Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith

Optimized normal and distance matching for heterogeneous object modeling

This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material governing features for designing a heterogeneous object. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into equal number of segments, a series of intermediate piecewise curves are generated to represent the material metamorphosis between the governing material features. Alternatively, a dynamic programming approach developed in our earlier work is presented for comparison purposes. Result and computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper

AT-GIS: highly parallel spatial query processing with associative transducers

Users in many domains, including urban planning, transportation, and environmental science want to execute analytical queries over continuously updated spatial datasets. Current solutions for largescale spatial query processing either rely on extensions to RDBMS, which entails expensive loading and indexing phases when the data changes, or distributed map/reduce frameworks, running on resource-hungry compute clusters. Both solutions struggle with the sequential bottleneck of parsing complex, hierarchical spatial data formats, which frequently dominates query execution time. Our goal is to fully exploit the parallelism offered by modern multicore CPUs for parsing and query execution, thus providing the performance of a cluster with the resources of a single machine. We describe AT-GIS, a highly-parallel spatial query processing system that scales linearly to a large number of CPU cores. ATGIS integrates the parsing and querying of spatial data using a new computational abstraction called associative transducers(ATs). ATs can form a single data-parallel pipeline for computation without requiring the spatial input data to be split into logically independent blocks. Using ATs, AT-GIS can execute, in parallel, spatial query operators on the raw input data in multiple formats, without any pre-processing. On a single 64-core machine, AT-GIS provides 3× the performance of an 8-node Hadoop cluster with 192 cores for containment queries, and 10× for aggregation queries