Ankur Bhargava

Pagoda: a dynamic overlay network for routing, data management, and multicasting

The tremendous growth of public interest in peer-to-peer systems in recent years has initiated a lot of research work on how to design efficient and robust overlay networks for these systems. While a large collection of scalable peer-to-peer overlay networks has been proposed in recent years, many fundamental questions have remained open. Some of these are: Is it possible to design deterministic peer-to-peer overlay networks with properties comparable to randomized peer-to-peer systems? How can peers of non-uniform bandwidth be organized in an overlay network?We propose a dynamic overlay network called Pagoda that provides solutions to both of these problems. The Pagoda network has a constant degree, a logarithmic diameter, and a 1/logarithmic expansion, and therefore matches the properties of the best randomized overlay networks known so far. However, in contrast to these networks, the Pagoda is deterministic and therefore guarantees these properties. The Pagoda can be used to organize both nodes with uniform bandwidth and nodes with non-uniform bandwidth. For nodes with uniform bandwidth, any node insertion or deletion can be executed with logarithmic work, and for nodes with non-uniform bandwidth, any node insertion and deletion can be executed with polylogarithmic work. Moreover, the Pagoda overlay network can route arbitrary multicast problems with a congestion that is within a logarithmic factor of what a best possible overlay network of logarithmic degree for that particular multicast problem can achieve, even though the Pagoda is a constant degree network. This holds even for nodes of arbitrary non-uniform bandwidths. We also show that the Pagoda network can be used for efficient data management.

The Effect of Faults on Network Expansion

We study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain and still contain a large (i.e., linear-sized) connected component with approximately the same expansion as the original fault-free network. We use a pruning technique that culls away those parts of the faulty network that have poor expansion. The faults may occur at random or be caused by an adversary. Our techniques apply in either case. In the adversarial setting we prove that for every network with expansion

Approximate maximum weight branchings

\alpha,

Derandomization of dimensionality reduction and SDP based algorithms

a large connected component with basically the same expansion as the original network exists for up to a constant times

An Algorithm for Computing DNA Walks

\alpha \cdot n

Web-based system for collaborative generation of interactive videos

faults. We show this result is tight in the sense that every graph G of size n and uniform expansion

Populating a structured presentation with new values

\alpha(\cdot)

Adding new attributes to a structured presentation

can be broken into components of size o(n) with

Adding new instances to a structured presentation

\omega(\alpha(n) \cdot n)

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faults. Unlike the adversarial case, the expansion of a graph gives a very weak bound on its resilience to random faults. While it is the case, as before, that there are networks of uniform expansion