Path Problems in Networks

Baras, John S.; Theodorakopoulos, George

doi:10.2200/s00245ed1v01y201001cnt003

Cited by 43 publications

(52 citation statements)

References 36 publications

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“…calculate and rank the paths). It is known that under the conditions of the proof in section VII the stable set of preferred routes can be obtained via matrix iteration [19]. The iteration starts with the identity matrix and each step consists on ⊗ adding the adjacency matrix A of the network and minimizing the results in the order.…”

Section: Methodsmentioning

confidence: 99%

“…Generically, two different routing metrics can be modelled in an algebraic form by taking the lexicographic product of the two algebras (one for each metric) [19] [20] [21]. In this case we have a lexicographic product between the ordered semigroup S composed by (S, , ⊗) and a secondary ordered semigroup N formed by (N, <, ⊗ n , ): N is the naturals set; ⊗ n is the addition operation + between the values y ∈ N for paths with a bkp value in S (it is not applied to other path weights); and < is the total order induced in the naturals by the min operator.…”

Section: Instantiating the Modelmentioning

confidence: 99%

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Multipath policy routing for the inter-domain scenario

Amaral

Bernardo

Pinto

2014

2014 IEEE International Conference on Communications (ICC)

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Multipath routing can provide a better solution for several of the current BGP's problems in the inter-domain scenario by allowing a cleaner separation between routing and traffic engineering and better failure containment. The separation between routing control logic and data forwarding, and the use of software defined networking principles open space to easier deployments of new routing protocols at the inter-domain level. This paper explores the potential of using a multipath policy based inter-domain routing algorithm based on an algebraic model. The algorithm establishes multiple paths to a destination following a policy-based architecture and works with simple destination-based hop-by-hop forwarding. We focus on the definition of algebraic models for the links, their composition and the resulting path's ranking. Our algorithm addresses the most common situations in the Internet and we include others not so common as backup links and sibling relations. We prove the correctness of the algorithm under conditions that open several implementation options and describe how it can use multipath for failure containment, using the extra paths to make each failure less important. The paper finishes with the presentation of some experimental results that illustrate the algorithm capabilities.

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Section: Methodsmentioning

confidence: 99%

Section: Instantiating the Modelmentioning

confidence: 99%

Multipath policy routing for the inter-domain scenario

Amaral

Bernardo

Pinto

2014

2014 IEEE International Conference on Communications (ICC)

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“…∀e ∈ E : x, y ∈ S : e(x ⊕ y) = e(x) ⊕ e(y) (2) and under this assumption one can prove that every entry of every routing table improves monotonically with each iteration when the protocol starts from the initial state I. Therefore for classical routing problems such as shortest-paths, it is relatively easy to construct an instance of SynchronousConditions.…”

Section: Synchronous Iteration Conditionsmentioning

confidence: 97%

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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“…To describe routing metrics, we use the standard terminology from routing algebras [29]. Each metric S = A, B, C has a domain D S and it is endowed with two binary operators ⊕ S and ⊗ S .…”

Section: Combining Popular Metrics Can Be Hard To Analyzementioning

confidence: 99%

Using routers to build logic circuits: How powerful is BGP?

Chiesa

Cittadini

Battista

et al. 2013

2013 21st IEEE International Conference on Network Protocols (ICNP)

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Abstract-Because of its practical relevance, the Border Gateway Protocol (BGP) has been the target of a huge research effort since more than a decade. In particular, many contributions aimed at characterizing the computational complexity of BGPrelated problems. In this paper, we answer computational complexity questions by unveiling a fundamental mapping between BGP configurations and logic circuits. Namely, we describe simple networks containing routers with elementary BGP configurations that simulate logic gates, clocks, and flip-flops, and we show how to interconnect them to simulate arbitrary logic circuits. We then investigate the implications of such a mapping on the feasibility of solving BGP fundamental problems, and prove that, under realistic assumptions, BGP has the same computing power as a Turing Machine. We also investigate the impact of restrictions on the expressiveness of BGP policies and route propagation (e.g., route propagation rules in iBGP and Local Transit Policies in eBGP) and the impact of different message timing models. Finally, we show that the mapping is not limited to BGP and can be applied to generic routing protocols that use several metrics.

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Path Problems in Networks

Cited by 43 publications

References 36 publications

Multipath policy routing for the inter-domain scenario

Multipath policy routing for the inter-domain scenario

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

Using routers to build logic circuits: How powerful is BGP?

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