2,016 research outputs found
Complexity of increasing the secure connectivity in wireless ad hoc networks
We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the post-deployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing a secret key using only the links that are already secured by shared keys. This problem is in NP-hard and does not accept polynomial time approximation scheme PTAS since minimum cutsets to be augmented do not admit constant costs. The second one extends the first problem by increasing the power level between a pair of nodes that has a secret key to enable them physically connect. This problem can be formulated as the optimal key establishment problem with interference constraints with bi-objectives: (i) maximizing the concurrent key establishment flow, (ii) minimizing the cost. We prove that both problems are NP-hard and MAX-SNP with a reduction to MAX3SAT problem
A Constant-Factor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model
In modern wireless networks, devices are able to set the power for each
transmission carried out. Experimental but also theoretical results indicate
that such power control can improve the network capacity significantly. We
study this problem in the physical interference model using SINR constraints.
In the SINR capacity maximization problem, we are given n pairs of senders
and receivers, located in a metric space (usually a so-called fading metric).
The algorithm shall select a subset of these pairs and choose a power level for
each of them with the objective of maximizing the number of simultaneous
communications. This is, the selected pairs have to satisfy the SINR
constraints with respect to the chosen powers.
We present the first algorithm achieving a constant-factor approximation in
fading metrics. The best previous results depend on further network parameters
such as the ratio of the maximum and the minimum distance between a sender and
its receiver. Expressed only in terms of n, they are (trivial) Omega(n)
approximations.
Our algorithm still achieves an O(log n) approximation if we only assume to
have a general metric space rather than a fading metric. Furthermore, by using
standard techniques the algorithm can also be used in single-hop and multi-hop
scheduling scenarios. Here, we also get polylog(n) approximations.Comment: 17 page
A note on uniform power connectivity in the SINR model
In this paper we study the connectivity problem for wireless networks under
the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio
transmitters distributed in some area, we seek to build a directed strongly
connected communication graph, and compute an edge coloring of this graph such
that the transmitter-receiver pairs in each color class can communicate
simultaneously. Depending on the interference model, more or less colors,
corresponding to the number of frequencies or time slots, are necessary. We
consider the SINR model that compares the received power of a signal at a
receiver to the sum of the strength of other signals plus ambient noise . The
strength of a signal is assumed to fade polynomially with the distance from the
sender, depending on the so-called path-loss exponent .
We show that, when all transmitters use the same power, the number of colors
needed is constant in one-dimensional grids if as well as in
two-dimensional grids if . For smaller path-loss exponents and
two-dimensional grids we prove upper and lower bounds in the order of
and for and
for respectively. If nodes are distributed
uniformly at random on the interval , a \emph{regular} coloring of
colors guarantees connectivity, while colors are required for any coloring.Comment: 13 page
Topology Control for Maintaining Network Connectivity and Maximizing Network Capacity Under the Physical Model
In this paper we study the issue of topology control under the physical Signal-to-Interference-Noise-Ratio (SINR) model, with the objective of maximizing network capacity. We show that existing graph-model-based topology control captures interference inadequately under the physical SINR model, and as a result, the interference in the topology thus induced is high and the network capacity attained is low. Towards bridging this gap, we propose a centralized approach, called Spatial Reuse Maximizer (MaxSR), that combines a power control algorithm T4P with a topology control algorithm P4T. T4P optimizes the assignment of transmit power given a fixed topology, where by optimality we mean that the transmit power is so assigned that it minimizes the average interference degree (defined as the number of interferencing nodes that may interfere with the on-going transmission on a link) in the topology. P4T, on the other hand, constructs, based on the power assignment made in T4P, a new topology by deriving a spanning tree that gives the minimal interference degree. By alternately invoking the two algorithms, the power assignment quickly converges to an operational point that maximizes the network capacity. We formally prove the convergence of MaxSR. We also show via simulation that the topology induced by MaxSR outperforms that derived from existing topology control algorithms by 50%-110% in terms of maximizing the network capacity
Algorithms for Fast Aggregated Convergecast in Sensor Networks
Fast and periodic collection of aggregated data
is of considerable interest for mission-critical and continuous
monitoring applications in sensor networks. In the many-to-one
communication paradigm, referred to as convergecast, we focus
on applications wherein data packets are aggregated at each hop
en-route to the sink along a tree-based routing topology, and
address the problem of minimizing the convergecast schedule
length by utilizing multiple frequency channels. The primary
hindrance in minimizing the schedule length is the presence of
interfering links. We prove that it is NP-complete to determine
whether all the interfering links in an arbitrary network can
be removed using at most a constant number of frequencies.
We give a sufficient condition on the number of frequencies for
which all the interfering links can be removed, and propose a
polynomial time algorithm that minimizes the schedule length
in this case. We also prove that minimizing the schedule length
for a given number of frequencies on an arbitrary network is
NP-complete, and describe a greedy scheme that gives a constant
factor approximation on unit disk graphs. When the routing tree
is not given as an input to the problem, we prove that a constant
factor approximation is still achievable for degree-bounded trees.
Finally, we evaluate our algorithms through simulations and
compare their performance under different network parameters
Benchmarking Practical RRM Algorithms for D2D Communications in LTE Advanced
Device-to-device (D2D) communication integrated into cellular networks is a
means to take advantage of the proximity of devices and allow for reusing
cellular resources and thereby to increase the user bitrates and the system
capacity. However, when D2D (in the 3rd Generation Partnership Project also
called Long Term Evolution (LTE) Direct) communication in cellular spectrum is
supported, there is a need to revisit and modify the existing radio resource
management (RRM) and power control (PC) techniques to realize the potential of
the proximity and reuse gains and to limit the interference at the cellular
layer. In this paper, we examine the performance of the flexible LTE PC tool
box and benchmark it against a utility optimal iterative scheme. We find that
the open loop PC scheme of LTE performs well for cellular users both in terms
of the used transmit power levels and the achieved
signal-to-interference-and-noise-ratio (SINR) distribution. However, the
performance of the D2D users as well as the overall system throughput can be
boosted by the utility optimal scheme, because the utility maximizing scheme
takes better advantage of both the proximity and the reuse gains. Therefore, in
this paper we propose a hybrid PC scheme, in which cellular users employ the
open loop path compensation method of LTE, while D2D users use the utility
optimizing distributed PC scheme. In order to protect the cellular layer, the
hybrid scheme allows for limiting the interference caused by the D2D layer at
the cost of having a small impact on the performance of the D2D layer. To
ensure feasibility, we limit the number of iterations to a practically feasible
level. We make the point that the hybrid scheme is not only near optimal, but
it also allows for a distributed implementation for the D2D users, while
preserving the LTE PC scheme for the cellular users.Comment: 30 pages, submitted for review April-2013. See also: G. Fodor, M.
Johansson, D. P. Demia, B. Marco, and A. Abrardo, A joint power control and
resource allocation algorithm for D2D communications, KTH, Automatic Control,
Tech. Rep., 2012, qC 20120910,
http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10205
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