An adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks

Hadid, Rachid; Karaata, Mehmet Hakan

doi:10.1016/j.comcom.2008.12.035

Cited by 7 publications

(4 citation statements)

References 39 publications

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“…The following example illustrates the concepts (see example 3). Self-stabilizing algorithms to find node disjoint paths are proposed in [11,12,16,28]. Self-stabilizing algorithms for finding one-to-one node disjoint paths between two endpoints for hypercube and mesh networks have been proposed in [11,28], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Self-stabilizing algorithms to find node disjoint paths are proposed in [11,12,16,28]. Self-stabilizing algorithms for finding one-to-one node disjoint paths between two endpoints for hypercube and mesh networks have been proposed in [11,28], respectively. A new self-stabilizing algorithm for finding two one-to-one node disjoint paths problem in arbitrary network was proposed in [12].…”

Section: Introductionmentioning

confidence: 99%

“…), it was shown that n − 1 disjoint paths for one-to-one node disjoint paths paradigm can be found in O(n 2 ) time [20] and n − 1 disjoint paths for one-to-many node disjoint paths can be found in O(n 2 ) time [8]. The time complexity of the above self-stabilizing algorithms is as follows: O(d) rounds for algorithm [11] (working in mesh network), whereas the time complexity of the algorithms [12,16,28] is O(d 2 ) rounds, where d the diameter of the network.…”

Section: Introductionmentioning

confidence: 99%

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A Self-stabilizing One-To-Many Node Disjoint Paths Routing Algorithm in Star Networks

Hadid¹,

Villain²

2020

Lecture Notes in Computer Science

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The purpose of the paper is to present the first self-stabilizing algorithm for finding n−1 one-to-many node-disjoint paths in message passing model. Two paths in a network are said to be node disjoint if they do not share any nodes except for the endpoints. Our proposed algorithm works on n-dimensional star networks Sn. Given a source node s and a set of D = {d1, d2, ..., dn−1} of n − 1 destination nodes in the n-dimensional star network, our algorithm constructs n − 1 node-disjoints paths P1, P2, ..., Pn−1, where Pi is a path from s to di, 1 ≤ i ≤ n − 1. Since the proposed solution is self-stabilizing [7], it does not require initialization and withstands transient faults. The stabilization time of our algorithm is O(n 2 ) rounds.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Self-stabilizing One-To-Many Node Disjoint Paths Routing Algorithm in Star Networks

Hadid¹,

Villain²

2020

Lecture Notes in Computer Science

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“…Self-stabilizing algorithms for finding vertex-disjoint paths for at most two paths between any pair of nodes, and for all vertex-disjoint paths in anonymous mesh networks appear in [4] and in [5], respectively. We propose self-stabilizing Byzantine resilient procedures for finding f + 1 vertex-disjoint paths in 2f + 1-connected graphs.…”

Section: Introductionmentioning

confidence: 99%

Self-stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Liba

Schiller

2013

Lecture Notes in Computer Science

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Abstract. Traditional Byzantine resilient algorithms use 2f + 1 vertex-disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task: dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually aware of all the other non-Byzantine nodes and their connecting communication links. Using the topology information, nodes can, for example, route messages across the network and deliver messages from one end user to another. We present the first deterministic, cryptographic-assumptions-free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which r and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical secret re-establishments.

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Brief Announcement: A Stabilizing Algorithm for Finding Two Edge-Disjoint Paths in Arbitrary Graphs

Alazemi

Karaata

2011

Lecture Notes in Computer Science

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An adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks

Cited by 7 publications

References 39 publications

A Self-stabilizing One-To-Many Node Disjoint Paths Routing Algorithm in Star Networks

A Self-stabilizing One-To-Many Node Disjoint Paths Routing Algorithm in Star Networks

Self-stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Brief Announcement: A Stabilizing Algorithm for Finding Two Edge-Disjoint Paths in Arbitrary Graphs

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