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Levi in kontaminacije na trikotniških mrežah
ID Uhan, Maša (Author), ID Virk, Žiga (Mentor) More about this mentor... This link opens in a new window, ID Franc, Aleksandra (Comentor)

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Abstract
Diplomska naloga obravnava problem levov in kontaminacije na trikotniških mrežah: po grafu se gibljejo levi, ki čistijo kontaminacijo, ta pa se hkrati ˇsiri na vsa nezasedena sosednja vozlišča. Zanima nas najmanjše število levov, potrebnih za očiščenje mreže Pn. Implementirali smo simulacijsko jedro in štiri modele gibanja (pasovni, vljudni, kofeinirani in monotoni) ter z izčrpnim preiskovanjem za n od 3 do 8 določili najmanjše število levov in ga primerjali z mejami iz literature. Pri pasovnem, vljudnem in monotonem modelu zadošča n levov, kofeinirani model pa mrežo P5 očisti s štirimi in P6 s petimi levi; torej z manj kot n. Rezultate smo prikazali v interaktivni spletni aplikaciji.

Language:Slovenian
Keywords:levi in kontaminacija, trikotniške mreže, igre zasledovanja in izmikanja, čiščenje grafov, izčrpno preiskovanje, Cheegerjeva konstanta
Work type:Bachelor thesis/paper
Typology:2.11 - Undergraduate Thesis
Organization:FRI - Faculty of Computer and Information Science
Year:2026
PID:20.500.12556/RUL-186420 This link opens in a new window
COBISS.SI-ID:289976323 This link opens in a new window
Publication date in RUL:01.09.2026
Views:147
Downloads:30
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Secondary language

Language:English
Title:Lions and contaminations on triangular grids
Abstract:
This thesis studies the lions and contamination problem on triangular grids: lions move along a graph and clean contamination, which simultaneously spreads to every unoccupied neighbouring vertex. We ask for the smallest number of lions needed to clean the grid Pn. We implement a simulation core and four movement models (strip, polite, caffeinated and monotone) and, through exhaustive search for n from 3 to 8, determine the minimum number of lions and compare it with bounds from the literature. The strip, polite and monotone models require n lions, whereas the caffeinated model cleans P5 with four and P6 with five lions; fewer than n. We presented the results in an interactive web application.

Keywords:lions and contamination, triangular grids, pursuit-evasion games, graph cleaning, exhaustive search, Cheeger constant

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