Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound

Kunde, Manfred

doi:10.1007/3-540-57273-2_62

Cited by 47 publications

(40 citation statements)

References 14 publications

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“…Since each neighborhood is chosen according to an i.i.d. distribution, the probability that the crowding factor in the central squarelet is larger than We used the inequality in arriving at (11) and substituted the value of in arriving at (12). Choosing and in (12), we conclude that Number of nodes in any fixed squarelet As before, using a simple union bound we have Using the Borel-Cantelli lemma, we conclude that, almost surely, the crowding factor is no more than .…”

Section: Proposition 42mentioning

confidence: 89%

A deterministic approach to throughput scaling in wireless networks

Kulkarni¹,

Viswanath²

Proceedings IEEE International Symposium on Information Theory,

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Abstract-We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second.We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the log throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.

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Section: Proposition 42mentioning

confidence: 89%

A deterministic approach to throughput scaling in wireless networks

Kulkarni¹,

Viswanath²

Proceedings IEEE International Symposium on Information Theory,

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“…Our analysis on Scheme 1 mainly relies on some well-known results about two-dimensional (2-D) arrays [28], [29], which have been extensively studied in the parallel and distributed computing research community. Therefore, we first review some related definitions and results.…”

Section: B Performance Analysis Of Schemementioning

confidence: 99%

“…Lemma 2: ( [28] and [29]) -routing on arrays can be performed deterministically in time slots, with average packet delay . We now point out the correspondence between Scheme 1 and the optimal communication scheme for the 2-D array.…”

Section: B Performance Analysis Of Schemementioning

confidence: 99%

On the Price of Security in Large-Scale Wireless Ad Hoc Networks

Zhang

Song

Fang

et al. 2011

IEEE/ACM Trans. Networking

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Abstract-Security always comes with a price in terms of performance degradation, which should be carefully quantified. This is especially the case for wireless ad hoc networks (WANETs), which offer communications over a shared wireless channel without any preexisting infrastructure. Forming end-to-end secure paths in such WANETs is more challenging than in conventional networks due to the lack of central authorities, and its impact on network performance is largely untouched in the literature. In this paper, based on a general random network model, the asymptotic behaviors of secure throughput and delay with the common transmission range and the probability of neighboring nodes having a primary security association are quantified when the network size is sufficiently large. The costs and benefits of secure-link-augmentation operations on the secure throughput and delay are also analyzed. In general, security has a cost: Since we require all the communications operate on secure links, there is a degradation in the network performance when 1. However, one important exception is that when is (1 log ), the secure throughput remains at the Gupta and Kumar bound of 2(1 log ) packets/time slot, wherein no security requirements are enforced on WANETs. This implies that even when the goes to zero as the network size becomes arbitrarily large, it is still possible to build throughput-order-optimal secure WANETs, which is of practical interest since is very small in many practical large-scale WANETs.Index Terms-Ad hoc networks, network performance, network security, wireless networks.

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“…Let each processor be a source and destination of exactly h packets. The problem of routing the hl 2 packets to their destinations is known as h × h permutation routing and can be characterized by the following result [19].…”

Section: Theorem 44mentioning

confidence: 99%

Optimal scaling of multicommodity flows in wireless ad hoc networks: Beyond the Gupta-Kumar barrier

Karande

Wang

Sadjadpour

et al. 2008

2008 5th IEEE International Conference on Mobile Ad Hoc and Sensor Systems

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Abstract-We establish a tight max-flow min-cut theorem for multi-commodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-capacity scale as Θ(n 2 r 3 (n)/k) for a random choice of k ≥ Θ(n) sourcedestination pairs, where r(n) is the communication range in the network. We exploit the fact that the MCF in a random geometric graph equals the capacity of an ad-hoc network under the protocol model and interference-free communication to derive scaling laws for interference-constrained network capacity. We generalize all existing results reported to date by showing that the per-commodity capacity of the network scales as Θ(1/r(n)k) for the single-packet reception model suggested by Gupta and Kumar, and as Θ(nr(n)/k) for the multiple-packet reception model suggested by others. More importantly, we show that, if the nodes in the network are capable of multiple-packet transmission and reception, then it is feasible to achieve the optimal scaling of Θ`n 2 r 3 (n)/k´, despite the presence of interference. This result provides an improvement of Θ`nr 2 (n)´over the highest achieved capacity reported to date. In stark contrast to the conventional wisdom that has evolved from the Gupta-Kumar results, our results show that the capacity of ad-hoc networks can actually increase with n while the communication range tends to zero!

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Block gossiping on grids and tori: Deterministic sorting and routing match the bisection bound

Cited by 47 publications

References 14 publications

A deterministic approach to throughput scaling in wireless networks

A deterministic approach to throughput scaling in wireless networks

On the Price of Security in Large-Scale Wireless Ad Hoc Networks

Optimal scaling of multicommodity flows in wireless ad hoc networks: Beyond the Gupta-Kumar barrier

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