Minimum-Energy Broadcast and disk cover in grid wireless networks

Calamoneri, Tiziana; Clementi, Andrea E. F.; Ianni, Miriam Di; Lauria, Massimo; Monti, Angelo; Silvestri, Riccardo

doi:10.1016/j.tcs.2008.02.005

Cited by 9 publications

(6 citation statements)

References 26 publications

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“…We remind that, while the energy cost of cell-alg is an upper bound on the work complexity of our distributed procedure Broadcast, the energy cost of the MST-based solution does not provide any information about the work complexity of its distributed implementations (this can be much larger). 4 Notice that, for the tested sizes n, this range is smaller than the threshold 2 √ 2c √ log n defined in Section 4: this is the reason why the feasibility rate is not 100% for large n. Table 1 shows, for all chosen values of p and √ n, the minimum, average and maximum ratio between the costs of the solutions returned by the two algorithms. As for cell-alg, only the costs of feasible solutions are considered.…”

Section: Resultsmentioning

confidence: 93%

“…Its present best version works in Θ(n 5 ) time and the design of any efficient distributed version seems to be a very hard task. It is important to observe that the MST-based heuristic is "far" from achieving optimal solutions even on a complete square grid of n points [4,17]: its worst-case approximation ratio on such grids is not smaller than 3. In [17], it is also experimentally observed that this heuristic has a bad behavior when applied to random regular instances such as faulty square grids.…”

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

“…Our algorithmic solution works in O(n log n) time and needs a set Γ of logarithmic size (in n). The range assignment is inspired to the one provided in [4] for complete square grids (i.e. every point of the grid is a node of the network).…”

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

“…every point of the grid is a node of the network). However, the probabilistic cost analysis of our construction for random grids is definitely not related to that in [4].…”

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

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Minimum-energy broadcast in random-grid ad-hoc networks

Calamoneri¹,

Clementi²,

Monti³

et al. 2008

Proceedings of the 11th International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems

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The Min Energy Broadcast problem consists in assigning transmission ranges to the nodes of an ad-hoc network in order to guarantee a directed spanning tree from a given source node and, at the same time, to minimize the energy consumption (i.e. the energy cost) yielded by the range assignment. Min Energy Broadcast is known to be NP-hard. We consider random-grid networks where nodes are chosen independently at random from the n points of a √ n × √ n square grid in the plane. The probability of the existence of a node at a given point of the grid does depend on that point, that is, the probability distribution can be non-uniform. By using information-theoretic arguments, we prove a lower bound (1 − ) n π on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than 1.1204 n π . Finally, we present a fully-distributed protocol that constructs a broadcast range assignment of energy cost not larger than 8n, thus still yielding constant approximation. The energy load is well balanced and, at the same time, the work complexity (i.e. the energy due to all message transmissions of the protocol) is asymptotically optimal. The completion time of the protocol is only a O(log n) factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least 1 − 1/n Θ(1) .

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Section: Resultsmentioning

confidence: 93%

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

“…every point of the grid is a node of the network). However, the probabilistic cost analysis of our construction for random grids is definitely not related to that in [4].…”

Section: Range Assignments In Ad-hoc Networkmentioning

confidence: 99%

See 2 more Smart Citations

Minimum-energy broadcast in random-grid ad-hoc networks

Calamoneri¹,

Clementi²,

Monti³

et al. 2008

Proceedings of the 11th International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore the MSTbased range assignment is unique. In [42,43] it is shown that even for 2-D networks with special topologies, i.e., when the nodes are located at the intersection points of a square grid, the MST-based range assignment is far from optimal. It is worth mentioning that the MST-based range assignment is the optimal solution for the minimum-energy broadcasting problem in wired networks.…”

Section: Previous Work 21 Energy-efficient Broadcastingmentioning

confidence: 99%

Analysis of Wireless Multi-Hop Broadcasting: Optimal and Approximate Solutions and Applications

Naeini¹

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In this work, we design and analyze transmission range assignments for broadcasting in wireless multi-hop networks. Moreover, we study different features of wireless networks. We consider network scenarios in which the exact location of the nodes is known and others where the nodes location is known probabilistically. For the former, we propose optimal and near-optimal algorithms to solve the Minimum-Energy Broadcasting problem for linear (one-dimensional) networks. We further extend our solutions to encompass cross networks, in which the nodes are located on two perpendicular lines. The proposed algorithms have polynomial-time complexity, and are shown to perform better than previously known algorithms (for some cases, they are the first polynomial-time solutions). For probabilistic networks, we propose a transmission range assignment such that for a given average total consumed power, the linear network is connected with high probability. We then analyze some features of these networks, including derivation of exact formulas for the probability of connectivity of any location of the network to the source, the hop-count probability mass function (pmf) of an arbitrary location of the network, and the pdf of the maximum coverage (last reachable distance from the source) for a given number of hops. The proposed analyses are applicable to networks with non-identical transmission range assignments, where the nodes are placed independently and identically according to a Poisson distribution with an arbitrary density function. Based on the derived formulas, we then propose localization and location verification methods. We show that our proposed localization method not only has a competitive performance for a range-free method, but also outperforms range-based methods with a local distance measurement error of 10% or more. Furthermore, the proposed location verification protocol is shown to have better results compared to the existing verification systems that also use the hop-count information. We also evaluate the proposed schemes in the presence of Rician fading and show that their performance is rather robust with respect to the change in the fading parameter.

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Minimum Energy Broadcast on Rectangular Grid Wireless Networks

Murata

Matsubayashi

2010

Algorithms for Sensor Systems

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The minimum energy broadcast problem is to assign a transmission range to each node in an ad hoc wireless network to construct a spanning tree rooted at a given source node such that any non-root node resides within the transmission range of its parent. The objective is to minimize the total energy consumption, i.e., the sum of the δth powers of a transmission range (δ ≥ 1). In this paper, we consider the case that δ = 2, and that nodes are located on a 2-dimensional rectangular grid. We prove that the minimum energy consumption for an n-node k × l-grid with n = kl and k ≤ l is at most

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Minimum-Energy Broadcast and disk cover in grid wireless networks

Cited by 9 publications

References 26 publications

Minimum-energy broadcast in random-grid ad-hoc networks

Minimum-energy broadcast in random-grid ad-hoc networks

Analysis of Wireless Multi-Hop Broadcasting: Optimal and Approximate Solutions and Applications

Minimum Energy Broadcast on Rectangular Grid Wireless Networks

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