Ad hoc networks beyond unit disk graphs

Kühn, Fabian; Wattenhofer, Roger; Zollinger, Aaron

doi:10.1007/s11276-007-0045-6

Cited by 177 publications

(145 citation statements)

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“…This simple model of connectivity for a sensor or communications network is widely used [13,20,30] and widely disparaged [3,8,18]. Our results hold in the context of more general flag complexes associated to network communication graphs, whether they are unit disc graphs or not.…”

Section: Simplicial Complexes For Networkmentioning

confidence: 55%

Distributed computation of coverage in sensor networks by homological methods

Dłotko

Ghrist

Juda

et al. 2012

AAECC

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Recent work on algebraic-topological methods for verifying coverage in planar sensor networks relied exclusively on centralized computation: a limiting constraint for large networks. This paper presents a distributed algorithm for homology computation over a sensor network, for purposes of verifying coverage. The techniques involve reduction and coreduction of simplicial complexes, and are of independent interest. Verification of the ensuing algorithms is proved, and simulations detail the improved network efficiency and performance.

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Section: Simplicial Complexes For Networkmentioning

confidence: 55%

Distributed computation of coverage in sensor networks by homological methods

Dłotko

Ghrist

Juda

et al. 2012

AAECC

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“…Yet, recent works [14,24] support the conjecture that the same asymptotic result on the value of k holds also in a cost-based connection model, which is shown in [24] to closely resemble lognormal shadowing propagation (i.e., irregular coverage regions).…”

Section: Setting the Value Of Kmentioning

confidence: 74%

Self Organization and Self Maintenance of Mobile Ad Hoc Networks through Dynamic Topology Control

Blough

Resta

Santi

et al. 2010

Architecting Dependable Systems VII

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Abstract.One way in which wireless nodes can organize themselves into an ad hoc network is to execute a topology control protocol, which is designed to build a network satisfying specific properties. A number of basic topology control protocols exist and have been extensively analyzed. Unfortunately, most of these protocols are designed primarily for static networks and the protocol designers simply advise that the protocols should be repeated periodically to deal with failures, mobility, and other sources of dynamism. However, continuously maintaining a network topology with basic connectivity properties is a fundamental requirement for overall network dependability. Current approaches consider failures only as an afterthought or take a static fault tolerance approach, which results in extremely high energy usage and low throughput. In addition, most of the existing topology control protocols assume that transmission power is a continuous variable and, therefore, nodes can choose an arbitrary power value between some minimum and maximum powers. However, wireless network interfaces with dynamic transmission power control permit the power to be set to one of a discrete number of possible values. This simple restriction complicates the design of the topology control protocol substantially. In this paper, we present a set of topology control protocols, which work with discrete power levels and for which we specify a version that deals specifically with dynamic networks that experience failures, mobility, and other dynamic conditions. Our protocols are also novel in the sense that they are the first to consider explicit coordination between neighboring nodes, which results in more efficient power settings. In this chapter, we present the design of these topology control protocols, and we report on extensive simulations to evaluate them and compare their performance against existing protocols. The results demonstrate that our protocols produce very similar topologies as the best protocols that assume power is a continuous variable, while having very low communication cost and seamlessly handling failures and mobility.

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“…For example, the quasi unit disk graph model (QUDG) [3,4] is a generalization of the UDG that takes imperfections into account as they may arise from non-omnidirectional antennas or small obstacles. These QUDGs are related to so-called civilized graphs.…”

Section: Model 422 (General Graph (Gg))mentioning

confidence: 99%

“…Interestingly, many algorithms can be transferred from the UDG to the QUDG at an additional cost of 1/ρ 2 [4]. Note that while for ρ ≈ .5 this factor is bearable, the algorithms are two orders of magnitude worse if ρ ≈ .1.…”

Section: Model 424 (Qudg Variations)mentioning

confidence: 99%

“…We have to prove that the total number of independent nodes in B u (r) grows polynomially in r. Observe that, due to the triangle inequality, in B u (1/2) there is at most one independent node. Thus, by the definition of a doubling metric, there are at most c independent nodes in B u (1), at most c 2 in B u (2), c 3 in B u (4), and so on. Generally, there are at most c log r+1 independent nodes in B u (r).…”

Section: Theorem 426 a Ubg Is A Bigmentioning

confidence: 99%

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