76,582 research outputs found
The Radio Number of Grid Graphs
The radio number problem uses a graph-theoretical model to simulate optimal
frequency assignments on wireless networks. A radio labeling of a connected
graph is a function such that for every pair
of vertices , we have where denotes the diameter of and
the distance between vertices and . Let be the
difference between the greatest label and least label assigned to . Then,
the \textit{radio number} of a graph is defined as the minimum
value of over all radio labelings of . So far, there have
been few results on the radio number of the grid graph: In 2009 Calles and
Gomez gave an upper and lower bound for square grids, and in 2008 Flores and
Lewis were unable to completely determine the radio number of the ladder graph
(a 2 by grid). In this paper, we completely determine the radio number of
the grid graph for , characterizing three subcases of the
problem and providing a closed-form solution to each. These results have
implications in the optimization of radio frequency assignment in wireless
networks such as cell towers and environmental sensors.Comment: 17 pages, 7 figure
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
Information Gathering in Ad-Hoc Radio Networks with Tree Topology
We study the problem of information gathering in ad-hoc radio networks
without collision detection, focussing on the case when the network forms a
tree, with edges directed towards the root. Initially, each node has a piece of
information that we refer to as a rumor. Our goal is to design protocols that
deliver all rumors to the root of the tree as quickly as possible. The protocol
must complete this task within its allotted time even though the actual tree
topology is unknown when the computation starts. In the deterministic case,
assuming that the nodes are labeled with small integers, we give an O(n)-time
protocol that uses unbounded messages, and an O(n log n)-time protocol using
bounded messages, where any message can include only one rumor. We also
consider fire-and-forward protocols, in which a node can only transmit its own
rumor or the rumor received in the previous step. We give a deterministic
fire-and- forward protocol with running time O(n^1.5), and we show that it is
asymptotically optimal. We then study randomized algorithms where the nodes are
not labelled. In this model, we give an O(n log n)-time protocol and we prove
that this bound is asymptotically optimal
Message Passing in C-RAN: Joint User Activity and Signal Detection
In cloud radio access network (C-RAN), remote radio heads (RRHs) and users
are uniformly distributed in a large area such that the channel matrix can be
considered as sparse. Based on this phenomenon, RRHs only need to detect the
relatively strong signals from nearby users and ignore the weak signals from
far users, which is helpful to develop low-complexity detection algorithms
without causing much performance loss. However, before detection, RRHs require
to obtain the realtime user activity information by the dynamic grant
procedure, which causes the enormous latency. To address this issue, in this
paper, we consider a grant-free C-RAN system and propose a low-complexity
Bernoulli-Gaussian message passing (BGMP) algorithm based on the sparsified
channel, which jointly detects the user activity and signal. Since active users
are assumed to transmit Gaussian signals at any time, the user activity can be
regarded as a Bernoulli variable and the signals from all users obey a
Bernoulli-Gaussian distribution. In the BGMP, the detection functions for
signals are designed with respect to the Bernoulli-Gaussian variable. Numerical
results demonstrate the robustness and effectivity of the BGMP. That is, for
different sparsified channels, the BGMP can approach the mean-square error
(MSE) of the genie-aided sparse minimum mean-square error (GA-SMMSE) which
exactly knows the user activity information. Meanwhile, the fast convergence
and strong recovery capability for user activity of the BGMP are also verified.Comment: Conference, 6 pages, 7 figures, accepted by IEEE Globecom 201
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