Survey of local algorithms

Suomela, Jukka

doi:10.1145/2431211.2431223

Cited by 159 publications

(135 citation statements)

References 143 publications

(217 reference statements)

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“…However, some tasks are local : to solve the task, it is sufficient that each device only responds to events that take place in its vicinity. More precisely, a task is local if it can be solved with a local algorithm; in a local algorithm each node only responds to events that take place within distance t for some constant t = O(1), independently of the size of the network [17,19].…”

Section: Traditional Network and Localitymentioning

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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166

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: Traditional Network and Localitymentioning

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

166

131

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“…A recent work [4] generalised these techniques even further to show that deterministic local algorithms in the LOCAL model are often no more powerful than algorithms running on anonymous port numbered networks. For more information on this line of research, see the survey of local algorithms [21]. Here, the inapproximability results typically exploit the inability of a local algorithm to break local symmetries.…”

Section: Related Lower Boundsmentioning

confidence: 99%

No sublogarithmic-time approximation scheme for bipartite vertex cover

Göös

Suomela

2013

Distrib. Comput.

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König's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every ε > 0 there exists a constant-time distributed algorithm that finds a (1 + ε)-approximation of a maximum matching on bounded-degree graphs. In this work, we show-somewhat surprisingly-that no sublogarithmic-time approximation scheme exists for the dual problem: there is a constant δ > 0 so that no randomised distributed algorithm with running time o(log n) can find a (1 + δ )-approximation of a minimum vertex cover on 2-coloured graphs of maximum degree 3. In fact, a simple application of the Linial-Saks (1993) decomposition demonstrates that this run-time lower bound is tight.Our lower-bound construction is simple and, to some extent, independent of previous techniques. Along the way we prove that a certain cut minimisation problem, which might be of independent interest, is hard to approximate locally on expander graphs.

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“…The study of constant-round distributed algorithms was proposed in [4,27,31], and today a multitude of such algo-rithms are known, as evidenced by the survey of Suomela [35]. Few non-trivial one-round distributed algorithms are known.…”

Section: Further Related Workmentioning

confidence: 99%

Computing large independent sets in a single round

Halldórsson

Konrad

2017

Distrib. Comput.

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Independent sets play a central role in distributed algorithmics. We examine here the minimal requirements for computing non-trivial independent sets. In particular, we focus on algorithms that operate in a single communication round. A classic result of Linial shows that a constant number of rounds does not suffice to compute a maximal independent set. We are therefore interested in the size of the solution that can be computed, especially in comparison to the optimal. Our main result is a randomized one-round algorithm that achieves poly-logarithmic approximation on graphs of polynomially bounded-independence. Specifically, we show that the algorithm achieves the Caro-Wei bound (an extension of the Turán bound for independent sets) in general graphs up to a constant factor, and that the Caro-Wei bound yields a poly-logarithmic approximation on bounded-independence graphs. The algorithm uses only a single bit message and operates in a beeping model, where a node receives only the disjunction of the bits transmitted by its neighbors. We give limitation results that show that these are the minimal requirements for obtaining non-trivial solutions. In particular, a sublinear approximation cannot be obtained in a single round on general graphs, nor when nodes cannot both transmit and receive messages. We also show that our analysis of the Caro-Wei bound on polynomially bounded-independence graphs is tight, and that the poly-logarithmic approximation factor does not extend to O(1)-claw free graphs.

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Survey of local algorithms

Cited by 159 publications

References 143 publications

Exploiting locality in distributed SDN control

Exploiting locality in distributed SDN control

No sublogarithmic-time approximation scheme for bipartite vertex cover

Computing large independent sets in a single round

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