Locally checkable proofs

Göös, Mika; Suomela, Jukka

doi:10.1145/1993806.1993829

Cited by 52 publications

(96 citation statements)

References 20 publications

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“…However, one of the nodes in the bad instance has to raise an alarm-if we attempt to do this based on local information only, we will occasionally make false alarms. Even though the task is inherently global, we can still use local algorithms if we resort to proof labeling schemes [6,12,13]. If we are given just an arbitrary spanning tree T , we cannot verify it locally.…”

Section: Alarm Ok Okmentioning

confidence: 99%

Exploiting locality in distributed SDN control

Schmid

Suomela

2013

Proceedings of the Second ACM SIGCOMM Workshop on Hot Topics in Software Defined Networking

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171

131

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Large SDN networks will be partitioned in multiple controller domains; each controller is responsible for one domain, and the controllers of adjacent domains may need to communicate to enforce global policies. This paper studies the implications of the local network view of the controllers. In particular, we establish a connection to the field of local algorithms and distributed computing, and discuss lessons for the design of a distributed control plane. We show that existing local algorithms can be used to develop efficient coordination protocols in which each controller only needs to respond to events that take place in its local neighborhood. However, while existing algorithms can be used, SDN networks also suggest a new approach to the study of locality in distributed computing. We introduce the so-called supported locality model of distributed computing. The new model is more expressive than the classical models that are commonly used in the design and analysis of distributed algorithms, and it is a better match with the features of SDN networks.

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Section: Alarm Ok Okmentioning

confidence: 99%

Exploiting locality in distributed SDN control

Schmid

Suomela

2013

Proceedings of the Second ACM SIGCOMM Workshop on Hot Topics in Software Defined Networking

Self Cite

171

131

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“…Paper [12] generated several following up contributions, including, e.g., studies on the impact of randomization [11], studies on the impact of node identifiers [10], studies on verification tasks where certificates include node IDs [17], etc. See also [16] for other forms of local checking, and for their impact on distributed graph-optimization problems.…”

Section: Related Workmentioning

confidence: 99%

Distributedly Testing Cycle-Freeness

Arfaoui

Fraigniaud

Ilcinkas

et al. 2014

Graph-Theoretic Concepts in Computer Science

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Abstract. We tackle local distributed testing of graph properties. This framework is well suited to contexts in which data dispersed among the nodes of a network can be collected by some central authority (like in, e.g., sensor networks). In local distributed testing, each node can provide the central authority with just a few information about what it perceives from its neighboring environment, and, based on the collected information, the central authority is aiming at deciding whether or not the network satisfies some property. We analyze in depth the prominent example of checking cycle-freeness, and establish tight bounds on the amount of information to be transferred by each node to the central authority for deciding cycle-freeness. In particular, we show that distributedly testing cycle-freeness requires at least ⌈log d⌉ − 1 bits of information per node in graphs with maximum degree d, even for connected graphs. Our proof is based on a novel version of the seminal result by Naor and Stockmeyer (1995) enabling to reduce the study of certain kinds of algorithms to order-invariant algorithms, and on an appropriate use of the known fact that every free group can be linearly ordered.

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“…Recent work in this area includes but is not limited to, deciding locally whether the nodes of a network are properly colored , checking the results obtained from the execution of a distributed program [13,15], designing time lower bounds on the hardness of distributed approximation [7], estimating the complexity of logics required for distributed run-time verification [14], and elaborating a distributed computing complexity theory [12,16].…”

Section: Introductionmentioning

confidence: 99%

“…The results where later on extended in [15] to the set agreement task and in [14] proving nearly tight bounds on the number of opinions required to check any distributed language. In [12,16] the context of local distributed network computing [23] is considered. It was shown that not all network decision tasks can be solved locally by a non-deterministic algorithm.…”

Section: Introductionmentioning

confidence: 99%

Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

Fraigniaud

Rajsbaum²,

Travers

2016

LATIN 2016: Theoretical Informatics

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The notion of deciding a distributed language L is of growing interest in various distributed computing settings. Each process p i is given an input value x i , and the processes should collectively decide whether their set of input values x = (x i ) i is a valid state of the system w.r.t. to some specification, i.e., if x ∈ L. In non-deterministic distributed decision each process p i gets a local certificate c i in addition to its input x i . If the input x ∈ L then there exists a certificate c = (c i ) i such that the processes collectively accept x, and if x ∈ L, then for every c, the processes should collectively reject x. The collective decision is expressed by the set of opinions emitted by the processes, and one aims at minimizing the number of possible opinions emitted by each process.In this paper we study non-deterministic distributed decision in asynchronous systems where processes may crash. In this setting, it is known that the number of opinions needed to deterministically decide a language can grow with n, the number of processes in the system. We prove that every distributed language L can be non-deterministically decided using only three opinions, with certificates of size O(log α(n)) bits, where α grows at least as slowly as the inverse of the Ackerman function. The result is optimal, as we show that there are distributed languages that cannot be decided using just two opinions, even with arbitrarily large certificates.To prove our upper bound, we introduce the notion of distributed encoding of the integers, that provides an explicit construction of a long bad sequence in the well-quasi-ordering ({0, 1} * , = ) controlled by the successor function. Thus, we provide a new class of applications for wellquasi-orderings that lies outside logic and complexity theory. For the lower bound we use combinatorial topology techniques.

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Locally checkable proofs

Cited by 52 publications

References 20 publications

Exploiting locality in distributed SDN control

Exploiting locality in distributed SDN control

Distributedly Testing Cycle-Freeness

Minimizing the Number of Opinions for Fault-Tolerant Distributed Decision Using Well-Quasi Orderings

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