Nearly optimal bounds for distributed wireless scheduling in the SINR model

Halldórsson, Magnús M.; Mitra, Pradipta

doi:10.1007/s00446-014-0222-7

Cited by 32 publications

(37 citation statements)

References 24 publications

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“…This is particularly important for link scheduling problems. While a constant-approximation algorithms are known for the independent set problem in metric spaces, the best results known for the corresponding coloring or scheduling problem give only logarithmic approximations [10,9]. It is not known if it possible to do better.…”

Section: Bounds On Sparse Instancesmentioning

confidence: 95%

Vertex coloring edge-weighted digraphs

Bang‐Jensen

Halldórsson

2015

Information Processing Letters

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Section: Bounds On Sparse Instancesmentioning

confidence: 95%

Vertex coloring edge-weighted digraphs

Bang‐Jensen

Halldórsson

2015

Information Processing Letters

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“…Other related problems are usually more expensive in terms of time complexity, for instance, local broadcast [10], in which every node has to inform its neighbors about its rumor, was done in time O(∆polylog(n)), where ∆ is the local density of a network. Another related problem studied in the SINR model is link scheduling, where particular direct connections have to be done (see e.g., [11]); because of specific links to be realized, scheduling often depends on so called "affectance" of the set of links, which might be large with respect to n. In [22], throughput optimization was challenged in the presence of jamming. Our solutions of symmetry-breaking problem on the SINR channel are much faster than the above solutions to related problems, which yields complexity separation between these problems and the one considered in this work Related work.…”

Section: Previous Work On Classical Multiple Access Channelmentioning

confidence: 99%

The Cost of Synchronizing Multiple-Access Channels

Jurdziński

Stachowiak

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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Multiple access channel is a communication model in which many users, also called stations, could exchange information. Since it offers limited capacity, some information sent through it might be lost due to signal interference (collision). Therefore, successful message delivery to a station requires breaking symmetry on the channel. In this work we consider the channel-synchronization problem on non-synchronized channels: assuming stations with messages wake-up dynamically on the channel, what is the minimum (expected) time needed for all stations to receive at least one message each.Historically, the first considered "classical" channel assu med that whenever two or more stations transmit simultaneously, the transmitted information is lost, otherwise it is delivered to all stations. In the seminal paper, Kushilevitz and Mansour [19] proved that the first successful transmission on the channel with n contending stations may require, in the worst case, Ω(log n) expected communication rounds for any protocol. The result, however, holds under assumption that all contenders start their protocols at the same round. We prove that in more general scenario, in which the stations may have different local clocks and start the protocol at arbitrary times, the lower bound increases quadratically to Ω(log 2 n) expected rounds. Both lower bounds are matched by corresponding algorithms developed in previous papers. Therefore, our lower bound proves the polynomial impact of synchronization on the classical multiple-access channels.Recently, more accurate channels based on Signal to Interference and Noise Ratio (SINR) were proposed and studied. The advantage of the SINR-based channel is that, apart of being closer to realistic physical scenario, some more demanding communication patterns could be scheduled in a single round. We support this intuition by showing that on such channel delivery of a message could be done faster than on the classical channel, mainly, in O(log 2 n/ log log n) expected number of rounds, thus separating the classical channel model from the SINR one. (The same time bound also holds with high probability.)Finally, we prove that for deterministic protocols receiving a message on the SINR channel requires time Ω(n), which surprisingly drops nearly exponentially to O(log 2 n) if the stations have access to the global clock, which also separates SINR channel from the classic one, due to the lower bound Ω(n log n) on the latter. We also match the latter bound by corresponding lower bound. This together with our O(log 2 / log log n) round randomized algorithm, also proves a gap between deterministic and randomized solutions to the synchronization problem.

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“…The algorithmic research on communication in the SINR networks started around 10 years ago. Most papers concentrate on one-hop communication, which includes the local broadcast problem [9,11,22], link scheduling [18,10], connectivity [2,12] and others. Among them, the most related to this work are papers on local broadcast, in which each node has to transmit a message only to its neighbors in the corresponding communication graph.…”

Section: Previous and Related Workmentioning

confidence: 99%

On the impact of geometry on ad hoc communication in wireless networks

Jurdziński

Kowalski

Różański

et al. 2014

Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing

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In this work we address the question how important is the knowledge of geometric location and network density to the efficiency of (distributed) wireless communication in ad hoc networks. We study fundamental communication task of broadcast and develop well-scalable, randomized algorithms that do not rely on GPS information, and which efficiency formulas do not depend on how dense the geometric network is. We consider two settings: with and without spontaneous wake-up of nodes. In the former setting, in which all nodes start the protocol at the same time, our algorithm accomplishes broadcast in O(D log n + log 2 n) rounds under the SINR model, with high probability (whp), where D is the diameter of the communication graph and n is the number of stations. In the latter setting, in which only the source node containing the original message is active in the beginning, we develop a slightly slower algorithm working in O(D log 2 n) rounds whp. Both algorithms are based on a novel distributed coloring method, which is of independent interest and potential applicability to other communication tasks under the SINR wireless model.

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Nearly optimal bounds for distributed wireless scheduling in the SINR model

Cited by 32 publications

References 24 publications

Vertex coloring edge-weighted digraphs

Vertex coloring edge-weighted digraphs

The Cost of Synchronizing Multiple-Access Channels

On the impact of geometry on ad hoc communication in wireless networks

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