{'fraction_non_alphanumeric': 0.024096385542168676, 'fraction_numerical': 0.011121408711770158, 'mean_word_length': 5.352941176470588, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Degree Constrained Topology Control for Very Dense Wireless Sensor Networks

We present a novel topology control algorithm for very dense wireless sensor networks that is constrained by a small maximum nodal degree k. Particularly, we limit k=4 which makes it challenging to formulate a connected network that possesses favorable properties such as a small diameter, short average path length and low energy consumption. Towards this goal, we introduce a graph theoretic approach that utilizes a Borel Cayley Graph as an underlying network topology. We call this approach Borel Cayley Graph Topology Control (BCG-TC). Simulation results for a network with 1081 nodes distributed over a 100m×100m area showed that BCG-TC can formulate connected networks for the radio range exceeding certain threshold. Furthermore, these connected networks generated by BCG-TC exhibit (i) a small nodal degree k≤4, (ii) a small diameter and short average path length, and (iii) fast information dissemination that leads to the least energy consumption among considered topology control protocols.