Energy-efficient algorithms

Energy-aware multicasting in wireless ad hoc networks: A survey and discussion

Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.

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An optimal bound for the MST algorithm to compute energy efficient broadcast trees in wireless networks

We propose a novel communication efficient topology control algorithm for each wireless node to select communication neighbors and adjust its transmission power, such that all nodes together self-form a topology that is energy efficient simultaneously for both unicast and broadcast communications. We prove that the proposed topology is planar, which guarantees packet delivery if a certain localized routing method is used; it is power efficient for unicast-- the energy needed to connect any pair of nodes is within a small constant factor of the minimum under a common power attenuation model; it is efficient for broadcast: the energy consumption for broadcasting data on top of it is asymptotically the best compared with structures constructed locally; it has a constant bounded logical degree, which will potentially reduce interference and signal contention. We further prove that the average physical degree of all nodes is bounded by a small constant. To the best of our knowledge, this is the first communication-efficient distributed algorithm to achieve all these properties. Previously, only a centralized algorithm was reported in [3]. Moreover, by assuming that the ID and position of every node can be represented in O(log n) bits for a wireless network of n nodes, our method uses at most 13n messages, where each message is of O(log n) bits. We also show that this structure can be efficiently updated for dynamical network environment. Our theoretical results are corroborated in the simulations.

/pdf/a-unified-energy-efficient-topology-for-unicast-and-2xjcgmfvvs.pdf

A unified energy-efficient topology for unicast and broadcast

We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method. Finally, we exhibit a total function with a quadratic gap between quantum query complexity and certificate complexity, which is optimal (up to log factors). These separations are shown using a new, general technique that we call the cheat sheet technique, which builds upon the techniques of Ambainis et al. [STOC 2016]. The technique is based on a generic transformation that converts any (possibly partial) function into a new total function with desirable properties for showing separations. The framework also allows many known separations, including some recent breakthrough results of Ambainis et al. [STOC 2016], to be shown in a unified manner.

https://dl.acm.org/doi/pdf/10.1145/2897518.2897644

Separations in query complexity using cheat sheets

In this paper we present new results on the performance of the Minimum Spanning Tree heuristic for the Minimum-Energy Broadcast Routing (MEBR) problem. We first prove that, for any number of dimensions d ≥ 2, the approximation ratio of the heuristic does not increase when the power attenuation coefficient α, that is the exponent to which the coverage distance must be raised to give the emission power, grows. Moreover, we show that, as a limit for α going to infinity, the ratio tends to the lower bound of [3, 15] given by the d-dimensional kissing number, thus closing the existing gap between the upper and the lower bound. We then introduce a new analysis allowing to establish a 7.6-approximation ratio for the 2-dimensional case, thus signifcantly decreasing the previously known 12 upper bound [15] (actually corrected to 12.15 in [10]). Starting from the above results, such an approximation holds for any α ≥ 2. Finally, we extend our analysis to any number of dimensions d ≥ 2 and any α ≥ d, obtaining a general approximation ratio of 3d-1, independent of α. The improvements of the approximation ratios are specifically significant in comparison with the lower bounds given by the kissing numbers, as these grow at least exponentially with respect to d. Note that for α ‹ d the ratios cannot be bounded by any function of α and d [3].

Improved approximation results for the minimum energy broadcasting problem

In this paper we present a new heuristic called Adaptive Broadcast Consumption (ABC for short) for the Minimum-Energy Broadcast Routing (MEBR) problem. We first investigate the problem trying to understand which are the main properties not taken into account by the classic and well-studied MST and BIP heuristics, then we propose a new algorithm proving that it computes the MEBR with an approximation ratio less than or equal to MST, for which we prove an approximation ratio of at most 12.15 instead of the well-known 12 [10]. Finally we present experimental results supporting our intuitive ideas, comparing ABC with other heuristics presented in the literature and showing its good performance on random instances even compared to the optimum.

Adaptive Broadcast Consumption (ABC), a new heuristic and new bounds for the Minimum Energy Broadcast Routing Problem

In this paper we dene and study a call scheduling problem that is motivated by radio networks. In such networks the physical space is a common resource that nodes have to share, since concurrent transmissions cannot be interfering. We study how one can satisfy steady bandwidth demands according to this constraint. This leads to the denition of a call scheduling problem. We show that it can be relaxed into a simpler problem: The call weighting problem, which is almost a usual multi-commodity o w problem, but the capacity constraints are replaced by the much more complex notion of non interference. Not surprisingly this notion involve independent sets, and we prove that the complexity of the call weighting problem is strongly related to the one of the independent set problem and its variants (maxweight, coloring, fractional coloring). The hardness of approximation follows when the interferences are described by an arbitrary graph. We rene our study by considering some particular cases for which ecien t polynomial algorithm can be provided: the Gathering in which all the demand are directed toward the same sink, and specic interference relations: namely those induced by the dimension 1 and 2 Euclidean space, those cases are likely to be the practical ones.

https://hal.inria.fr/inria-00070575/document

On the Complexity of Bandwidth Allocation in Radio Networks with Steady Traffic Demands

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Adaptive Broadcast Consumption (ABC), a New Heuristic and New Bounds for the Minimum Energy Broadcast Routing Problem

https://hal.archives-ouvertes.fr/hal-00530172/document

Ralf Klasing

Papers

Improved approximation results for the minimum energy broadcasting problem

Adaptive Broadcast Consumption (ABC), a new heuristic and new bounds for the Minimum Energy Broadcast Routing Problem

On the Complexity of Bandwidth Allocation in Radio Networks with Steady Traffic Demands

Adaptive Broadcast Consumption (ABC), a New Heuristic and New Bounds for the Minimum Energy Broadcast Routing Problem

On the size of identifying codes in triangle-free graphs