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Predmet raziskovanja tega magistrskega dela je problem zapiranja centrov, ki spada med probleme razmeščanja ponudnikov. Predstavljene so osnovne lastnosti ter natančni algoritmi za reševanje problema. Zaradi NP-polnosti so predstavljeni tudi aproksimacijski algoritmi. Empirični testi na različnih omrežjih preverjajo časovno zahtevnost in kakovost rešitev aproksimacijskih algoritmov. Razmerje teh dveh lastnosti je prav tako primerjano. V namen testiranja algoritmov je razvito tudi poštno omrežje Slovenije, cilj katerega je reševanje problema zapiranja poštnih poslovalnic. The main topic of this thesis is the center closing problem, which is a facility location problem. Basic properties and exact algorithms for solving the problem are presented. Because the problem is NP-complete, approximation algorithms are also presented. Time complexity, the quality of results, and the ratio between the two are tested for approximation algorithms using empirical tests. For the purpose of testing the algorithms a postal network of Slovenia was constructed, the goal of which was to solve the post office closing problem.

Preiskovali smo problem iskanja ravnin na trianguliranem terenu. Za množico točk v prostoru zgradimo Delaunayjevo triangulacijo in z dvema različnima metodama poiščemo ravnino na terenu. V prvi metodi uporabimo algoritem za iskanje največjega konveksnega poligona. Algoritem se dobro obnese na manjši množici točk, na večji množici točk, pa zaradi svoje kvadratične časovne zahtevnosti ne pride v poštev. V drugi metodi uporabimo aproksimacijski algoritem. Ta se bolje obnese tudi na večji množici podatkov, kot tudi na realnih geografskih podatkih, ki jih lahko dobimo na spletnem portalu LIDAR. Implementiran vmesnik nam pomaga, da na enostaven način testiramo obe metodi in vizualiziramo rezultate. We studied the problem of finding planar regions in a triangulated terrain. For a set of points in 3-space, we construct the Delaunay triangulation. Then, with two different methods we look for a region which is flat. The first method uses an algorithm to find the largest convex polygon. The algorithm works well on smaller sets of points, but on larger sets of points it performs poorly due to its quadratic time complexity. In the second method, we use an approximation algorithm. It performs better on larger data sets, as well as on real geographical data, which can be obtained on the web portal LIDAR. The implemented interface helps us to test both methods in an easy way and visualize the results.