555 research outputs found
Simplicial Homology for Future Cellular Networks
Simplicial homology is a tool that provides a mathematical way to compute the
connectivity and the coverage of a cellular network without any node location
information. In this article, we use simplicial homology in order to not only
compute the topology of a cellular network, but also to discover the clusters
of nodes still with no location information. We propose three algorithms for
the management of future cellular networks. The first one is a frequency
auto-planning algorithm for the self-configuration of future cellular networks.
It aims at minimizing the number of planned frequencies while maximizing the
usage of each one. Then, our energy conservation algorithm falls into the
self-optimization feature of future cellular networks. It optimizes the energy
consumption of the cellular network during off-peak hours while taking into
account both coverage and user traffic. Finally, we present and discuss the
performance of a disaster recovery algorithm using determinantal point
processes to patch coverage holes
Computing the -coverage of a wireless network
Coverage is one of the main quality of service of a wirelessnetwork.
-coverage, that is to be covered simultaneously by network nodes, is
synonym of reliability and numerous applicationssuch as multiple site MIMO
features, or handovers. We introduce here anew algorithm for computing the
-coverage of a wirelessnetwork. Our method is based on the observation that
-coverage canbe interpreted as layers of -coverage, or simply
coverage. Weuse simplicial homology to compute the network's topology and
areduction algorithm to indentify the layers of -coverage. Weprovide figures
and simulation results to illustrate our algorithm.Comment: Valuetools 2019, Mar 2019, Palma de Mallorca, Spain. 2019. arXiv
admin note: text overlap with arXiv:1802.0844
Homology-based Distributed Coverage Hole Detection in Wireless Sensor Networks
Homology theory provides new and powerful solutions to address the coverage
problems in wireless sensor networks (WSNs). They are based on algebraic
objects, such as Cech complex and Rips complex. Cech complex gives accurate
information about coverage quality but requires a precise knowledge of the
relative locations of nodes. This assumption is rather strong and hard to
implement in practical deployments. Rips complex provides an approximation of
Cech complex. It is easier to build and does not require any knowledge of nodes
location. This simplicity is at the expense of accuracy. Rips complex can not
always detect all coverage holes. It is then necessary to evaluate its
accuracy. This work proposes to use the proportion of the area of undiscovered
coverage holes as performance criteria. Investigations show that it depends on
the ratio between communication and sensing radii of a sensor. Closed-form
expressions for lower and upper bounds of the accuracy are also derived. For
those coverage holes which can be discovered by Rips complex, a homology-based
distributed algorithm is proposed to detect them. Simulation results are
consistent with the proposed analytical lower bound, with a maximum difference
of 0.5%. Upper bound performance depends on the ratio of communication and
sensing radii. Simulations also show that the algorithm can localize about 99%
coverage holes in about 99% cases
Distributed Coverage Verification in Sensor Networks Without Location Information
In this paper, we present three distributed algorithms for coverage verification in sensor networks with no location information. We demonstrate how, in the absence of localization devices, simplicial complexes and tools from algebraic topology can be used in providing valuable information about the properties of the cover. Our approach is based on computation of homologies of the Rips complex corresponding to the sensor network. First, we present a decentralized scheme based on Laplacian flows to compute a generator of the first homology, which represents coverage holes. Then, we formulate the problem of localizing coverage holes as an optimization problem for computing a sparse generator of the first homology. Furthermore, we show that one can detect redundancies in the sensor network by finding a sparse generator of the second homology of the cover relative to its boundary. We demonstrate how subgradient methods can be used in solving these optimization problems in a distributed manner. Finally, we provide simulations that illustrate the performance of our algorithms
Efficient Algorithms for Distributed Detection of Holes and Boundaries in Wireless Networks
We propose two novel algorithms for distributed and location-free boundary
recognition in wireless sensor networks. Both approaches enable a node to
decide autonomously whether it is a boundary node, based solely on connectivity
information of a small neighborhood. This makes our algorithms highly
applicable for dynamic networks where nodes can move or become inoperative.
We compare our algorithms qualitatively and quantitatively with several
previous approaches. In extensive simulations, we consider various models and
scenarios. Although our algorithms use less information than most other
approaches, they produce significantly better results. They are very robust
against variations in node degree and do not rely on simplified assumptions of
the communication model. Moreover, they are much easier to implement on real
sensor nodes than most existing approaches.Comment: extended version of accepted submission to SEA 201
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