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Dense Subgraphs on Dynamic Networks

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Distributed Computing (DISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7611))

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Abstract

In distributed networks, it is often useful for the nodes to be aware of dense subgraphs, e.g., such a dense subgraph could reveal dense substructures in otherwise sparse graphs (e.g. the World Wide Web or social networks); these might reveal community clusters or dense regions for possibly maintaining good communication infrastructure. In this work, we address the problem of self-awareness of nodes in a dynamic network with regards to graph density, i.e., we give distributed algorithms for maintaining dense subgraphs that the member nodes are aware of. The only knowledge that the nodes need is that of the dynamic diameter D, i.e., the maximum number of rounds it takes for a message to traverse the dynamic network. For our work, we consider a model where the number of nodes are fixed, but a powerful adversary can add or remove a limited number of edges from the network at each time step. The communication is by broadcast only and follows the CONGEST model. Our algorithms are continuously executed on the network, and at any time (after some initialization) each node will be aware if it is part (or not) of a particular dense subgraph. We give algorithms that (2 + ε)-approximate the densest subgraph and (3 + ε)-approximate the at-least-k-densest subgraph (for a given parameter k). Our algorithms work for a wide range of parameter values and run in O(Dlog1 + ε n) time. Further, a special case of our results also gives the first fully decentralized approximation algorithms for densest and at-least-k-densest subgraph problems for static distributed graphs.

Full version available as [13] at http://arxiv.org/abs/1208.1454

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Author information

Authors and Affiliations

  1. eBay Research Labs, San Jose, CA, USA

    Atish Das Sarma

  2. Department of Mathematics and Computer Science, Denison University, Granville, OH, USA

    Ashwin Lall

  3. University of Vienna, Austria

    Danupon Nanongkai

  4. Nanyang Technological University, Singapore

    Danupon Nanongkai

  5. Information Systems group, Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Haifa, Israel, 32000

    Amitabh Trehan

Authors
  1. Atish Das Sarma
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  2. Ashwin Lall
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  3. Danupon Nanongkai
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  4. Amitabh Trehan
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Editor information

Editors and Affiliations

  1. Microsoft Corporation, Building SVC6, 1065 La Avenida, 94043, Mountain View, CA, USA

    Marcos K. Aguilera

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Das Sarma, A., Lall, A., Nanongkai, D., Trehan, A. (2012). Dense Subgraphs on Dynamic Networks. In: Aguilera, M.K. (eds) Distributed Computing. DISC 2012. Lecture Notes in Computer Science, vol 7611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33651-5_11

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  • DOI: https://doi.org/10.1007/978-3-642-33651-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33650-8

  • Online ISBN: 978-3-642-33651-5

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