Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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In the on-line nearest-neighbor graph (ONG), each point afterthe first in a sequence of points in Rd is joinedby an edge to its nearest neighbor amongst those points thatprecede it in the sequence. We study the large-sample asymptoticbehavior of the total power-weighted length of the ONG on uniformrandom points in (0,1)d. In particular, ford = 1 and weight exponent ± 1-2, thelimiting distribution of the centered total weight is characterizedby a distributional fixed-point equation. As an ancillary result,we give exact expressions for the expectation and variance of thestandard nearest-neighbor (directed) graph on uniform random pointsin the unit interval. © 2007 Wiley Periodicals, Inc. RandomStruct. Alg., 2008