Bounded-Hop Energy-Efficient Broadcast in Low-Dimensional Metrics Via Coresets

Funke, Stefan; Laue, Sören

doi:10.1007/978-3-540-70918-3_24

Cited by 13 publications

(8 citation statements)

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“…In [7] the authors obtain bicriteria approximation algorithms for connectivity and broadcast while minimizing the hop-diameter and energy consumption. Funke and Laue [18] provide a PTAS for the h-broadcast algorithm in time linear in n. Elkin et al [16] proposed the solution for the broadcast tree construction (which is easily deformable into the data collection tree) such that the total energy consumption and transport are of factor ρ from optimal bound (which is proportional to the weight of minimal spanning tree for the set of nodes where the weight of edge is defined as the squared Euclidean distance between the nodes) and the hopdiameter is n/ρ + log ρ, for any chosen integer parameter ρ, 1 ≤ ρ ≤ n. Additional results for bounded range assignments can be found in [11,13,41].…”

Section: Related Workmentioning

confidence: 98%

Using central nodes for efficient data collection in wireless sensor networks

2015

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Section: Related Workmentioning

confidence: 98%

Using central nodes for efficient data collection in wireless sensor networks

2015

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“…In [3] the authors examine a bounded-hop broadcast operation where the resulting communication graph has to contain a spanning tree rooted at the source node s of depth at most k. They show how to compute an optimal k-hop broadcast range assignment for k = 2 in time O(n 7 ). For k > 2 they show how to obtain a (1 + )-approximation in time O(n O(μ) ) where μ = (k 2 / ) 2 k , that is, their running time is triply exponential in the number of hops k and this shows up in the exponent of n. In [10], Funke and Laue show how to obtain a (1+ ) approximation for the k-hop broadcast problem in time doubly exponential in k based on a coreset which has size exponential in k, though.…”

Section: Related Workmentioning

confidence: 99%

“…Also based on the construction of a (different) coreset of small size, we show in Section 3 how to obtain a (1 + ) approximate solution to the k-hop multicast problem with respect to a constant-size set C of receivers/clients. Different from the solution for the k-hop broadcast problem presented in [10] we can exhibit a coreset of size polynomial in k, 1/ and r. The approach in [10] requires a coreset of size exponential in k.…”

Section: Our Contributionmentioning

confidence: 99%

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Power assignment problems in wireless communication: Covering points by disks, reaching few receivers quickly, and energy-efficient travelling salesman tours

Funke¹,

Laue²,

Zvi³

et al. 2011

Ad Hoc Networks

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Abstract.A fundamental class of problems in wireless communication is concerned with the assignment of suitable transmission powers to wireless devices/stations such that the resulting communication graph satisfies certain desired properties and the overall energy consumed is minimized. Many concrete communication tasks in a wireless network like broadcast, multicast, point-to-point routing, creation of a communication backbone, etc. can be regarded as such a power assignment problem.This paper considers several problems of that kind; the first problem was studied before in [1,6] and aims to select and assign powers to k out of a total of n wireless network stations such that all stations are within reach of at least one of the selected stations. We show that the problem can be (1+ ) approximated by only looking at a small subset of the input,, i.e. independent of n and polynomial in k and 1/ . Here d denotes the dimension of the space where the wireless devices are distributed, so typically d ≤ 3 and α describes the relation between the Euclidean distance between two stations and the power consumption for establishing a wireless connection between them. Using this coreset we are able to improve considerably on the running time of n ((α/ ) O(d) ) for the algorithm by Bilo et al. at ESA'05 ([6]) actually obtaining a running time that is linear in n. Furthermore we sketch how outliers can be handled in our coreset construction. The second problem deals with the energy-efficient, bounded-hop multicast operation: Given a subset C out of a set of n stations and a designated source node s we want to assign powers to the stations such that every node in C is reached by a transmission from s within k hops. Again we show that a coreset of size independent of n and polynomial in k, |C|, 1/ exists, and use this to provide an algorithm which runs in time linear in n.The last problem deals with a variant of non-metric TSP problem where the edge costs are the squared Euclidean distances; this problem is motivated by data aggregation schemes in wireless sensor networks. We show that a good TSP tour under Euclidean edge costs can be very bad in the squared distance measure and provide a simple constant approximation algorithm, partly improving upon previous results in [5], [4].

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“…running time is triply exponential in the number of hops h and this shows up in the exponent of n. In [9] Funke and Laue show how to obtain a (1 + ) approximation for the h-hop broadcast problem in time doubly exponential in h. Their approach is also based on a synopsis of the network, but in contrast to this paper they require a synopsis S that has size exponential in h. We note that bounded-hop broadcasts address the issue of latency since a message will arrive at any network node after at most h intermediate stations, still the reliability and interference problems remain as potentially very many network nodes might actively participate in the broadcast. General surveys of algorithmic range assignment problems can be found in [5,16,12].…”

Section: Related Workmentioning

confidence: 99%

Minimum-Energy Broadcast with Few Senders

Funke¹,

Laue²,

Naujoks³

Distributed Computing in Sensor Systems

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Abstract. Broadcasting a message from a given source node to all other nodes is a fundamental task during the operation of a wireless network. In many application scenarios the network nodes have only a limited energy supply, hence minimizing the energy consumption of any communication task prolongs the lifetime of the network. During a broadcast operation using intermediate nodes to relay messages within the network might decrease the overall energy consumption since the cost of transmitting a message grows super-linearly with the distance. On the other hand using too many intermediate nodes during a broadcast operation increases both latency as well as the chances that some transmission could not properly received (e.g. due to interference).In this paper we consider a constrained broadcast operation, where a source node wants to send a message to all other nodes in the network but at most k nodes are allowed to participate actively, i.e. transmit the message. Restricting the number of transmitting nodes helps in reducing interference, latency and increasing reliability of the broadcast operation, of course at the cost of a slightly higher energy consumption. For the case of network nodes embedded in the Euclidean plane we provide a (1 + )-approximation algorithm which runs in time linear in n and polynomial in 1/ but with an exponential dependence on k. As an alternative we therefore also provide an O(1)-approximation whose running time is linear in n and polynomial in k. The existence of a (1 + )-approximation algorithm is in stark contrast to the unconstrained broadcast problem where even in the Euclidean plane no algorithm with approximation factor better than 6 is known so far.

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Bounded-Hop Energy-Efficient Broadcast in Low-Dimensional Metrics Via Coresets

Cited by 13 publications

References 7 publications

Using central nodes for efficient data collection in wireless sensor networks

Using central nodes for efficient data collection in wireless sensor networks

Power assignment problems in wireless communication: Covering points by disks, reaching few receivers quickly, and energy-efficient travelling salesman tours

Minimum-Energy Broadcast with Few Senders

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