## Abstract

Consider the following stochastic process executed on a graph G = (V, E) whose nodes are initially uncovered. In each step, pick a node at random and if it is uncovered, cover it. Otherwise, if it has an uncovered neighbor, cover a random uncovered neighbor. Else, do nothing. This can be viewed as a structured coupon collector process. We show that for a large family of graphs. O(n) steps suffice to cover all nodes of the graph with high probability, where n is the number of vertices. Among these graphs are d-regular graphs with d = Ω(log n log log n), random d-regular graphs with d = Ω(log n) and the k-dimensional hypercube where n = 2^{k}. This process arises naturally in answering a question on load balancing in peer-to-peer networks. We consider a distributed hash table in which keys are partitioned across a set of processors, and we assume that the number of processors grows dynamically, starting with a single processor. If at some stage there are n processors, the number of queries required to find a key is log_{2} n + O(1), the number of pointers maintained by each processor is log_{2} n + O(1), and moreover the worst ratio between the loads of processors is O(1), with high probability. To the best of our knowledge, this is the first analysis of a distributed hash table that achieves asymptotically optimal load balance, while still requiring only O (log n) pointers per processor and O(log n) queries for locating a key; previous methods required Ω(log^{2} n) pointers per processor and Ω(log n) queries for locating a key.

Original language | English |
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Pages (from-to) | 575-584 |

Number of pages | 10 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 2003 |

Externally published | Yes |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: 9 Jun 2003 → 11 Jun 2003 |

## Keywords

- Coupon collector
- Hash table
- Hypercube
- Load balancing
- Peer to peer