Rangiranje z upoštevanjem negativnih povezav : delo diplomskega seminarja

Raspet, Matevž (author), Košir, Tomaž (mentor)

Naslov mojega dela pri predmetu Diplomski seminar je bil Rangiranje z upoštevanjem negativnih povezav. Namen seminarske naloge je bil predstaviti delovanje PageRank algoritma in razširiti njegov nacin delovanja na PageTrust algoritem, algoritem, ki pri rangiranju spletnih strani upošteva tudi negativne povezave. PageRank algoritem velja za enega izmed osnovnih algoritmov delovanja Googlovega spletnega brskalnika. Na Googlovi spletni strani je bilo napisano, da je PageRank algoritem srce njihove programske opreme. Algoritem sta leta 1998 izumila danes zelo znana Larry Page in Sergey Brin. V prvem delu seminarske naloge sem najprej opisal delovanje PageRank algoritma, utemeljeno s teorijo, definicijami ter dokazi potrebnimi za razumevanje delovanja algoritma. Opisal sem probleme, ki se pojavljajo pri algoritmu in njihove najboljše rešitve, na koncu prvega dela diplomske naloge pa sem za lažje razumevanje celotni PageRank algoritem predstavil še na preprostem primeru. V drugem delu seminarske naloge sem delovanje PageRank algoritma razširil na delovanje algoritma PageTrust, katerega sem prav tako utemeljil s potrebnimi definicijami, trditvami in dokazi ter na koncu vse skupaj povzel še na preprostih primerih. Bralec te seminarske naloge se mora zavedati, da sta algoritma v današnjih casih obstoja spletnih brskalnikov zelo pomembna, tako da prihaja do vsakdanjih optimizacij delovanja in izboljšav obeh algoritmov.

• Language: Slovenian
• Keywords: usmerjeni grafi, potenčna metoda, markovske verige, naključni sprehod, konvergenca potenčne metode, stohastične matrike, ireducibilna matrika, Perron-Frobeniusov izrek
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-109344
• UDC: 519.2
• COBISS.SI-ID: 18710873
• Publication date in RUL: 30.08.2019

Secondary language

• Language: English
• Title: How to rank web pages when negative links are allowed?

Abstract

The title of my work of the Diplomski Seminar course was How to rank web pages when negative links are allowed? The purpose of my work was to explain to the readers how PageRank algorithm works and how its expansion to PageTrust algorithm is implemented. PageTrust algorithm is an algorithm, which includes negative links during the computation of ranking vector. PageRank algorithm is regarded to be as one of the basic algorithms for Google’s search machine. Google’s engineers present it as a heart of Google’s software. PageRank algorithm was invented by Larry Page and Sergey Brin in 1998. In the first part of my diploma I wrote how PageRank algorithm works. I described theorems and definitions required for understanding the background of algorithm’s ideas and proved them. I described problems which happen during the computation of power method on Google matrix, wrote about convergence issues and concluded every topic with a discussion on best solutions to those problems. At the end of the first part PageRank algorithm is described through a simple example on directed graph with 6 nodes. In the second part of my diploma I made expansion to Page-Trust algorithm with all the definitions, theorems and proofs made for understanding the algorithm. Reader must be aware that both algorithms, PageRank and Page-Trust, are very popular nowadays, because of fast improvements of computational technologies.

• Keywords: directed graph, power method, Markov chain, random walk, convergence of the power method, stochastic matrix, reducible matrix, Perron-Frobenius Theorem