Tiara: A self-stabilizing deterministic skip list and skip graph

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

Strothmann

2015

Self Cite

A fundamental problem for overlay networks is to safely exclude leaving nodes, i.e., the nodes requesting to leave the overlay network are excluded from it without affecting its connectivity. There are a number of studies for safe node exclusion if the overlay is in a well-defined state, but almost no formal results are known for the case in which the overlay network is in an arbitrary initial state, i.e., when looking for a self-stabilizing solution for excluding leaving nodes. We study this problem in two variants: the Finite Departure Problem (F DP) and the Finite Sleep Problem (FSP). In the F DP the leaving nodes have to irrevocably decide when it is safe to leave the network, whereas in the FSP, this leaving decision does not have to be final: the nodes may resume computation when woken up by an incoming message. We are the first to present a self-stabilizing protocol for the F DP and the F SP that can be combined with a large class of overlay maintenance protocols so that these are then guaranteed to safely exclude leaving nodes from the system from any initial state while operating as specified for the staying nodes. In order to formally define the properties these overlay maintenance protocols have to satisfy, we identify four basic primitives for manipulating edges in an overlay network that might be of independent interest.

Section: Our Resultsmentioning

confidence: 99%

Towards a Universal Approach for the Finite Departure Problem in Overlay Networks

Koutsopoulos

Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures

Strothmann

2015

Self Cite

“…The concept of self-stabilization has first been introduced by E. W. Dijkstra in 1974 via a self-stabilizing token-based ring [4]. This led to the introduction of various other selfstabilizing protocols for network topologies such as sorted lists [13] [6], De Bruijn graphs [14], Chord graphs [10], Skip graphs [3] [8] and many more. A universal approach that is able to derive self-stabilizing protocols for several types of topologies was introduced in [2].…”

Section: Related Workmentioning

confidence: 99%

Self-stabilizing Overlays for High-Dimensional Monotonic Searchability

Feldmann

Kolb

Lecture Notes in Computer Science

2018

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We extend the concept of monotonic searchability [16] [17] for self-stabilizing systems from one to multiple dimensions. A system is self-stabilizing if it can recover to a legitimate state from any initial illegal state. These kind of systems are most often used in distributed applications. Monotonic searchability provides guarantees when searching for nodes while the recovery process is going on. More precisely, if a search request started at some node u succeeds in reaching its destination v, then all future search requests from u to v succeed as well. Although there already exists a self-stabilizing protocol for a two-dimensional topology [9] and an universal approach for monotonic searchability [17], it is not clear how both of these concepts fit together effectively. The latter concept even comes with some restrictive assumptions on messages, which is not the case for our protocol. We propose a simple novel protocol for a self-stabilizing two-dimensional quadtree that satisfies monotonic searchability. Our protocol can easily be extended to higher dimensions and offers routing in O(log n) hops for any search request.

“…The concept of self-stabilizing algorithms for distributed systems goes back to the year 1974, when E. W. Dijkstra introduced the idea of self-stabilization in a token-based ring [7]. People came up with self-stabilizing protocols for various types of overlays, like sorted lists [17], rings [19], spanning trees [1], Chord graphs [11], Skip graphs [5] and many more. A self-stabilizing protocol for the clique has been presented in [12].…”

Section: Related Workmentioning

confidence: 99%

A Self-stabilizing General De Bruijn Graph

Feldmann

Lecture Notes in Computer Science

2017

Self Cite

Searching for other participants is one of the most important operations in a distributed system. We are interested in topologies in which it is possible to route a packet in a fixed number of hops until it arrives at its destination. Given a constant d, this paper introduces a new self-stabilizing protocol for the q-ary d-dimensional de Bruijn graph (q = d √ n) that is able to route any search request in at most d hops w.h.p., while significantly lowering the node degree compared to the clique: We require nodes to have a degree of O( d √ n), which is asymptotically optimal for a fixed diameter d. The protocol keeps the expected amount of edge redirections per node in O( d √ n), when the number of nodes in the system increases by factor 2 d . The number of messages that are periodically sent out by nodes is constant.