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13
Spatial networks
 PHYSICS REPORTS
, 2010
"... Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topolo ..."
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Cited by 93 (5 self)
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Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural networks, are all examples where space is relevant and where topology alone does not contain all the information. Characterizing and understanding
Interacting Particle Systems as Stochastic Social Dynamics
 SUBMITTED TO THE BERNOULLI
"... The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying conceptual picture is of a social network, where individuals meet ..."
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Cited by 9 (3 self)
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The style of mathematical models known to probabilists as Interacting Particle Systems and exemplified by the Voter, Exclusion and Contact processes have found use in many academic disciplines. In many such disciplines the underlying conceptual picture is of a social network, where individuals meet pairwise and update their “state ” (opinion, activity etc) in a way depending on the two previous states. This picture motivates a precise general setup we call Finite Markov Information Exchange (FMIE) processes. We briefly describe a few less familiar models (Averaging, Compulsive Gambler, Deference, Fashionista) suggested by the social network picture, as well as a few familiar ones.
The stretchlength tradeoff in geometric networks: Worstcase and averagecase study
 In preparation
, 2010
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Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in dDimensions
, 2011
"... Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obta ..."
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Cited by 2 (1 self)
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Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphs.
DistributionSensitive Construction of the Greedy Spanner
, 2014
"... The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Ω(n2) time, limiting its applicability on large data sets. We observe that for ..."
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The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Ω(n2) time, limiting its applicability on large data sets. We observe that for many point sets, the greedy spanner has many ‘short’ edges that can be determined locally and usually quickly, and few or no ‘long ’ edges that can usually be determined quickly using local information and the wellseparated pair decomposition. We give experimental results showing large to massive performance increases over the stateoftheart on nearly all tests and reallife data sets. On the theoretical side we prove a nearlinear expected time bound on uniform point sets and a nearquadratic worstcase bound. Our bound for point sets drawn uniformly and independently at random in a square follows from a local characterization of tspanners we give on such point sets: we give a geometric property that holds with high probability on such point sets. This property implies that if an edge set on these points has tpaths between pairs of points ‘close’ to each other, then it has tpaths between all pairs of points. This characterization gives a O(n log2 n log2 log n) expected time bound on our greedy spanner algorithm, making it the first subquadratic time algorithm for this problem on any interesting class of points. We also use this characterization to give a O((n + E) log2 n log log n) expected time algorithm on uniformly distributed points that determines if E is a tspanner, making it the first subquadratic time algorithm for this problem that does not make assumptions on E.
Empirical Study on RouteLength Efficiency of Road Networks
, 2012
"... What does it mean to say that a physical network (such as a road network, electricity grid, or telephone network) is optimal? Different optimality criteria for different networks have been developed and studied. In the case of road networks connecting cities, an intuitive notion of an “optimal ” net ..."
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What does it mean to say that a physical network (such as a road network, electricity grid, or telephone network) is optimal? Different optimality criteria for different networks have been developed and studied. In the case of road networks connecting cities, an intuitive notion of an “optimal ” network is one that provides the shortest routes between any two cities in the network while requiring a minimal total road network
Theorem
, 2010
"... A conference in Honour of Louis Chen on his 70th birthday Shortlength routes versus lowcost networks Examples of frustrated optimization in networks Finessing tradeoff using Poisson line process cell Mean perimeter length as double integral Asymptotically efficient networks A theoretical lower bo ..."
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A conference in Honour of Louis Chen on his 70th birthday Shortlength routes versus lowcost networks Examples of frustrated optimization in networks Finessing tradeoff using Poisson line process cell Mean perimeter length as double integral Asymptotically efficient networks A theoretical lower bound