Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks

Ambühl, Christoph; Clementi, Andrea E. F.; Ianni, Miriam Di; Lev-Tov, Nissan; Monti, Angelo; Peleg, David; Rossi, Gianluca Del; Silvestri, Riccardo

doi:10.1007/978-3-540-24749-4_37

Cited by 27 publications

(27 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…There has also been work on restricted broadcast operations more in the spirit of the k-hop multicast problem we consider in this paper. 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%

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

View full text Add to dashboard Cite

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].

show abstract

Section: Related Workmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…P l is the single cluster containing X and every point forms one separate cluster in P 0 . 1 We refer to clusters of P i as clusters at level i. A hierarchical decomposition where each cluster of the same level i is contained in a ball of radius r i , contains a ball of radius α·r i , and r i−1 ≤ β ·r i for constants α and β < 1 is called a hierarchical fat decomposition (HFD).…”

Section: Hierarchical Fat Decompositions (Hfd)mentioning

confidence: 99%

“…each point forms a separate cluster. Obviously, each cluster is contained in a ball of radius 1 and contains a ball of radius 1 2 . Starting from the lowest level we construct the next level recursively as follows.…”

Section: Hierarchical Fat Decompositions (Hfd)mentioning

confidence: 99%

“…Interestingly, the size of this 'problem sketch' only depends on k and the desired approximation quality (1 + ǫ) but is independent of n. Hence we can approximate the bounded-hop broadcast problem -even using a brute force algorithm -in time linear in n and only doubly exponential in k (in contrast to the result in [1] which is triply exponential in k where it is also an exponent of n).…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

Funke

Laue

Stacs 2007

View full text Add to dashboard Cite

Abstract. We consider the problem of assigning powers to nodes of a wireless network in the plane such that a message from a source node s reaches all other nodes within a bounded number k of transmissions and the total amount of assigned energy is minimized. By showing the existence of a coreset of size O(`1 ǫ´4 k ) we are able to (1 + ǫ)-approximate the bounded-hop broadcast problem in time linear in n which is a drastic improvement upon the previously best known algorithm. While actual network deployments often are in a planar setting, the experienced metric for several reasons is typically not exactly of the Euclidean type, but in some sense 'close'. Our algorithm (and others) also work for non-Euclidean metrics provided they exhibit a certain similarity to the Euclidean metric which is known in the literature as bounded doubling dimension. We give a novel characterization of such metrics also pointing out other applications such as space-efficient routing schemes.

show abstract

“…There has also been work on more restricted broadcast operations in the spirit of k-SEMBC. In [2] the authors consider 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 h. They show how to compute an optimal h-hop broadcast range assignment for h = 2 in time O(n 7 ). For h > 2 they show how to obtain…”

Section: Related Workmentioning

confidence: 99%

Minimum-Energy Broadcast with Few Senders

Funke¹,

Laue²,

Naujoks³

Distributed Computing in Sensor Systems

View full text Add to dashboard Cite

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.

show abstract

Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks

Cited by 27 publications

References 9 publications

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

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

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

Minimum-Energy Broadcast with Few Senders

Contact Info

Product

Resources

About