NDLI: Xheal: localized self-healing using expanders

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Xheal: localized self-healing using expanders

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Xheal: localized self-healing using expanders

Content Provider	ACM Digital Library
Author	Pandurangan, Gopal Trehan, Amitabh
Abstract	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(κ d) in the actual graph, for a small parameter κ. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Our distributed data structure has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] and Forgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.
Starting Page	301
Ending Page	310
Page Count	10
File Format	PDF
ISBN	9781450307192
DOI	10.1145/1993806.1993865
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-06
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Expanders Randomized Spectral properties Distributed Local Self-healing Expansion Reconfiguration
Content Type	Text
Resource Type	Article

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