The diameter of a cycle plus a random matching
SIAM Journal on Discrete Mathematics
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Internet Galaxy: Reflections on the Internet, Business, and Society
The Internet Galaxy: Reflections on the Internet, Business, and Society
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
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Complex Graphs and Networks (Cbms Regional Conference Series in Mathematics)
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A geometric preferential attachment model of networks II
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
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We study a geometric random tree model which is a variant of the FKP model proposed in [1]. We choose vertices v1, ..., vnin some convex body uniformly and fix a point . We then build our tree inductively, where at time twe add an edge from vtto the vertex in v1, ..., vt驴 1which minimizes for it, where 驴 0. We categorize an edge vi驴vjin this graph as local or global depending on the edge length relative to the distance from vito . It is shown that for 驴bounded away from 1 either all edges are local or all are global a.a.s. However, as 驴驴1 we show that in fact the number of local and global edges are asymptotically balanced.