Efficient PRAM simulation on a distributed memory machine
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Balanced allocations (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Power of Two Choices in Randomized Load Balancing
IEEE Transactions on Parallel and Distributed Systems
Compact routing with name independence
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
On Certain Connectivity Properties of the Internet Topology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Compact name-independent routing with minimum stretch
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
The Power of Choice in a Generalized Pólya Urn Model
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Decompositions of triangle-dense graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
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A linked decomposition of a graph with n nodes is a set of subgraphs covering the n nodes such that all pairs of subgraphs intersect; we seek linked decompositions such that all subgraphs have about √n vertices, logarithmic diameter, and each vertex of the graph belongs to either one or two subgraphs. A linked decomposition enables many control and management functions to be implemented locally, such as resource sharing, maintenance of distributed directory structures, deadlock-free routing, failure recovery and load balancing, without requiring any node to maintain information about the state of the network outside the subgraphs to which it belongs. Linked decompositions also enable efficient routing, schemes with small routing tables, which we describe in Section 5. Our main contribution is to show that "Internet-like graphs" (e.g. the preferential attachment model proposed by Barabasi et al. [10] and other similar models) have linked decompositions with the parameters described above with high probability; moreover, our experiments show that the Internet topology itself can be so decomposed. Our proof proceeds by analyzing a novel process, which we call Polya urns with the power of choice, which may be of great independent interest. In this new process, we start with n nonempty bins containing O(n) balls total, and each arriving ball is placed in the least loaded of m bins, drawn independently at random with probability proportional to load. Our analysis shows that in our new process, with high probability the bin loads become roughly balanced some time before O(n2+ε) further balls have arrived and stay roughly balanced, regardless of how the initial O(n) balls were distributed, where ε 0 can be arbitrarily small, provided m is large enough.