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Monkey Bank Robbers
Škoda, Dominik ; Lidický, Bernard (advisor) ; Cibulka, Josef (referee)
The project concerns of creation of computer game inspirated by the game RoboRally. The program is based on Client-Server architecture and allowes players to play together via Internet. The application running on server manages individual games and takes care of synchronization between players. The program allowes to implement artificial inteligence which can join individual game with another players. Each player can create any map and play a game with any map. The project is designed for simple extension in future. The program is developed in JAVA language.
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Samodlážditelné simplexy
Safernová, Zuzana ; Matoušek, Jiří (advisor) ; Cibulka, Josef (referee)
In the present work we study tetrahedral k-reptiles. A d-dimensional simplex is called a k-reptile if it can be tiled in k simplices with disjoint interiors that are all congruent and similar to S. For d = 2, triangular k-reptiles exist for many values of k and they have been completely characterized. On the other hand, the only simplicial k-reptiles that are known for d 3 have k = md, where m 2 (Hill simplices). We prove that for d = 3, tetrahedral k-reptiles exist only for k = m3. This partially confirms the Hertel's conjecture, asserting that the only tetrahedral k-reptiles are the Hill tetrahedra. We conjecture that k = md is necessary condition for existence of d-dimensional simplicial k-reptiles, d > 3.
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Konvexně nezávislé podmnožiny konečných množin bodů
Zajíc, Vítězslav ; Valtr, Pavel (advisor) ; Cibulka, Josef (referee)
Let fd(n), n > d ≥ 2, be the smallest positive integer such that any set of fd(n) points, in general position in Rd , contains n points in convex position. Let hd(n, k), n > d ≥ 2 and k ≥ 0, denote the smallest number with the property that in any set of hd(n, k) points, in general position in Rd , there are n points in convex position whose convex hull contains at most k other points. Previous result of Valtr states that h4(n, 0) does not exist for all n ≥ 249. We show that h4(n, 0) does not exist for all n ≥ 137. We show that h3(8, k) ≤ f3(8) for all k ≥ 26, h4(10, k) ≤ f4(10) for all k ≥ 147 and h5(12, k) ≤ f5(12) for all k ≥ 999. Next, let fd(k, n) be the smallest number such that in every set of fd(k, n) points, in general position in Rd , there are n points whose convex hull has at least k vertices. We show that, for arbitrary integers n ≥ k ≥ d + 1, d ≥ 2, fd(k, n) ≥ (n − 1) (k − 1)/(cd logd−2 (n − 1)) , where cd > 0 is a constant dependent only on the dimension d. 1
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Perfect tilings of simplices
Safernová, Zuzana ; Matoušek, Jiří (advisor) ; Cibulka, Josef (referee)
In the present work we study the problem of k-reptile d-dimensional simplices. A simplex is called a k-reptile if it can be tiled in k simplices with disjoint interiors that are all congruent and similar to S. The only k-reptile simplices that are known for d 3 have k = md, where m 2. We also show an idea of Matoušek's proof of nonexistence of 2-reptile simplices of dimensions d 3. We correct a mistake in the proof. Then we give several geometric observations for k = 2. At the end we prove that there is no 3-reptile simplex for d = 3.
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Strategies for generalized Reversi
Tupec, Radek ; Cibulka, Josef (advisor) ; Lidický, Bernard (referee)
The aim of this work is to design generalized Reversi (also known as Othello) and implement the application for editing and testing strategies of artificial intelligence. In the beginning of the work full rules of the game and solved problems are presented. After that follows detailed description of implemented strategies, programmer and user manual. At the conclusion of the work there is the report about using the application and possible extensions of the application.
