Corona: A stabilizing deterministic message-passing skip list

Abstract

a b s t r a c tWe present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales well. We prove the general necessary conditions limiting the initial states from which a self-stabilizing structured overlay network in a messagepassing system can be constructed. The conditions require that initial state information has to form a weakly connected graph and it should only contain identifiers that are present in the system. We formally describe Corona and rigorously prove that it stabilizes from an arbitrary initial state subject to the necessary conditions. We extend Corona to construct a skip graph.

A Self-stabilizing General De Bruijn Graph

“…A directed graph G = (V, E) is weakly connected, if the undirected version of G, namely G = (V, E ) is connected, i.e., for two nodes u, v ∈ V there is a path from u to v in G . Once there are multiple weakly connected components in G, these components cannot be connected to each other anymore as it has been shown in [16] for compare-store-send protocols. For a graph that contains multiple weakly connected components, our protocol converts each of these components to our desired topology.…”

Skip List Data Structure Based New Searching Algorithm and Its Applications: Priority Search

“…Various data structures and algorithms were also created apart from skip list data structure such as Tiara: A selfstabilizing deterministic skip list and skip graph [22],Corona: A Stabilizing Deterministic Message-Passing Skip List [23] and Skip lift: A probabilistic alternative to red-black trees [24].…”

HSkip+: A self-stabilizing overlay network for nodes with heterogeneous bandwidths

“…Similar to Nor et al [16], we assume that we have a (potentially dynamic) set V of n nodes with unique identifiers. Each node v maintains a set of variables (determined by the protocol) that define the state of node v. For each pair of nodes u and v we have a channel C u,v that holds messages that are currently in transit from u to v. We assume that the channel capacity is unbounded, there is no message loss, and the messages are delivered asynchronously to v in FIFO order.…”

“…Topological self-stabilization has recently attracted a lot of attention. Various topologies have been considered such as simple line and ring networks (e.g., [20,9]), skip lists and skip graphs (e.g., [16,10]), expanders [8], the Delaunay graph [11], the hypertree [7], and Chord [12]. Also a universal protocol for topological self-stabilization has been proposed [3].…”