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Heuristics for paths in maps
Kudláčková, Lada ; Mareš, Martin (advisor) ; Kratochvíl, Miroslav (referee)
The content of the thesis is a description of heuristic procedures, which are used to find the shortest paths in the graphs and verify their effec- tiveness on the actual data. It deals with heuristics for Dijkstra's algorithm, especially the A* algorithm, which uses a lower distance-to-target estimate. Heuristics are implemented and tested on the road network of the Czech Re- public. 1
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On the Dijkstra's algorithm in the pedestrian flow problem
Petrášová, Tereza ; Felcman, Jiří (advisor) ; Kučera, Václav (referee)
Title: On the Dijkstra's algorithm in the Pedestrian Flow Problem Author: Tereza Petrášová Department: Department of Numerical Mathematics Supervisor: doc. RNDr. Jiří Felcman, CSc., Department of Numerical Mathe- matics Abstract: The pedestrian flow problem is described by a coupled system of the first order hyperbolic partial differential equations with the source term and by the functional minimization problem for the desired direction of motion. The functional minimization is based on the modified Dijkstra's algorithm used to find the minimal path to the exit. The original modification of the Dijkstra's algorithm is proposed to increase its efficiency in the pedestrian flow problem. This approach is compared with the algorithm of Bornemann and Rasch for determination of the desired direction of motion based on the solution of the so- called Eikonal equation. Both approaches are numerically tested in the framework of two splitting algorithms for solution of the coupled problem. The former splitting algorithm is based on the finite volume method yielding for the given time instant the piecewise constant approximation of the solution. The latter one uses the implicit discretization by a space-time discontinuous Galerkin method based on the discontinuous piecewise polynomial approximation. The numerical examples...
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Searching and Updating Public Transport Timetables
Havel, Filip ; Zavoral, Filip (advisor) ; Škoda, Petr (referee)
Most of the people who use public transportation have specific areas of interests which can be used to cut down the transport network to several smaller parts. It is reasonable to assume that these people will want to be informed in case a change occurs in the restricted part of transport network they are interested in. For this reason, we created an application which informs its users about the changes in public transportation that concern them. We assume that for users, the most important area of interest are the connections between individual stations, which is why this thesis mainly focuses on the possibility of search for connection in timetables. In addition to this search, we also deal with the application's adaptability and we have implemented examples of expansions for various result outputs, user interfaces and data sources. To improve general user experience, we have developed a mobile application that communicates with the main application and displays updated timetables according to the user's area of interest. 1
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Application of the Dijkstra's Algorithm in the Pedestrian Flow Problem
Petrášová, Tereza ; Felcman, Jiří (advisor) ; Dolejší, Vít (referee)
The purpose of this work is to study the pedestrian flow equations as the coupled system formed by the eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and the equations of motion of a compressible inviscid fluid. To specify the outer volume forces in the latter equation it is assumed that the pedestrians try to move in a desired direction with a desired velocity, which are dependent on the density in their surroundings. The desired direction is obtained as the gradient of the solution of the eikonal equation. We show that the solution of the eikonal equation has the meaning of the time needed to pass the fastest path to the exit. We suggest avoiding solving the eikonal equation by using the graph theory, where as the graph we use the underlying triangulation. The norm of each edge in the graph is density-dependent and has the dimension of time. This is together with the use of the modified Dijkstra's algorithm the novelty of the work. Numerical results of the two approaches are presented. Powered by TCPDF (www.tcpdf.org)
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Graph Theory in Economic Practice
Geško, Dávid ; Půža, Bedřich (referee) ; Novotná, Veronika (advisor)
In Bachelor’s thesis we deal with Traveling salesman person problem. In theoretical part are introduced basic terms of graphs theory and methods to solve Traveling salesman person problem. Practical part draws a comparison among efficiency of several methods solving this problem in environment of real world examples. In summary analysis are these methods evaluated and consequently chosen and implemented most effective method for company, which want to use it to determining most optimized tours for distributing goods.
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The Shortest Graph's Pahts Finding
Jágr, Petr ; Ohlídal, Miloš (referee) ; Jaroš, Jiří (advisor)
The aim of this thesis is finding, comparing and implementation of algorithms for finding the shortest paths between each of pairs of nodes in a graph. For this task I use modifications of existing algorithms to achive the lowest time consumption of the computation. Modifications are established on Dijkstra's and Floyd-Warshall's algorithm. We also familiarize with Bellman-Ford algorithm.
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Shopping Advisor
Kocourek, Jakub ; Bartík, Vladimír (referee) ; Kolář, Dušan (advisor)
The attached bachelor thesis deals with nding the shortest ways in a shop for the selected purchase. The different technologies of creating web pages are described. As for the state space search algorithms are given for nding the shortest path between two points and for solving the travel salesmen problem. The thesis continues with the description of a design and implementation of application with all used technologies (PHP, Nette, MySQL, JS, JQuery) applying the Dijkstra's algorithm for nding the shortest path and genetic algorithm for solving the travel salesmen problem.
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