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Xheal: a localized self-healing algorithm using expanders

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Abstract

We consider the problem of self-healing in reconfigurable networks e.g., peer-to-peer and wireless mesh networks. For such networks under repeated attack by an omniscient adversary, we propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, while 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 also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Xheal 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.

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Acknowledgments

We would like to thank the anonymous referees for their comments. G. Pandurangan’s research was supported in part by Nanyang Technological University grant M58110000, Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 2 grant MOE2010-T2-2-082, US NSF grant CCF-1023166, by a grant from the United States-Israel Binational Science Foundation (BSF). A. Trehan’s research was supported at the Technion by a fellowship of the Israel Council for Higher Education, and was conducted (and supported) partly at Brown University, USA and at University of Victoria, Canada. A preliminary version of this paper was published at the 30th ACM Symposium on Principles of Distributed Computing (PODC), 2011, San Jose, CA, USA.

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Authors and Affiliations

  1. Division of Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Gopal Pandurangan

  2. Department of Computer Science, Brown University, Providence, RI, 02912, USA

    Gopal Pandurangan

  3. Faculty of Industrial Engineering and Management, Technion—Israel Institute of Technology, 32000 , Haifa, Israel

    Amitabh Trehan

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  1. Gopal Pandurangan
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  2. Amitabh Trehan
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Correspondence to Amitabh Trehan.

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Pandurangan, G., Trehan, A. Xheal: a localized self-healing algorithm using expanders. Distrib. Comput. 27, 39–54 (2014). https://doi.org/10.1007/s00446-013-0192-1

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