scholarly journals Memory and communication efficient algorithm for decentralized counting of nodes in networks

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0259736
Author(s):  
Arindam Saha ◽  
James A. R. Marshall ◽  
Andreagiovanni Reina
Keyword(s):  
Distributed Algorithm ◽  
Time Complexity ◽  
World Systems ◽  
Size Estimation ◽  
Distributed Sensor Networks ◽  
Average Case ◽  
Distributed Sensor ◽  
Deterministic Algorithms ◽  
Graph Size ◽  
Aggregation Of Information

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.

scholarly journals Clique Size in Sensor Networks with Key Pre-Distribution Based on Transversal Design

2005 ◽  
Vol 1 (3-4) ◽  
pp. 345-354 ◽  
Author(s):  
Dibyendu Chakrabarti ◽  
Subhamoy Maitra ◽  
Bimal Roy
Keyword(s):  
Sensor Networks ◽  
Distributed Computing ◽  
Secure Communication ◽  
Sensor Nodes ◽  
Transversal Design ◽  
Secret Key ◽  
Distributed Sensor Networks ◽  
Distributed Sensor

Key pre-distribution is an important area of research in Distributed Sensor Networks (DSN). Two sensor nodes are considered connected for secure communication if they share one or more common secret key(s). It is important to analyse the largest subset of nodes in a DSN where each node is connected to every other node in that subset (i.e., the largest clique). This parameter (largest clique size) is important in terms of resiliency and capability towards efficient distributed computing in a DSN. In this paper, we concentrate on the schemes where the key pre-distribution strategies are based on transversal design and study the largest clique sizes. We show that merging of blocks to construct a node provides larger clique sizes than considering a block itself as a node in a transversal design.

ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

1995 ◽  
Vol 05 (02) ◽  
pp. 275-280 ◽  
Author(s):  
BEATE BOLLIG ◽  
MARTIN HÜHNE ◽  
STEFAN PÖLT ◽  
PETR SAVICKÝ
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Time Complexity ◽  
Upper And Lower Bounds ◽  
Average Case ◽  
Asymptotically Optimal ◽  
Circuit Delay ◽  
Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

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