Procedural Content Generation innebär att spelinnehåll automatiskt genereras för att dels både öka variationen i spel dels och minska arbetsbelastningen hos designers. Ett användningsområde för detta är rumbaserad bangenerering. Målet med detta  här arbetet är var att jämföra två algoritmer som gör just detta:; Binary Space Partitioning och Delaunay Triangulation. De kriterier som algoritmerna utvärderades på var tidseffektivitet, variation, likhet och möjligheten att nå alla rum. Resultatet visade att Binary Space Partitioning hade snabbare genereringstid samtidigt som Delaunay Triangulation gav utvecklaren mer valmöjligheter. Vilken algoritm som var att föredra ifall tidsaspekten inte bar mest tyngd blev helt en en mestadels subjektiv fråga där varje enskild utvecklares önskemål kommer påverka svaret. Ifall arbetet skulle fortsättas i framtiden skulle det vara intressant att utföra fler tester med flera olika mätvärden samt använda algoritmerna i ett spel och sedan påta låta spelare testare bedöma kvalitén hos banorna som genereras.

A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of perfect matchings in a bipartite graph. We focus on the problem of counting the common bases in pairs of regular matroids, and describe a class called <i>Pfaffian matroid pairs</i> for which this enumeration problem can be solved. We prove that when a pair of regular matroids is non-Pfaffian, there is a set of common bases which certifies this, and that the number of bases in the certificate is linear in the size of the ground set of the matroids. When both matroids in a pair are series-parallel, we prove that determining if the pair is Pfaffian is equivalent to finding an edge signing in an associated graph, and in the case that the pair is non-Pfaffian, we obtain a characterization of this associated graph. Pfaffian bipartite graphs are a class of graphs for which the number of perfect matchings can be determined; we show that the class of series-parallel Pfaffian matroid pairs is an extension of the class of Pfaffian bipartite graphs. Edmonds proved that the polytope generated by the common bases of a pair of matroids is equal to the intersection of the polytopes generated by the bases for each matroid in the pair. We consider when a similar property holds for the binary space, and give an excluded minor characterization of when the binary space generated by the common bases of two matroids can not be determined from the binary spaces for the individual matroids. As a result towards a description of the lattice of common bases for a pair of matroids, we show that the lattices for the individual matroids determine when all common bases of a pair of matroids intersect a subset of the ground set with fixed cardinality.

A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of perfect matchings in a bipartite graph. We focus on the problem of counting the common bases in pairs of regular matroids, and describe a class called <i>Pfaffian matroid pairs</i> for which this enumeration problem can be solved. We prove that when a pair of regular matroids is non-Pfaffian, there is a set of common bases which certifies this, and that the number of bases in the certificate is linear in the size of the ground set of the matroids. When both matroids in a pair are series-parallel, we prove that determining if the pair is Pfaffian is equivalent to finding an edge signing in an associated graph, and in the case that the pair is non-Pfaffian, we obtain a characterization of this associated graph. Pfaffian bipartite graphs are a class of graphs for which the number of perfect matchings can be determined; we show that the class of series-parallel Pfaffian matroid pairs is an extension of the class of Pfaffian bipartite graphs. Edmonds proved that the polytope generated by the common bases of a pair of matroids is equal to the intersection of the polytopes generated by the bases for each matroid in the pair. We consider when a similar property holds for the binary space, and give an excluded minor characterization of when the binary space generated by the common bases of two matroids can not be determined from the binary spaces for the individual matroids. As a result towards a description of the lattice of common bases for a pair of matroids, we show that the lattices for the individual matroids determine when all common bases of a pair of matroids intersect a subset of the ground set with fixed cardinality.

A common type of problems that exist in both industrial and scientific spaces are optimization problems. These problems can be found in among other things manufacturing, pathfinding, network routing and more. Because of the wide area of application, optimization is well a studied area. One solution to these types of problems is the Ant Colony Optimization algorithm that has been around since 1991 and has undergone a lot of developments over the years. This algorithm draws inspiration from real ant colonies and their procedure for foraging. However, a common criticism of this algorithm is its poor scalability. To tackle the scalability problem this thesis will combine the concept of binary space partitioning with the Ant Colony Optimization algorithm. The goal is to examine the algorithms convergence times and lengths of the paths produced. The results are measured in intervals by calculating the best possible path found at every interval. The findings showed that given an unlimited execution time the original Ant Colony Optimization algorithm produced shorter paths. But when a limit on execution time was introduced and the problem sizes grew the performance began to favor the partitioned versions. These findings could be useful in areas where complex optimization problems need to be solved within a limited timeframe. / <p>The presentation took place via an online conference call using the software "Zoom"</p>

The recent growth in wireless communications presents a new challenge to multimedia communications. Digital image transmission is a very common form of multimedia communication. Due to limited bandwidth and broadcast nature of the wireless medium, it is necessary to compress and encrypt images before they are sent. On the other hand, it is important to efficiently utilize the limited energy in wireless devices. In a wireless device, two major sources of energy consumption are energy used for computation and energy used for transmission. Computation energy can be reduced by minimizing the time spent on compression and encryption. Transmission energy can be reduced by sending a smaller image file that is obtained by compressing the original highest quality image. Image quality is often sacrificed in the compression process. Therefore, users should have the flexibility to control the image quality to determine whether such a tradeoff is acceptable. It is also desirable for users to have control over image quality in different areas of the image so that less important areas can be compressed more, while retaining the details in important areas. To reduce computations for encryption, a partial encryption scheme can be employed to encrypt only the critical parts of an image file, without sacrificing security. This thesis proposes a scalable and secure image representation scheme that allows users to select different image quality and security levels. The binary space partitioning (BSP) tree presentation is selected because this representation allows convenient compression and scalable encryption. The Advanced Encryption Standard (AES) is chosen as the encryption algorithm because it is fast and secure. Our experimental result shows that our new tree construction method and our pruning formula reduces execution time, hence computation energy, by about 90%. Our image quality prediction model accurately predicts image quality to within 2-3dB of the actual image PSNR.

The recent growth in wireless communications presents a new challenge to multimedia communications. Digital image transmission is a very common form of multimedia communication. Due to limited bandwidth and broadcast nature of the wireless medium, it is necessary to compress and encrypt images before they are sent. On the other hand, it is important to efficiently utilize the limited energy in wireless devices. In a wireless device, two major sources of energy consumption are energy used for computation and energy used for transmission. Computation energy can be reduced by minimizing the time spent on compression and encryption. Transmission energy can be reduced by sending a smaller image file that is obtained by compressing the original highest quality image. Image quality is often sacrificed in the compression process. Therefore, users should have the flexibility to control the image quality to determine whether such a tradeoff is acceptable. It is also desirable for users to have control over image quality in different areas of the image so that less important areas can be compressed more, while retaining the details in important areas. To reduce computations for encryption, a partial encryption scheme can be employed to encrypt only the critical parts of an image file, without sacrificing security. This thesis proposes a scalable and secure image representation scheme that allows users to select different image quality and security levels. The binary space partitioning (BSP) tree presentation is selected because this representation allows convenient compression and scalable encryption. The Advanced Encryption Standard (AES) is chosen as the encryption algorithm because it is fast and secure. Our experimental result shows that our new tree construction method and our pruning formula reduces execution time, hence computation energy, by about 90%. Our image quality prediction model accurately predicts image quality to within 2-3dB of the actual image PSNR.

The purpose of this thesis is to present methods for visibility determination and to design and implement an application to demonstrate visibility determination in a 3D maze.