3,431 research outputs found
Virtual backbone formation in wireless ad hoc networks
We study the problem of virtual backbone formation in wireless ad hoc networks. A virtual backbone provides a hierarchical infrastructure that can be used to address important challenges in ad hoc networking such as efficient routing, multicasting/broadcasting, activity-scheduling, and energy efficiency. Given a wireless ad hoc network with symmetric links represented by a unit disk graph G = (V, E ), one way to construct this backbone is by finding a Connected Dominating Set (CDS) in G , which is a subset V' ✹ V such that for every node u, u is either in V' or has a neighbor in V' and the subgraph induced by V' is connected. In a wireless ad hoc network with asymmetric links represented by a directed graph G = (V, E ), finding such a backbone translates to constructing a Strongly Connected Dominating and Absorbent Set (SCDAS) in G . An SCDAS is a subset of nodes V' ✹ V such that every node u is either in V' or has an outgoing and an incoming neighbor in V' , and the subgraph induced by V' is strongly connected. Based on most of its applications, minimizing the size of the virtual backbone is an important objective. Therefore, we are interested in constructing CDSs and SCDASs of minimal size. We give efficient distributed algorithms with linear time and message complexities for the construction of the CDS in ad hoc networks with symmetric links. Since topology changes are quite frequent in most ad hoc networks, we propose schemes to locally maintain the CDS in the face of such changes. We also give a distributed algorithm for the construction of the SCDAS in ad hoc networks with asymmetric links. Extensive simulations show that our algorithms outperform all previously known algorithms in terms of the size of the constructed sets
Message and time efficient multi-broadcast schemes
We consider message and time efficient broadcasting and multi-broadcasting in
wireless ad-hoc networks, where a subset of nodes, each with a unique rumor,
wish to broadcast their rumors to all destinations while minimizing the total
number of transmissions and total time until all rumors arrive to their
destination. Under centralized settings, we introduce a novel approximation
algorithm that provides almost optimal results with respect to the number of
transmissions and total time, separately. Later on, we show how to efficiently
implement this algorithm under distributed settings, where the nodes have only
local information about their surroundings. In addition, we show multiple
approximation techniques based on the network collision detection capabilities
and explain how to calibrate the algorithms' parameters to produce optimal
results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459
Approximating Minimum Independent Dominating Sets in Wireless Networks
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+")- pproximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint
In the problem of minimum connected dominating set with routing cost
constraint, we are given a graph , and the goal is to find the
smallest connected dominating set of such that, for any two
non-adjacent vertices and in , the number of internal nodes on the
shortest path between and in the subgraph of induced by is at most times that in . For general graphs, the only
known previous approximability result is an -approximation algorithm
() for by Ding et al. For any constant , we
give an -approximation
algorithm. When , we give an -approximation
algorithm. Finally, we prove that, when , unless , for any constant , the problem admits no
polynomial-time -approximation algorithm, improving
upon the bound by Du et al. (albeit under a stronger hardness
assumption)
- …