What cannot be computed locally!

Kühn, Fabian; Moscibroda, Thomas; Wattenhofer, Rogert

doi:10.1145/1011767.1011811

Cited by 227 publications

(196 citation statements)

References 19 publications

(16 reference statements)

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“…al. [19], which states that at least Ω( log n/ log log n) communication rounds are needed to find a constant or polylogarithmic approximation 1 . Their proof relies on a construction of a special family of graphs in which the maximal node degree depends on the size of the graph.…”

Section: Related Workmentioning

confidence: 99%

“…As have been already stated above, in the general case, Kuhn et al [19] provide a negative answer and state that at least Ω( log n/ log log n) communication rounds are needed. Along with that, in several other related communication models, such as the unit disc graph, local approximation algorithms are known to exist [6].…”

Section: Introductionmentioning

confidence: 97%

“…Although the approximation ratio of existing solutions for the dominating set problem, O(log Δ), was found to be the best possible (to within a lower order additive factor, unless NP has an n O(log log n) -time deterministic algorithm [9]), the gap between lower and upper bounds on the running time of distributed deterministic solutions remains wide. Kuhn et al [19] showed that any distributed approximation algorithm for the dominating set problem with a polylogarithmic approximation ratio requires at least Ω( log n/ log log n) communication rounds. Along with that, the existing distributed deterministic algorithms incur a linear (in number of nodes) running time [7,23,29].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Deterministic Dominating Set Construction in Networks with Bounded Degree

Friedman

Kogan

2011

Distributed Computing and Networking

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Abstract. This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usually significantly smaller than n, the total number of nodes in the system. Such networks arise in various settings of wireless and peer-to-peer communication. A trivial approach of choosing all nodes into the dominating set yields an algorithm with the approximation ratio of Δ + 1. We show that any deterministic algorithm with non-trivial approximation ratio requires Ω(log * n) rounds, meaning effectively that no o(Δ)-approximation deterministic algorithm with a running time independent of the size of the system may ever exist. On the positive side, we show two deterministic algorithms that achieve log Δ and 2 log Δ-approximation in O(Δ 3 + log * n) and O(Δ 2 log Δ + log * n) time, respectively. These algorithms rely on coloring rather than node IDs to break symmetry.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Deterministic Dominating Set Construction in Networks with Bounded Degree

Friedman

Kogan

2011

Distributed Computing and Networking

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“…Kuhn et al [17] proved that no clustering approach can achieve a constant approximation ratio in constant rounds.…”

Section: Related Workmentioning

confidence: 99%

Virtual Backbone Construction in MANETs Using Adjustable Transmission Ranges

Dai

2006

IEEE Trans. on Mobile Comput.

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Recently, the use of a virtual backbone in various applications in mobile ad hoc networks (MANETs) has become popular. These applications include topology management, point and area coverage, and routing protocol design. In a MANET, one challenging issue is to construct a virtual backbone in a distributed and localized way while balancing several conflicting objectives: small approximation ratio, fast convergence, and low computation cost. Many existing distributed and localized algorithms select a virtual backbone without resorting to global or geographical information. However, these algorithms incur a high computation cost in a dense network. In this paper, we propose a distributed solution based on reducing the density of the network using two mechanisms: clustering and adjustable transmission range. By using adjustable transmission range, we also achieve another objective, energy-efficient design, as a by-product. As an application, we show an efficient broadcast scheme where nodes (and only * This work was supported in part by NSF grants CCR 0329741, CNS 0434533, CNS 0422762, and EIA 0130806. 1 nodes) in a virtual backbone are used to forward the broadcast message. The virtual backbone is constructed using Wu and Li's marking process [37] and the proposed density reduction process. The application of the density reduction process to other localized algorithms is also discussed. The efficiency of our approach is confirmed through both analytical and simulation study.keywords: Adjustable transmission range, broadcasting, clustering, connected dominating set (CDS), energy efficiency, mobile ad hoc networks (MANETs).

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“…For more scalable approaches, researchers explored the paradigm of local algorithms for doing data mining in P2P network. Local algorithms [12,16,2,11,10] are ones in which the result is usually computed using information from just a handful of nearby neighbors. Still, it is possible to make definite claims about the correctness of the result.…”

Section: Data Mining In P2p Networkmentioning

confidence: 99%

Peer-to-Peer Data Mining, Privacy Issues, and Games

Bhaduri

Das

Kargupta

Autonomous Intelligent Systems: Multi-Agents and Data Mining

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Abstract. Peer-to-Peer (P2P) networks are gaining increasing popularity in many distributed applications such as file-sharing, network storage, web caching, searching and indexing of relevant documents and P2P network-threat analysis. Many of these applications require scalable analysis of data over a P2P network. This paper starts by offering a brief overview of distributed data mining applications and algorithms for P2P environments. Next it discusses some of the privacy concerns with P2P data mining and points out the problems of existing privacy-preserving multi-party data mining techniques. It further points out that most of the nice assumptions of these existing privacy preserving techniques fall apart in real-life applications of privacy-preserving distributed data mining (PPDM). The paper offers a more realistic formulation of the PPDM problem as a multi-party game and points out some recent results.

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What cannot be computed locally!

Cited by 227 publications

References 19 publications

Deterministic Dominating Set Construction in Networks with Bounded Degree

Deterministic Dominating Set Construction in Networks with Bounded Degree

Virtual Backbone Construction in MANETs Using Adjustable Transmission Ranges

Peer-to-Peer Data Mining, Privacy Issues, and Games

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