0000000000124499
AUTHOR
Zbigniew Lipinski
showing 10 related works from this author
Maximum Lifetime of the Wireless Sensor Network and the Gossip Problem
2018
In the gossip problem each node of the graph G possesses a unique piece of information - the gossip message. A sequence of one-way or two-way communications between pair of nodes is made to spread the messages so that any node of the graph knows all the gossips. The question is, what is the minimum number of calls between pairs of nodes needed to exchange all gossip messages? The solution to the two-way communication gossip problem is that \(2N-4\) calls (\(N\ge 4\)) suffice if and only if the graph contains a four cycle subgraph. For one-way communication problem the classical results states that in a strongly connected graph \(2N-2\) calls (\(N\ge 4\)) suffice. In this paper we consider t…
Classification of Solutions to the Minimum Energy Problem in One Dimensional Sensor Networks
2016
We classify of the minimum energy problem in one dimensional wireless sensor networks for the data transmission cost matrix which is a power function of the distance between transmitter and receiver with any real exponent. We show, how these solutions can be utilized to solve the minimum energy problem for the data transmission cost matrix which is a linear combination of two power functions. We define the minimum energy problem in terms of the sensors signal power, transmission time and capacities of transmission channels. We prove, that for the point-to-point data transmission method utilized by the sensors in the physical layer, when the transmitter adjust the power of its radio signal t…
Maximum Lifetime Problem in Sensor Networks with Limited Channel Capacity
2016
We analyze the maximum lifetime problem in sensor networks with limited channel capacity for multipoint-to-multipoint and broadcast data transmission services. For the transmission model in which the transmitter adjust the power of its radio signal to the distance to the receiver we propose a new Signal to Interference plus Noise Ratio function and use it to modify the Shannon-Hartley channel capacity formula. We show, that in order to achieve an optimal data transmission regarding considered the maximum lifetime problem we cannot allow for any interference of signals. For considered transmission model and the modified capacity formula we solve the maximum lifetime problem in one dimensiona…
UML-Based Reliability Modeling of Network Services, a UDP Echo Service Case Study
2009
In the paper, we discuss state space reliability modeling formalism of distributed systems and services compliant with UML metamodel. Behavior of modeled application system we describe in terms of states. Service generation process we represent as a sequence of application system states. State space approach allows us to define dependence between application system components via dependence between components states and states input, output parameters. Reliability of application system component we define for each simply action state. Reliability of a service we express by components reliability in states determined by service generation process. As an example, we analyze reliability of cli…
Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks
2017
A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…
On the role of symmetry in solving maximum lifetime problem in two-dimensional sensor networks
2016
We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group $G$ can be utilized to simplify its solution. We prove, that for a $G$-invariant maximum lifetime problem there exists a $G$-invariant solution. Constrains which follow from the $G$-invariance allow to reduce the problem and its solution to a subset, an optimal fundamental region of the sensor network. We analyze in detail solutions of the maximum lifetime problem invariant under a group of isometry transformations of a two dimensional Euclidean plane.
Routing Algorithm for Maximizing Lifetime of Wireless Sensor Network for Broadcast Transmission
2018
In the article we discuss solutions of the maximum lifetime broadcasting problem in wireless sensor networks. Due to limited energy resources of the network nodes to find an optimal transmission route of the broadcasted data we minimize the maximum energy consumed by the nodes. We give an analytical solution of the problem in one dimensional regular sensor network for the point-to-point and point-to-multipoint data transmission scheme. We show that in such a network, when the cost of data transmission is a polynomial function of distance between transmitter and receiver, there exist solutions with an equal energy, i.e., all nodes of the network consume the same amount of energy. We assume t…
Symmetric and asymmetric cryptographic key exchange protocols in the octonion algebra
2019
AbstractWe propose three cryptographic key exchange protocols in the octonion algebra. Using the totient function, defined for integral octonions, we generalize the RSA public-key cryptosystem to the octonion arithmetics. The two proposed symmetric cryptographic key exchange protocols are based on the automorphism and the derivation of the octonion algebra.
Stability Analysis of Routing Strategies for the Maximum Lifetime Problem in One-Dimensional Ad-Hoc Wireless Networks
2017
In the paper we discuss solutions of the maximum network lifetime problem in one-dimensional, regular ad-hoc wireless networks. For the problem, nodes of the network generate given amount of data and send it possibly via other nodes to the data collector. To extend the network lifetime the data should be transmitted in such a way, that the energy utilized by the most overloaded node is minimized. We assume, that the nodes use the point-to-point data transmission scheme and the cost of transmission of one unit of data is arbitrary superadditive function of a distance between transmitter and receiver. We show that for the one-dimensional network in which the nodes are evenly distributed on th…
State Model of Service Reliability
2006
We propose a simple formalism for modelling of a service reliability. A service is defined as an ordered set of states of a modelled application. In the model, a certain reliability is assigned to each application state. Reliability of a service is expressed in terms of above partial reliabilities.