Energy-Efficient Broadcasting in All-Wireless Networks

In all-wireless networks, minimizing energy consumption is crucial as in most cases the nodes are battery-operated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of radio transmissions can be exploited to optimize energy consumption. This problem appears to be difficult to solve [30]. We provide a formal proof of NP-completeness for the general case and give an NP-completeness result for the geometric case; in the former, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. For the general case, we show that it cannot be approximated better than O(log N), where N is the total number of nodes. We then describe an approximation algorithm that achieves the O(log N) approximation ratio. We also describe a new heuristic, Embedded Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distribute

Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms

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 $\sqrt n \times \sqrt n$ 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 $(1-\epsilon) \frac n{\pi}$ on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than $1.1204 \frac n{\pi}$. 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 an $O(\log n)$ factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least $1-1/n^{\Theta(1)}$.Comment: 13 pages, 3 figures, 1 tabl

Minimum Energy Broadcast and Disk Cover in Grid Wireless Networks

Abstract. The Minimum Energy Broadcast problem consists in finding the minimum-energy range assignment for a given set S of n stations of an ad hoc wireless network that allows a source station to perform broadcast operations over S. We prove a nearly tight asymptotical bound on the optimal cost for the Minimum Energy Broadcast problem on square grids. We emphasize that finding tight bounds for this problem restriction is far to be easy: it involves the Gauss’s Circle problem and the Apollonian Circle Packing. We also derive near-tight bounds for the Bounded-Hop version of this problem. Our results imply that the best-known heuristic, the MST-based one, for the Minimum Energy Broadcast problem is far to achieve optimal solutions (even) on very regular, well-spread instances: its worst-case approximation ratio is about pi and it yields Ω( n) hops. As a by product, we get nearly tight bounds for the Minimum Disk Cover problem and for its restriction in which the allowed disks must have non-constant radius. Finally, we emphasize that our upper bounds are obtained via polynomial time constructions.

Power assignment problems in wireless communication

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; for example one problem studied before in (Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) and (Helmut Alt et al.: Minimum-cost coverage of point sets by disks, SCG 2006) aims to select and assign powers to $k$ of the stations such that all other stations are within reach of at least one of the selected stations. We improve the running time for obtaining a $(1+\epsilon)$-approximate solution for this problem from $n^{((\alpha/\epsilon)^{O(d)})}$ as reported by Bil{\`o} et al. (see Vittorio Bil{\`o} et al: Geometric Clustering to Minimize the Sum of Cluster Sizes, ESA 2005) to $O\left( n+ {\left(\frac{k^{2d+1}}{\epsilon^d}\right)}^{ \min{\{\; 2k,\;\; (\alpha/\epsilon)^{O(d)} \;\}} } \right)$ that is, we obtain a running time that is \emph{linear} in the network size. Further results include a constant approximation algorithm for the TSP problem under squared (non-metric!) edge costs, which can be employed to implement a novel data aggregation protocol, as well as efficient schemes to perform $k$-hop multicasts

Minimum-energy broadcast in all-wireless networks: NP-Completeness and distribution issues

In all-wireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are battery-operated. We focus on the problem of power-optimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consumption. Several authors have conjectured that the problem of power-optimal broadcast is NP-complete. We provide here a formal proof, both for the general case and for the geometric one; in the former case, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. We then describe a new heuristic, Embedding Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distributed