Abstract
Euclidean functionals having a certain “quasi-additivity” property are shown to provide a general approach to the limit theory of a broad class of random processes which arise in stochastic matching problems. Via the theory of quasi-additive functionals, we obtain a Beardwood-Halton-Hammersley type of limit theorem for the TSP, MST, minimal matching, Steiner tree, and Euclidean semi-matching functionals. One minor but technically useful consequence of the theory is that it often shows that the asymptotic behavior of functionals on the d-dimensional cube coincides with the behavior of the same functional defined on the d-dimensional torus. A more pointed consequence of the theory is that it leads in a natural way to a result on rates of convergence. Finally, we show that the quasi-additive functionals may be approximated by a heuristic with polynomial mean execution time.
Research supported in part by NSF Grant Number DMS-9200656.
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© 1995 Springer Science+Business Media New York
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Yukich, J.E. (1995). Quasi-Additive Euclidean Functionals. In: Aldous, D., Diaconis, P., Spencer, J., Steele, J.M. (eds) Discrete Probability and Algorithms. The IMA Volumes in Mathematics and its Applications, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0801-3_11
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DOI: https://doi.org/10.1007/978-1-4612-0801-3_11
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