Physical expander in Virtual Tree Overlay
Taisuke Izumi, Maria Potop-Butucaru (LIP6, INRIA Rocquencourt),, Mathieu Valero (LIP6, INRIA Rocquencourt)

TL;DR
This paper introduces a new method for constructing constant-degree expanders in virtual tree overlays, enhancing robustness in P2P networks through a local, self-organizing pairing algorithm validated by simulations.
Contribution
Proposes a novel construction of constant-degree expanders for virtual tree overlays using a random pairing approach and a local algorithm that is resilient to churn.
Findings
Achieves constant node expansion with high probability.
Provides a local, self-organizing pairing algorithm with O(log^2 n) complexity.
Demonstrates robustness and efficiency through extensive simulations.
Abstract
In this paper, we propose a new construction of constantdegree expanders motivated by their application in P2P overlay networks and in particular in the design of robust trees overlay. Our key result can be stated as follows. Consider a complete binary tree T and construct a random pairing {\Pi} between leaf nodes and internal nodes. We prove that the graph G\Pi obtained from T by contracting all pairs (leaf-internal nodes) achieves a constant node expansion with high probability. The use of our result in improving the robustness of tree overlays is straightforward. That is, if each physical node participating to the overlay manages a random pair that couples one virtual internal node and one virtual leaf node then the physical-node layer exhibits a constant expansion with high probability. We encompass the difficulty of obtaining this random tree virtualization by proposing a local,…
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Taxonomy
TopicsPeer-to-Peer Network Technologies · Caching and Content Delivery · Opportunistic and Delay-Tolerant Networks
