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We present four algorithms to perform template matching of an N×N image with an M×M template. The first algorithm is sequential, and the others are based on a SIMD mesh connected computer with N×N processors. In the first three algorithms, both the image and the template are represented by quadtrees, whereas in the last one, the template is represented by a quadtree, and the image is represented by a matrix. The time complexities of the four algorithms are respectively upper-bounded by α₁N²M², α₂N+β₂M², α₃N+β₃M², and β₄M², where α₁, α₂, β₂, α₃, β₃, and β₄ are constants.

Milling is the mechanical process of removing material from a piece of stock through the use of a rapidly spinning circular milling tool in order to form some desired geometric shape. An important problem in computer-aided design and manufacturing is the automated generation of efficient milling plans for computerized numerically controlled (CNC) milling machines. Among the most common milling problems is simple 2-dimensional pocket milling: cut a given 2-dimensional region down to some constant depth using a given set of milling tools. Most of the research in this area has focused on generating such milling plans assuming that the machine has a tool of a single size. Since modern CNC milling machines typically have access to a number of milling tools of various sizes and the ability to change tools automatically, this raises the important optimization problem of generating efficient milling plans that take advantage of this capability to reduce the total milling time. We consider the following multiple-tool milling problem: Given a region in the plane and a set of tools of different sizes, determine how to mill the desired region with minimum cost. The problem is known to be NP-hard even when restricted to the case of a single tool. In this paper, we present a polynomial-time approximation algorithm for the multiple-tool milling problem. The running time and approximation ratio of our algorithm depend on the simple cover complexity (introduced by Mitchell, Mount, and Suri) of the milling region.

Majority of the e-commerce sites implement Recommender Systems (RS) to help users navigate through the large search space and assist their decision making process by suggesting products that the user may like. Collaborative Filtering (CF) is the most successful and widely used algorithm in the domain of RS. However, due to the exponential growth of the web in terms of both content and number of users, CF based RS face serious scalability issues. To alleviate this problem, we propose a clustering based CF approach using two hierarchical space partitioning data structures — K-d tree and Quadtree. We cluster or partition the users’ space of the system on the basis of user location and then use the resultant clusters for predicting ratings of a target user. Since the CF based recommendation algorithm is applied separately to the clusters and not on the entire rating data, it helps in bringing down the runtime of the algorithm substantially. We further measure spatial autocorrelation indices in the clusters to justify our clustering method. However, our objective is not only to reduce the runtime but also to maintain an acceptable recommendation quality. This requirement is rightly addressed by the proposed method which assures scalability, by processing very large datasets using the same computing resource. Moreover our proposed clustering scheme is oblivious of the underlying CF algorithm. Results from the extensive experiments conducted, show that our hierarchical clustering based recommendation approach reduces runtime of the standard CF algorithms by about 88%, 82%, 79% and 85% for MovieLens-100K, MovieLens-1M, Book-Crossing and TripAdvisor data respectively, while maintaining good recommendation quality.

We present four algorithms to perform template matching of an N × N image with an M × M template. The first algorithm is sequential, and the others are based on a SIMD mesh connected computer with N × N processors. In the first three algorithms, both the image and the template are represented by quadtrees, whereas in the last one, the template is represented by a quadtree, and the image is represented by a matrix. The time complexities of the four algorithms are respectively upper-bounded by α₁N²M², α₂N + β₂M², α₃N + β₃M², and β₄M², where α₁, α₂, β₂, α₃, β₃, and β₄ are constants.