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Triplanetary
Huječek, Adam ; Cibulka, Josef (advisor) ; Gemrot, Jakub (referee)
The main purpose of this work is to bring the almost forgotten turn-based board game Triplanetary from the 70s and the beginning of the 80s of the last century to the screens of today's computers. The program allows multiple players to play on one computer in the so called hotseat mode two of the several scenarios available in the original game - racing Grand Tour with the option to play with computer controlled opponents and battle Nova for three players. However thanks to the suitable design it is easy to implement the rest of scenarios or of course add completely new ones provided the user has the knowledge of JAVA which the game is programmed in. Another advantage is the option to save and exit the game at any time and return to it later.
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Ditchers
Slabý, David ; Lidický, Bernard (advisor) ; Cibulka, Josef (referee)
The aim of this work is to combine the playability and the idea of the legendary game Tunneler with the option of programming arti cial intelligence for computer players. Writing scripts and their use in the game is separated from the game itself, so the author of a script only has to know the scripting language and a few interface functions to successfully create an intelligent robot. At the same time the game is suffciently attractive to casual players, it is easy to operate and has some additional features, such as multiple weapons, maps and robot types. Another important feature is the option of playing over LAN.
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Extremal combinatorics of matrices, sequences and sets of permutations
Cibulka, Josef ; Valtr, Pavel (advisor) ; Füredi, Zoltán (referee) ; Jelínek, Vít (referee)
Title: Extremal combinatorics of matrices, sequences and sets of permutations Author: Josef Cibulka Department: Department of Applied Mathematics Supervisor: Doc. RNDr. Pavel Valtr, Dr., Department of Applied Mathematics Abstract: This thesis studies questions from the areas of the extremal theory of {0, 1}-matrices, sequences and sets of permutations, which found many ap- plications in combinatorial and computational geometry. The VC-dimension of a set P of n-element permutations is the largest integer k such that the set of restrictions of the permutations in P on some k-tuple of positions is the set of all k! permutation patterns. We show lower and upper bounds quasiexponential in n on the maximum size of a set of n-element permutations with VC-dimension bounded by a constant. This is used in a paper of Jan Kynčl to considerably improve the upper bound on the number of weak isomorphism classes of com- plete topological graphs on n vertices. For some, mostly permutation, matrices M, we give new bounds on the number of 1-entries an n × n M-avoiding matrix can have. For example, for every even k, we give a construction of a matrix with k2 n/2 1-entries that avoids one specific k-permutation matrix. We also give almost tight bounds on the maximum number of 1-entries in matrices avoiding a fixed layered...
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Ramseyovské otázky v euklidovském prostoru
Cibulka, Josef ; Valtr, Pavel (advisor) ; Černý, Jakub (referee)
One of the problems in Euclidean Ramsey theory is to determine the chromatic number of the Euclidean space. The chromatic number of a space is the minimum number of colors with which the whole space can be colored so that no two points of the same color are at unit distance. We prove that the chromatic number of the six-dimensional real space is at least 11 and that the chromatic number of the seven-dimensional rational space is at least 15. In addition we give a new proof of the lower bound 9 for the chromatic number of the five-dimensional real space. We also simplify the proof of the lower bound 7 for the four-dimensional real space. It is known that the chromatic number of the n-dimensional real space grows exponentially in n. We show some of its subspaces, in which the growth is slower than exponential. We also summarize previous results for normed spaces in general and for some interesting non-Euclidean spaces.
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Ramseyovské otázky v euklidovském prostoru
Cibulka, Josef
One of the problems in Euclidean Ramsey theory is to determine the chromatic number of the Euclidean space. The chromatic number of a space is the minimum number of colors with which the whole space can be colored so that no two points of the same color are at unit distance. We prove that the chromatic number of the six-dimensional real space is at least 11 and that the chromatic number of the seven-dimensional rational space is at least 15. In addition we give a new proof of the lower bound 9 for the chromatic number of the five-dimensional real space. We also simplify the proof of the lower bound 7 for the four-dimensional real space. It is known that the chromatic number of the n-dimensional real space grows exponentially in n. We show some of its subspaces, in which the growth is slower than exponential. We also summarize previous results for normed spaces in general and for some interesting non-Euclidean spaces.
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