Asynchronous convergence of policy-rich distributed bellman-ford routing protocols

Daggitt, Matthew L.; Gurney, Alexander J. T.; Griffin, Timothy G.

doi:10.1145/3230543.3230561

Cited by 18 publications

(30 citation statements)

References 24 publications

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“…We briefly outline how this work can be applied to reasoning about convergence of a very general class of internet routing protocols. Full details can be found in Daggitt et al [5].…”

Section: Preliminariesmentioning

confidence: 99%

“…As explained in [5], an asynchronous version of F provides a good model of Distributed BellmanFord (DBF) routing protocols. At each asynchronous iteration in the distributed setting, each node i will compute only the i-th row of F(X) from the rows communicated by its adjacent neighbors.…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section we discuss three different proposed sufficient conditions. The first two are from UD and the third is a modified version of a new sufficient condition found in a recent paper by Gurney [11] (which was essential for the results described in Daggitt et al [5]). During the formalization process, we discovered counterexamples to the two conditions from UD.…”

Section: Expiry : T → T Expiry T = Max T (Expiry I T)mentioning

confidence: 99%

“…The Border Gateway Protocol [18] is used by all Internet Service Providers (ISPs) to maintain connectivity in the global internet. As explained in [5], distributivity (Eq. 2) cannot be guaranteed in this setting primarily because of the competing interests of service providers and the very expressive policy languages needed to implement these interests in routing.…”

Section: Ultrametricsmentioning

confidence: 99%

“…This represents one part of a larger project in which we are developing formalized proofs of the asynchronous convergence for policy-rich distributed Bellman-Ford routing protocols (see [5]). This work required formalizing a new sufficient condition not found in UD, based on the ultrametric theory of Gurney [11].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Agda Formalization of Üresin & Dubois’ Asynchronous Fixed-Point Theory

Zmigrod

Daggitt

Griffin

2018

Interactive Theorem Proving

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Abstract. In this paper we describe an Agda-based formalization of results from Üresin & Dubois' "Parallel Asynchronous Algorithms for Discrete Data." That paper investigates a large class of iterative algorithms that can be transformed into asynchronous processes. In their model each node asynchronously performs partial computations and communicates results to other nodes using unreliable channels. Üresin & Dubois provide sufficient conditions on iterative algorithms that guarantee convergence to unique fixed points for the associated asynchronous iterations. Proving such sufficient conditions for an iterative algorithm is often dramatically simpler than reasoning directly about an asynchronous implementation. These results are used extensively in the literature of distributed computation, making formal verification worthwhile.Our Agda library provides users with a collection of sufficient conditions, some of which mildly relax assumptions made in the original paper. Our primary application has been in reasoning about the correctness of network routing protocols. To do so we have derived a new sufficient condition based on the ultrametric theory of Alexander Gurney. This was needed to model the complex policy-rich routing protocol that maintains global connectivity in the internet. Additionally we highlight and discuss two propositions from Üresin & Dubois, which during the course of the formalisation, turned out to be false.

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“…We briefly outline how this work can be applied to reasoning about convergence of a very general class of internet routing protocols. Full details can be found in Daggitt et al [5].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Expiry : T → T Expiry T = Max T (Expiry I T)mentioning

confidence: 99%

Section: Ultrametricsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Agda Formalization of Üresin & Dubois’ Asynchronous Fixed-Point Theory

Zmigrod

Daggitt

Griffin

2018

Interactive Theorem Proving

Self Cite

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Efficient Verification of Network Fault Tolerance via Counterexample-Guided Refinement

Giannarakis

Beckett

Mahajan

et al. 2019

Computer Aided Verification

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We show how to verify that large data center networks satisfy key properties such as all-pairs reachability under a bounded number of faults. To scale the analysis, we develop algorithms that identify network symmetries and compute small abstract networks from large concrete ones. Using counterexample guided abstraction refinement, we successively refine the computed abstractions until the given property may be verified. The soundness of our approach relies on a novel notion of network approximation: routing paths in the concrete network are not precisely simulated by those in the abstract network but are guaranteed to be "at least as good." We implement our algorithms in a tool called Origami and use them to verify reachability under faults for standard data center topologies. We find that Origami computes abstract networks with 1-3 orders of magnitude fewer edges, which makes it possible to verify large networks that are out of reach of existing techniques.

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A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

2019

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Üresin and Dubois' paper "Parallel Asynchronous Algorithms for Discrete Data" shows how a class of synchronous iterative algorithms may be transformed into asynchronous iterative algorithms. They then prove that the correctness of the resulting asynchronous algorithm can be guaranteed by reasoning about the synchronous algorithm alone. These results have been used to prove the correctness of various distributed algorithms, including in the fields of routing, numerical analysis and peer-to-peer protocols. In this paper we demonstrate several ways in which the assumptions that underlie this theory may be relaxed. Amongst others, we (i) expand the set of schedules for which the asynchronous iterative algorithm is known to converge and (ii) weaken the conditions that users must prove to hold to guarantee convergence. Furthermore, we demonstrate that two of the auxiliary results in the original paper are incorrect, and explicitly construct a counterexample. Finally, we also relax the alternative convergence conditions proposed by Gurney based on ultrametrics. Many of these relaxations and errors were uncovered after formalising the work in the proof assistant Agda. This paper describes the Agda code and the library that has resulted from this work. It is hoped that the library will be of use to others wishing to formally verify the correctness of asynchronous iterative algorithms.

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Asynchronous convergence of policy-rich distributed bellman-ford routing protocols

Cited by 18 publications

References 24 publications

An Agda Formalization of Üresin & Dubois’ Asynchronous Fixed-Point Theory

An Agda Formalization of Üresin & Dubois’ Asynchronous Fixed-Point Theory

Efficient Verification of Network Fault Tolerance via Counterexample-Guided Refinement

A Relaxation of Üresin and Dubois’ Asynchronous Fixed-Point Theory in Agda

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