Power Spanner Research Articles

Local Construction of Near-Optimal Power Spanners for Wireless Ad Hoc Networks

We present a local distributed algorithm that, given a wireless ad hoc network modeled as a unit disk graph U in the plane, constructs a planar power spanner of U whose degree is bounded by k and whose stretch factor is bounded by 1 + (2sin pi/k)p, where k ges 10 is an integer parameter and p isin [2, 5] is the power exponent constant. For the same degree bound k, the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of 1 + (2sin pi/k+1)p is unattainable for the same degree bound k. In contrast to previous algorithms for the problem, the presented algorithm is local. As a consequence, the algorithm is highly scalable and robust. Finally, while the algorithm is efficient and easy to implement in practice, it relies on deep insights on the geometry of unit disk graphs and novel techniques that are of independent interest.

An Energy-Efficient Distributed Topology-Control Algorithm for Ad Hoc Networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. The primary goal of topology control is to design power-efficient algorithms that maintain network connectivity and optimize performance metrics such as nodes lifetime and throughput. An energy-efficient distributed topology-control algorithm is proposed, briefly called VCGG (A varying-cone distributed topology-control algorithm on Gabriel graph). Using a new mechanism of selecting the logic neighbor nodes by firstly deleting the farthest node (FDFN), the VCGG algorithm builds a degree-bounded, power spanner and planar subgraph by making use of merit of the varying cone. The simulation results show that the VCGG algorithm performs better, in terms of power efficiency, number of communication neighbors and interference, than the existing SΘGG and SYaoGG algorithms.

Geometric spanners with applications in wireless networks

In this paper we investigate the relations between spanners, weak spanners, and power spanners in R D for any dimension D and apply our results to topology control in wireless networks. For c ∈ R , a c- spanner is a subgraph of the complete Euclidean graph satisfying the condition that between any two vertices there exists a path of length at most c-times their Euclidean distance. Based on this ability to approximate the complete Euclidean graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks. In a weak c-spanner, this path may be arbitrarily long, but must remain within a disk or sphere of radius c-times the Euclidean distance between the vertices. Finally in a c- power spanner, the total energy consumed on such a path, where the energy is given by the sum of the squares of the edge lengths on this path, must be at most c-times the square of the Euclidean distance of the direct edge or communication link. While it is known that any c-spanner is also both a weak C 1 -spanner and a C 2 -power spanner for appropriate C 1 , C 2 depending only on c but not on the graph under consideration, we show that the converse is not true: there exists a family of c 1 -power spanners that are not weak C-spanners and also a family of weak c 2 -spanners that are not C-spanners for any fixed C. However a main result of this paper reveals that any weak c-spanner is also a C-power spanner for an appropriate constant C. We further generalize the latter notion by considering ( c , δ ) -power spanners where the sum of the δth powers of the lengths has to be bounded; so ( c , 2 )-power spanners coincide with the usual power spanners and ( c , 1 )-power spanners are classical spanners. Interestingly, these ( c , δ )-power spanners form a strict hierarchy where the above results still hold for any δ ⩾ D some even hold for δ > 1 while counter-examples exist for δ < D . We show that every self-similar curve of fractal dimension D f > δ is not a ( C , δ ) -power spanner for any fixed C, in general. Finally, we consider the sparsified Yao-graph (SparsY-graph or YY) that is a well-known sparse topology for wireless networks. We prove that all SparsY-graphs are weak c-spanners for a constant c and hence they allow us to approximate energy-optimal wireless networks by a constant factor.

Efficient Topology Control for Ad-Hoc Wireless Networks with Non-Uniform Transmission Ranges

Wireless network topology control has drawn considerable attention recently. Priori arts assumed that the wireless ad hoc networks are modeled by unit disk graphs (UDG), i.e., two mobile hosts can communicate as long as their Euclidean distance is no more than a threshold. However, practically, the networks are never so perfect as unit disk graphs: the transmission ranges may vary due to various reasons such as the device differences, the network control necessity, and the perturbation of the transmission ranges even the transmission ranges are set as the same originally. Thus, we assume that each mobile host has its own transmission range. The networks are modeled by mutual inclusion graphs (MG), where two nodes are connected iff they are within the transmission range of each other. Previously, no method is known for topology control when the networks are modeled as mutual inclusion graphs.The paper proposes the first distributed mechanism to build a sparse power efficient network topology for ad hoc wireless networks with non-uniform transmission ranges. We first extend the Yao structure to build a spanner with a constant length and power stretch factor for mutual inclusion graph. We then propose two efficient localized algorithms to construct connected sparse network topologies. The first structure, called extended Yao-Yao, has node degree at most O(log γ), where γ = maxu maxuv∈MG ru/rv. The second structure, called extended Yao and Sink, has node degree bounded by O(log γ), and is a length and power spanner. The methods are based on a novel partition strategy of the space surrounded each mobile host. Both algorithms have communication cost O(n) under a local broadcasting communication model, where each message has O(log n) bits.