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13
Geometric And Computational Aspects Of Manufacturing Processes
 Comput. & Graphics
, 1994
"... Two of the fundamental questions that arise in the manufacturing industry concerning every type of manufacturing process are: 1. Given an object, can it be built using a particular process? 2. Given that an object can be built using a particular process, what is the best way to construct the objec ..."
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Cited by 18 (7 self)
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Two of the fundamental questions that arise in the manufacturing industry concerning every type of manufacturing process are: 1. Given an object, can it be built using a particular process? 2. Given that an object can be built using a particular process, what is the best way to construct the object? The latter question gives rise to many different problems depending on how best is qualified. We address these problems for two complimentary categories of manufacturing processes: rapid prototyping systems and casting processes. The method we use to address these problems is to first define a geometric model of the process in question and then answer the questions on that model. In the category of rapid prototyping systems, we concentrate on stereolithography, which is emerging as one of the most popular rapid prototyping systems. We model stereolithography geometrically and then study the class of objects that admit a construction in this model. For the objects that admit a constructio...
Solving the AllPair Shortest Path Query Problem on Interval and CircularArc Graphs
 Networks
, 1998
"... In this paper, we study the following allpair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed efficiently ..."
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Cited by 12 (1 self)
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In this paper, we study the following allpair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed efficiently (both sequentially and in parallel). We show that, after sorting the input intervals by their endpoints, a data structure can be constructed sequentially in O(n) time and O(n) space; using this data structure, each query on the length of the shortest path between any two intervals can be answered in O(1) time, and each query on the actual shortest path can be answered in O(k) time, where k is the number of intervals on that path. Furthermore, this data structure can be constructed optimally in parallel, in O(log n) time using O(n= log n) CREW PRAM processors; each query on the actual shortest path can be answered in O(1) time using k processors. Our techniques can be extended to solving the ...
An Optimal Algorithm for Shortest Paths on Weighted Interval and CircularArc Graphs, with Applications
 Algorithmica
, 1995
"... We give the first lineartime algorithm for computing singlesource shortest paths in a weighted interval or circulararc graph, when we are given the model of that graph, i.e., the actual weighted intervals or circulararcs and the sorted list of the interval endpoints. Our algorithm solves this pr ..."
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Cited by 12 (1 self)
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We give the first lineartime algorithm for computing singlesource shortest paths in a weighted interval or circulararc graph, when we are given the model of that graph, i.e., the actual weighted intervals or circulararcs and the sorted list of the interval endpoints. Our algorithm solves this problem optimally in O(n) time, where n is the number of intervals or circulararcs in a graph. An immediate consequence of our result is an O(qn+n log n) time algorithm for the minimumweight circlecover problem, where q is the minimumnumber of arcs crossing any point on the circle; the n log n term in this time complexity is from a preprocessing sorting step when the sorted list of endpoints is not given as part of the input. The previously best time bounds were O(n log n) for this shortest paths problem, and O(qn log n) for the minimumweight circlecover problem. Thus we improve the bounds of both problems. More importantly, the techniques we give hold the promise of achieving similar lo...
Computing the Constrained Euclidean, Geodesic and Link Centre of a Simple Polygon with Applications
"... In the manufacturing industry, finding a suitable location for the pin gate (the pin gate is the point from which liquid is poured or injected into a mold) is a difficult problem when viewed from the fluid dynamics of the molding process. However, experience has shown that a suitable pin gate locati ..."
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Cited by 12 (5 self)
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In the manufacturing industry, finding a suitable location for the pin gate (the pin gate is the point from which liquid is poured or injected into a mold) is a difficult problem when viewed from the fluid dynamics of the molding process. However, experience has shown that a suitable pin gate location possesses several geometric characteristics, namely the distance from the pin gate to any point in the mold should be small and the number of turns on the path from a point in the mold to the pin gate should be small. We address the problem of computing locations that possess these geometric characteristics. Given a mold M (modeled by an n vertex simple polygon) we show how to compute the Euclidean center of M constrained to lie in the interior of M or on the boundary of M in O(n log n+k) time where k is the number of intersections between M and the furthest point Voronoi diagram of the vertices of M . We show how to compute the geodesic center of M constrained to the boundary in O(n log n) time and the geodesic center of M constrained to lie in a polygonal region in O(n(n + k)) time. Finally, we show how to compute the link center of M constrained to the boundary of M in O(n log n) time.
