Topološki model za brezžična senzorska omrežja : diplomsko delo

Terzer, Jan (author), Mramor Kosta, Nežka (mentor)

Senzorji so naprave za pridobivanje informacij iz okolja. Da pokrijemo večjo površino zaznavanja, jih razporedimo po željeni domeni in med seboj povežemo v senzorsko omrežje. Postavi se vprašanje ali senzorji pokrivajo celotno površino domene, oz. ali obstaja območje znotraj domene, ki ga senzorji ne dosežejo. Taka območja imenujemo luknje. V brezžičnem senzorskem omrežju s senzorji, ki se lahko premikajo, poznamo samo njihovo medsebojno povezanost, ne pa tudi položaja. Pokritost območja lahko v takšnih primerih ugotovimo s topološkimi metodami, tako da iz podatkov o povezanosti senzorjev zgradimo Ripsov kompleks in izračunamo njegove homološke grupe oziroma Bettijeva števila. V diplomski nalogi je predstavljen simulator za generiranje senzorskih omrežij in za izračun števila lukenj v domeni pokritosti na podlagi izračuna prvega Bettijevega števila ustreznega Ripsovega kompleksa.

• Language: Slovenian
• Keywords: Bettijeva števila, homološke grupe, Ripsov kompleks, simplicialni kompleks, brezžična senzorska omrežja, območje pokritosti
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: [J. Terzer]
• Year: 2016
• Number of pages: 26, 3 str.
• PID: 20.500.12556/RUL-80207
• COBISS.SI-ID: 1536792771
• Publication date in RUL: 12.02.2016

Licences

• License: CC BY-SA 2.5 SI, Creative Commons Attribution-ShareAlike 2.5 Slovenia
• Link: https://creativecommons.org/licenses/by-sa/2.5/si/deed.en
• Description: You are free to reproduce and redistribute the material in any medium or format. You are free to remix, transform, and build upon the material for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.

Secondary language

• Language: English
• Title: A topological model for wireless sensor networks

Abstract

Sensors are devices for extracting information from the environment. In order to cover a larger area of detection, they are spread across the desired domain and connected in a sensor network. The question arises whether the sensors cover the entire area of domain or in other words whether there is an area within the domain that sensors do not detect. An area such as this is called a hole. In wireless non-stationary sensor networks the location of the individual sensors is not known, only information on which sensors are connected is available. The coverage of the domain of such a sensor network can be determined using topological methods. Using information on connectivity between the sensors we build the Rips complex and compute its homology groups and Betti numbers. The thesis presents a simulator for generating sensor networks and calculating the number of holes in it by computing the first Betti number of the corresponding Rips complex.

• Keywords: Betti numbers, homology groups, Rips complex, simplicial complex, wireless sensor networks, domain coverage