Building a Coverage Hole-free Communication Tree

Wireless networks are present everywhere but their management can be tricky since their coverage may contain holes even if the network is fully connected. In this paper we propose an algorithm that can build a communication tree between nodes of a wireless network with guarantee that there is no coverage hole in the tree. We use simplicial homology to compute mathematically the coverage, and Prim's algorithm principle to build the communication tree. Some simulation results are given to study the performance of the algorithm and compare different metrics. In the end, we show that our algorithm can be used to create coverage hole-free communication groups with a limited number of hops.

[1]  Wei Chen,et al.  A Case Study on Regularity in Cellular Network Deployment , 2015, IEEE Wireless Communications Letters.

[2]  Gunnar E. Carlsson,et al.  Topological estimation using witness complexes , 2004, PBG.

[3]  Muhammad Ali Imran,et al.  A Survey of Self Organisation in Future Cellular Networks , 2013, IEEE Communications Surveys & Tutorials.

[4]  Philippe Martins,et al.  Accuracy of homology based approaches for coverage hole detection in wireless sensor networks , 2012, 2012 IEEE International Conference on Communications (ICC).

[5]  M. Mrozek,et al.  Homology Computation by Reduction of Chain Complexes , 1998 .

[6]  Abubakr Muhammad,et al.  Coverage and hole-detection in sensor networks via homology , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[7]  Christian Bonnet,et al.  Implementation and validation of Multimedia Broadcast Multicast Service for LTE/LTE-advanced in OpenAirInterface platform , 2013, 38th Annual IEEE Conference on Local Computer Networks - Workshops.

[8]  Philippe Martins,et al.  Simplicial Homology for Future Cellular Networks , 2015, IEEE Transactions on Mobile Computing.

[9]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[10]  Hugues Randriam,et al.  Simplicial Homology of Random Configurations , 2011, Advances in Applied Probability.

[11]  R. Ho.  Algebraic Topology , 2022 .

[12]  Philippe Martins,et al.  Homology-Based Distributed Coverage Hole Detection in Wireless Sensor Networks , 2013, IEEE/ACM Transactions on Networking.

[13]  Vin de Silva,et al.  Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology , 2006, Int. J. Robotics Res..

[14]  A. Jadbabaie,et al.  Decentralized Computation of Homology Groups in Networks by Gossip , 2007, 2007 American Control Conference.

[15]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[16]  Afra Zomorodian,et al.  Computing Persistent Homology , 2004, SCG '04.

[17]  Wuyang Zhou,et al.  The Ginibre Point Process as a Model for Wireless Networks With Repulsion , 2014, IEEE Transactions on Wireless Communications.