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ON LOCALITY IN GEOMETRIC RANDOM GRAPHS
"... Abstract. We address the question of locality in random graphs. In particular, we study a geometric random tree model Tα,n which is a variant of the FKP model proposed in [FKP02]. We choose vertices v1,..., vn in some convex body uniformly and fix a point o. We then build our tree inductively, where ..."
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Abstract. We address the question of locality in random graphs. In particular, we study a geometric random tree model Tα,n which is a variant of the FKP model proposed in [FKP02]. We choose vertices v1,..., vn in some convex body uniformly and fix a point o. We then build our tree inductively
Mixing times for random walks on geometric random graphs
 In Proc. 7th Workshop on Algorithm Eng. and Experiments and 2nd Workshop on Analytic Algorithmics and Combinatorics (ALENEX/ANALCO 2005
, 2005
"... A geometric random graph, Gd (n, r), is formed as follows: place n nodes uniformly at random onto the surface of the ddimensional unit torus and connect nodes which are within a distance r of each other. The Gd (n, r) has been of great interest due to its success as a model for adhoc wireless netw ..."
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Cited by 38 (2 self)
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A geometric random graph, Gd (n, r), is formed as follows: place n nodes uniformly at random onto the surface of the ddimensional unit torus and connect nodes which are within a distance r of each other. The Gd (n, r) has been of great interest due to its success as a model for adhoc wireless
Approximating Layout Problems on Geometric Random Graphs (Extended abstract)
 Algorithms and Complexity in Information Technology
, 1998
"... We show two simple algorithms that, with high probability, approximate within a constant several layout problems for geometric random graphs drawn from the Gn (r) model with r = c p log n=n for any constant c 6. The layout problems that we consider are: Bandwidth, Minimum Linear Arrangement, Mini ..."
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Cited by 1 (0 self)
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We show two simple algorithms that, with high probability, approximate within a constant several layout problems for geometric random graphs drawn from the Gn (r) model with r = c p log n=n for any constant c 6. The layout problems that we consider are: Bandwidth, Minimum Linear Arrangement
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 532 (5 self)
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and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the socalled Preferential Connectivity (PC) model.
Fine Gaussian fluctuations on the Poisson space I: contraction, cumulants and geometric random graphs
, 2013
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On the Evolution of Random Graphs
 PUBLICATION OF THE MATHEMATICAL INSTITUTE OF THE HUNGARIAN ACADEMY OF SCIENCES
, 1960
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A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 507 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
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