Load balancing is a critical issue for the efficient operation of peerto-peer networks. We give two new load-balancing protocols whose provable performance guarantees are within a constant factor of optimal. Our protocols refine the consistent hashing data structure that underlies the Chord (and Koorde) P2P network. Both preserve Chord's logarithmic query time and near-optimal data migration cost.Consistent hashing is an instance of the distributed hash table (DHT) paradigm for assigning items to nodes in a peer-to-peer system: items and nodes are mapped to a common address space, and nodes have to store all items residing closeby in the address space.Our first protocol balances the distribution of the key address space to nodes, which yields a load-balanced system when the DHT maps items "randomly" into the address space. To our knowledge, this yields the first P2P scheme simultaneously achieving O(log n) degree, O(log n) look-up cost, and constant-factor load balance (previous schemes settled for any two of the three).Our second protocol aims to directly balance the distribution of items among the nodes. This is useful when the distribution of items in the address space cannot be randomized. We give a simple protocol that balances load by moving nodes to arbitrary locations "where they are needed." As an application, we use the last protocol to give an optimal implementation of a distributed data structure for range searches on ordered data.
Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is non-Euclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes of metric spaces that can be tractably searched.In this paper, we develop an efficient dynamic data structure for nearest neighbor queries in growth-constrained metrics. These metrics satisfy the property that for any point q and distance d the number of points within distance 2d of q is at most a constant factor larger than the number of points within distance d. Spaces of this kind may occur in networking applications, such as the Internet or Peer-to-peer networks, and vector quantization applications, where feature vectors fall into low-dimensional manifolds within high-dimensional vector spaces.
We consider the DIRECTED STEINER NETWORK problem, or the POINT-TO-POINT CONNECTION problem. Given a directed graph G and p pairs {(si, ti), .. ., (s,, tp)} of nodes in the graph, one has to find the smallest subgraph H of G that contains paths from si to tj for all i.
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