TY - GEN

T1 - Universal augmentation schemes for network navigability

T2 - SPAA'07: 19th Annual Symposium on Parallelism in Algorithms and Architectures

AU - Fraigniaud, Pierre

AU - Gavoille, Cyril

AU - Kosowski, Adrian

AU - Lebhar, Emmanuelle

AU - Lotker, Zvi

PY - 2007/10/18

Y1 - 2007/10/18

N2 - Augmented graphs were introduced for the purpose of analyzing the "six degrees of separation between individuals" observed experimentally by the sociologist Standley Milgram in the 60's. Formally, an augmented graph is a pair (G,ψ) where G is a graph, and ψ is a collection of probability distributions {ψu, u ∈ V(G)}. Every node u ∈ V(G) is given an extra link, called a long range link, pointing to some node v, called the long range contact of u. The head v of this link is chosen at random by Pr{u → v} = ψu(v). In augmented graphs, greedy routing is the oblivious routing process in which every intermediate node chooses among all its neighbors (including its long range contact) the one that is closest to the target according to the distance measured in the underlying graph G, and forwards to it. Roughly, augmented graphs aim at modeling the structure of social networks, while greedy routing aims at modeling the searching procedure applied in Milgram's experiment. Our objective is to design efficient universal augmentation schemes, i.e., augmentation schemes that give to any graph G a collection of probability distributions ψ such that greedy routing in (G,ψ) is fast. It is known that the uniform scheme ψunif is a universal scheme ensuring that, for any n-node graph G, greedy routing in (G,ψunif) performs in O(√n) expected number of steps. Our main result is the design of a universal augmentation scheme ψ such that greedy routing in (G,ψ) performs in Õ(n1/3) expected number of steps for any n-node graph G. We also show that under some more restricted model, the √n-barrier cannot be overcome.

AB - Augmented graphs were introduced for the purpose of analyzing the "six degrees of separation between individuals" observed experimentally by the sociologist Standley Milgram in the 60's. Formally, an augmented graph is a pair (G,ψ) where G is a graph, and ψ is a collection of probability distributions {ψu, u ∈ V(G)}. Every node u ∈ V(G) is given an extra link, called a long range link, pointing to some node v, called the long range contact of u. The head v of this link is chosen at random by Pr{u → v} = ψu(v). In augmented graphs, greedy routing is the oblivious routing process in which every intermediate node chooses among all its neighbors (including its long range contact) the one that is closest to the target according to the distance measured in the underlying graph G, and forwards to it. Roughly, augmented graphs aim at modeling the structure of social networks, while greedy routing aims at modeling the searching procedure applied in Milgram's experiment. Our objective is to design efficient universal augmentation schemes, i.e., augmentation schemes that give to any graph G a collection of probability distributions ψ such that greedy routing in (G,ψ) is fast. It is known that the uniform scheme ψunif is a universal scheme ensuring that, for any n-node graph G, greedy routing in (G,ψunif) performs in O(√n) expected number of steps. Our main result is the design of a universal augmentation scheme ψ such that greedy routing in (G,ψ) performs in Õ(n1/3) expected number of steps for any n-node graph G. We also show that under some more restricted model, the √n-barrier cannot be overcome.

KW - Small world phenomenon

UR - http://www.scopus.com/inward/record.url?scp=35248894870&partnerID=8YFLogxK

U2 - 10.1145/1248377.1248379

DO - 10.1145/1248377.1248379

M3 - Conference contribution

AN - SCOPUS:35248894870

SN - 159593667X

SN - 9781595936677

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 1

EP - 7

BT - SPAA'07

Y2 - 9 June 2007 through 11 June 2007

ER -