[ACM Press the 30th annual ACM SIGACT-SIGOPS symposium - San Jose, California, USA (2011.06.06-2011.06.08)] Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '11 - Xheal
β Scribed by Pandurangan, Gopal; Trehan, Amitabh
- Book ID
- 120966230
- Publisher
- ACM Press
- Year
- 2011
- Tongue
- English
- Weight
- 536 KB
- Category
- Article
- ISBN
- 1450307191
No coin nor oath required. For personal study only.
β¦ Synopsis
We consider the problem of self-healing in reconfigurable networks (e.g. peer-to-peer and wireless mesh networks) that are under repeated attack by an omniscient adversary and propose a fully distributed algorithm, Xheal , that maintains good expansion and spectral properties of the network, also keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We use a model similar to that used in recent work on self-healing. In our model, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds by quick "repairs," which consist of adding or deleting edges in an efficient localized manner.These repairs preserve the edge expansion, spectral gap, and network stretch, after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, the expansion of the graph will be either 'better' than the expansion of the graph formed by considering only the adversarial insertions (not the adversarial deletions) or the expansion will be, at least, a constant. Also, the stretch i.e. the distance between any pair of nodes in the healed graph is no more than a O(log n) factor. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most O(ΞΊd) in the actual graph, for a small
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