Power Assignment Problems in Wireless Communication: Covering Points by Disks, Reaching few Receivers Quickly, and Energy-Efficient Travelling Salesman Tours

Funke, Stefan; Laue, Sören; Naujoks, Rouven; Lotker, Zvi

doi:10.1007/978-3-540-69170-9_19

Cited by 8 publications

(15 citation statements)

References 14 publications

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“…4. Can our findings about power assignments be generalized to other problems in wireless communication, such as the k-station network coverage problem of Funke, Laue, Lotker, and Naujoks [6], where transmit powers are assigned to at most k stations such that X can be reached from at least one sender, or power assignments in the SINR model [8,10]? Interestingly, in the SINR model the MST turns out to be a good solution to schedule all links within a short time [9,11].…”

Section: Conclusion and Open Problemsmentioning

confidence: 98%

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Probabilistic Analysis of Power Assignments

Graaf

Manthey

2014

Mathematical Foundations of Computer Science 2014

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A fundamental problem for wireless ad hoc networks is the assignment of suitable transmission powers to the wireless devices such that the resulting communication graph is connected. The goal is to minimize the total transmit power in order to maximize the lifetime of the network. Our aim is a probabilistic analysis of this power assignment problem. We prove complete convergence for arbitrary combinations of the dimension d and the distance-power gradient p. Furthermore, we prove that the expected approximation ratio of the simple spanning tree heuristic is strictly less than its worst-case ratio of 2. Our main technical novelties are twofold: First, we find a way to deal with the unbounded degree that the communication network induced by the optimal power assignment can have. Minimum spanning trees and traveling salesman tours, for which strong concentration results are known in Euclidean space, have bounded degree, which is heavily exploited in their analysis. Second, we apply a recent generalization of Azuma-Hoeffding's inequality to prove complete convergence for the case p ≥ d for both power assignments and minimum spanning trees (MSTs). As far as we are aware, complete convergence for p > d has not been proved yet for any Euclidean functional.

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Section: Conclusion and Open Problemsmentioning

confidence: 98%

“…The expected values of PT and MST differ by a factor of 2 − 2 −p + o (1). The approximation ratio is given by (6). The probability that numerator or denominator differ by more than a factor of 1 ± o(1) from their expected value is o (1).…”

Section: Improved Bound For the One-dimensional Casementioning

confidence: 99%

Probabilistic Analysis of Power Assignments

Graaf

Manthey

2014

Mathematical Foundations of Computer Science 2014

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show abstract

“…We refer to two surveys for an overview . ) Can our findings about power assignments be generalized to other problems in wireless communication, such as the k ‐station network coverage problem of Funke, Laue, Lotker, and Naujoks , where transmit powers are assigned to at most k stations such that X can be reached from at least one sender, or power assignments in the SINR model ? Interestingly, in the SINR model the MST turns out to be a good solution to schedule all links within a short time .…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Probabilistic analysis of power assignments

Graaf

Manthey

2017

Random Struct Algorithms

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ABSTRACT:A fundamental problem for wireless ad hoc networks is the assignment of suitable transmission powers to the wireless devices such that the resulting communication graph is connected. The goal is to minimize the total transmit power in order to maximize the life-time of the network. Our aim is a probabilistic analysis of this power assignment problem. We prove complete convergence for arbitrary combinations of the dimension d and the distance-power gradient p. Furthermore, we prove that the expected approximation ratio of the simple spanning tree heuristic is strictly less than its worst-case ratio of 2.Our main technical novelties are two-fold: First, we find a way to deal with the unbounded degree that the communication network induced by the optimal power assignment can have. Minimum spanning trees and traveling salesman tours, for which strong concentration results are known in Euclidean space, have bounded degree, which is heavily exploited in their analysis. Second, we apply a recent generalization of Azuma-Hoeffding's inequality to prove complete convergence for the case p ≥ d for both power assignments and minimum spanning trees (MSTs). As far as we are aware, complete convergence for p > d has not been proved yet for any Euclidean functional.

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“…Subsequently, we introduce a new algorithm based on Markovian approximation, called distributed BS selection algorithm. We refer to [2][3][4][5][6][7] for further reading as related literature to our work.…”

Section: Introductionmentioning

confidence: 99%

Energy-Efficient User Association in Broadcast Transmission

Hasan

Marina

2017

Static &Amp; Dynamic Game Theory: Foundations &Amp; Applications

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This paper addresses the user association problem in a multi-cell broadcast transmission. We seek minimal total energy consumption by considering both transmission power and operational power cost. We propose a novel distributed solution based on network utility games and using so-called Markovian approximation we design the distributed base station (BS) selection algorithm. Extensive simulation results are provided and highlight the relative performance of the algorithm.

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Power Assignment Problems in Wireless Communication: Covering Points by Disks, Reaching few Receivers Quickly, and Energy-Efficient Travelling Salesman Tours

Cited by 8 publications

References 14 publications

Probabilistic Analysis of Power Assignments

Probabilistic Analysis of Power Assignments

Probabilistic analysis of power assignments

Energy-Efficient User Association in Broadcast Transmission

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