8,568 research outputs found

    Relating broadcast independence and independence

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    An independent broadcast on a connected graph GG is a function f:V(G)→N0f:V(G)\to \mathbb{N}_0 such that, for every vertex xx of GG, the value f(x)f(x) is at most the eccentricity of xx in GG, and f(x)>0f(x)>0 implies that f(y)=0f(y)=0 for every vertex yy of GG within distance at most f(x)f(x) from xx. The broadcast independence number αb(G)\alpha_b(G) of GG is the largest weight ∑x∈V(G)f(x)\sum\limits_{x\in V(G)}f(x) of an independent broadcast ff on GG. Clearly, αb(G)\alpha_b(G) is at least the independence number α(G)\alpha(G) for every connected graph GG. Our main result implies αb(G)≀4α(G)\alpha_b(G)\leq 4\alpha(G). We prove a tight inequality and characterize all extremal graphs

    Distributed Deterministic Broadcasting in Uniform-Power Ad Hoc Wireless Networks

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    Development of many futuristic technologies, such as MANET, VANET, iThings, nano-devices, depend on efficient distributed communication protocols in multi-hop ad hoc networks. A vast majority of research in this area focus on design heuristic protocols, and analyze their performance by simulations on networks generated randomly or obtained in practical measurements of some (usually small-size) wireless networks. %some library. Moreover, they often assume access to truly random sources, which is often not reasonable in case of wireless devices. In this work we use a formal framework to study the problem of broadcasting and its time complexity in any two dimensional Euclidean wireless network with uniform transmission powers. For the analysis, we consider two popular models of ad hoc networks based on the Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links, and the other with randomly disturbed SINR. In the former model, we show that one of our algorithms accomplishes broadcasting in O(Dlog⁥2n)O(D\log^2 n) rounds, where nn is the number of nodes and DD is the diameter of the network. If nodes know a priori the granularity gg of the network, i.e., the inverse of the maximum transmission range over the minimum distance between any two stations, a modification of this algorithm accomplishes broadcasting in O(Dlog⁥g)O(D\log g) rounds. Finally, we modify both algorithms to make them efficient in the latter model with randomly disturbed SINR, with only logarithmic growth of performance. Ours are the first provably efficient and well-scalable, under the two models, distributed deterministic solutions for the broadcast task.Comment: arXiv admin note: substantial text overlap with arXiv:1207.673

    Data Dissemination in Unified Dynamic Wireless Networks

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    We give efficient algorithms for the fundamental problems of Broadcast and Local Broadcast in dynamic wireless networks. We propose a general model of communication which captures and includes both fading models (like SINR) and graph-based models (such as quasi unit disc graphs, bounded-independence graphs, and protocol model). The only requirement is that the nodes can be embedded in a bounded growth quasi-metric, which is the weakest condition known to ensure distributed operability. Both the nodes and the links of the network are dynamic: nodes can come and go, while the signal strength on links can go up or down. The results improve some of the known bounds even in the static setting, including an optimal algorithm for local broadcasting in the SINR model, which is additionally uniform (independent of network size). An essential component is a procedure for balancing contention, which has potentially wide applicability. The results illustrate the importance of carrier sensing, a stock feature of wireless nodes today, which we encapsulate in primitives to better explore its uses and usefulness.Comment: 28 pages, 2 figure

    The Homogeneous Broadcast Problem in Narrow and Wide Strips

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    Let PP be a set of nodes in a wireless network, where each node is modeled as a point in the plane, and let s∈Ps\in P be a given source node. Each node pp can transmit information to all other nodes within unit distance, provided pp is activated. The (homogeneous) broadcast problem is to activate a minimum number of nodes such that in the resulting directed communication graph, the source ss can reach any other node. We study the complexity of the regular and the hop-bounded version of the problem (in the latter, ss must be able to reach every node within a specified number of hops), with the restriction that all points lie inside a strip of width ww. We almost completely characterize the complexity of both the regular and the hop-bounded versions as a function of the strip width ww.Comment: 50 pages, WADS 2017 submissio

    Network correlated data gathering with explicit communication: NP-completeness and algorithms

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    We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal
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