorithms, in preparation [79].
C.H. Papadimitriou, M. Yannakakis, unpublished, [77].
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© 1979 Springer-Verlag Berlin Heidelberg
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Papadimitriou, C.H., Yannakakis, M. (1979). The complexity of restricted minimum spanning tree problems. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_36
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DOI: https://doi.org/10.1007/3-540-09510-1_36
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