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.

The circuit represented by a VLSI layout must be verified by checking it against the schematic circuit as an important part of the functional verification step. This involves two central problems of matching the circuit graphs with each other (graph isomorphism) and extracting a higher level of circuit from a given level by finding subcircuits in the circuit graph (subgraph isomorphism). Modern day VLSI layouts contain millions of devices. Hence the memory requirements of the data structures required by tools for verifying them become huge and can easily exceed the amount of internal memory available on a computer. In such a scenario, a program not aware of the memory hierarchy performs badly because of its unorganized input/output operations (I/Os) as the speed of a disk access is about a million times slower than accessing a main memory location. In this article, we present I/O-efficient algorithms for the graph isomorphism and subgraph isomorphism problems in the context of verification of VLSI layouts. Experimental results show the need and utility of I/O-efficient algorithms for handling problems with large memory requirements.

Determining the influence of an object on other objects in a database, based on proximity, is important in many applications. Abstractly, we wish to pre-process a set, P, of points in d-space so that the points of P that are assigned a new query point q as a Euclidean nearest neighbor can be reported quickly. These are the reverse nearest neighbors of q and are the ones most influenced by q. This generalizes to bichromatic reverse nearest neighbors, in which two sets, clients and servers, are given, where each client is influenced by some server, and of interest are the clients that are assigned a new server q as a nearest neighbor. Both extend to higher orders k > 1, where we seek the points that are assigned q as one of their k nearest neighbors, indicating varying degrees of influence. Each version also has a counterpart where "nearest" is replaced by "farthest", signifying low influence.

Generalized intersection searching problems are a class of geometric query-retrieval problems where the questions of interest concern the intersection of a query object with aggregates of geometric objects (rather than with individual objects.) This class contains, as a special case, the well-studied class of standard intersection searching problems and is rich in applications. Unfortunately, the solutions known for the standard problems do not yield efficient solutions to the generalized problems. Recently, efficient solutions have been given for generalized problems where the input and query objects are iso-oriented (i.e., axes-parallel) or where the aggregates satisfy additional properties (e.g., connectedness). In this paper, efficient algorithms are given for several generalized problems involving non-iso-oriented objects. These problems include: generalized halfspace range searching, segment intersection searching, triangle stabbing, and triangle range searching. The techniques used include: computing suitable sparse representations of the input, persistent data structures, and filtering search.