Some scalable parallel algorithms for geometric problems
 Journal of Parallel and Distributed Computing
, 1999
"... This paper considers a variety of geometric pattern recognition problems on input sets of size n using a coarse grained multicomputer model consisting of p processors with 0(n p) local memory each (i.e., 0(n p) memory cells of 3(log n) bits apiece), where the processors are connected to an arbitrary ..."
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Cited by 6 (2 self)
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This paper considers a variety of geometric pattern recognition problems on input sets of size n using a coarse grained multicomputer model consisting of p processors with 0(n p) local memory each (i.e., 0(n p) memory cells of 3(log n) bits apiece), where the processors are connected to an arbitrary interconnection network. It introduces efficient scalable parallel algorithms for a number of geometric problems including the rectangle finding problem, the maximal equally spaced collinear points problem, and the point set pattern matching problem. All of the algorithms presented are scalable in that they are applicable and efficient over a very wide range of ratios of problem size to number of processors. In addition to the practicality imparted by scalability, these algorithms are easy to implement in that all required communications can be achieved by a small number of calls to standard global routing operations.
Geometric and Computational Aspects of Gravity Casting
 COMPUTERAIDED DESIGN
, 1995
"... In the manufacturing industry, finding an orientation for a mold that eliminates surface defects and insures a complete fill after the termination of the gravity casting process is an important and difficult problem which has not previously been investigated formally. We initiate the study of the ..."
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Cited by 6 (3 self)
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In the manufacturing industry, finding an orientation for a mold that eliminates surface defects and insures a complete fill after the termination of the gravity casting process is an important and difficult problem which has not previously been investigated formally. We initiate the study of the gravity casting process from a geometric perspective and present an optimal `(n log n) time algorithm that solves this problem in two dimensions given an object of size n.
Eliminating wire crossings for molecular quantumdot cellular automata implementation
 ICCAD
, 2005
"... Abstract — When exploring computing elements made from technologies other than CMOS, it is imperative to investigate the effects of physical implementation constraints. This paper focuses on molecular Quantumdot Cellular Automata circuits. For these circuits, it is very difficult for chemists to fa ..."
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Cited by 6 (5 self)
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Abstract — When exploring computing elements made from technologies other than CMOS, it is imperative to investigate the effects of physical implementation constraints. This paper focuses on molecular Quantumdot Cellular Automata circuits. For these circuits, it is very difficult for chemists to fabricate wire crossings (at least in the near future). A novel technique is introduced to remove wire crossings in a given circuit to facilitate the self assembly of real circuits – thus providing meaningful and functional design targets for both physical and computer scientists. The technique eliminates all wire crossings with minimal logic gate/node duplications. Experimental results based on existing QCA circuits and other benchmarks are quite encouraging, and suggest that further investigation is needed. I.
TwoCenter Problems for a Convex Polygon
 In proceedings of ESA'98
"... this paper, we consider some variants of the 2center problems for the point set. Let ..."
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Cited by 5 (1 self)
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this paper, we consider some variants of the 2center problems for the point set. Let
Hypercrossing Number: A New and Effective Cost Function for Cell Placement Optimization
 CBL, CS Dept., NCSU, Box 7550, Raleigh, NC 27695
, 1998
"... Traditionally, the algorithms that optimize placement of cells in a VLSI layout rely on a cost function that includes a distance metric. The choice of a cost function may limit the choices in devising new, more efficient and more effective algorithms. The metric we propose relies on the interval gra ..."
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Cited by 3 (3 self)
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Traditionally, the algorithms that optimize placement of cells in a VLSI layout rely on a cost function that includes a distance metric. The choice of a cost function may limit the choices in devising new, more efficient and more effective algorithms. The metric we propose relies on the interval graph of net nodes, induced by each specific placement of cells into a row. Nominally, the metric associated with this graph is the chromatic number (Ø). The new cost function, proposed in this paper, is the hypercrossing number (HC), defined by the cardinality of the edgeset of the interval graph. This metric relates to the edge crossing number (EC) in the corresponding bipartite graph, depends on cell and net order only, and is independent of the target technology. Currently, there is no explicit algorithm to place cells such that the hypercrossing number is minimal, but edge crossing minimization algorithms are available. We demonstrate, experimentally and with statistical significance, th...