3,431 research outputs found

    Virtual backbone formation in wireless ad hoc networks

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    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

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    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

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    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

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    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

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    In the problem of minimum connected dominating set with routing cost constraint, we are given a graph G=(V,E)G=(V,E), and the goal is to find the smallest connected dominating set DD of GG such that, for any two non-adjacent vertices uu and vv in GG, the number of internal nodes on the shortest path between uu and vv in the subgraph of GG induced by D{u,v}D \cup \{u,v\} is at most α\alpha times that in GG. For general graphs, the only known previous approximability result is an O(logn)O(\log n)-approximation algorithm (n=Vn=|V|) for α=1\alpha = 1 by Ding et al. For any constant α>1\alpha > 1, we give an O(n11α(logn)1α)O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})-approximation algorithm. When α5\alpha \geq 5, we give an O(nlogn)O(\sqrt{n}\log n)-approximation algorithm. Finally, we prove that, when α=2\alpha =2, unless NPDTIME(npolylogn)NP \subseteq DTIME(n^{poly\log n}), for any constant ϵ>0\epsilon > 0, the problem admits no polynomial-time 2log1ϵn2^{\log^{1-\epsilon}n}-approximation algorithm, improving upon the Ω(logn)\Omega(\log n) bound by Du et al. (albeit under a stronger hardness assumption)
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