This paper presents a grid-based multi-layer, multi-terminal autorouter with the unique feature of diagonal routing. The router is suitable for routing memory boards and highly congested printed circuit boards. Diagon...
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This paper presents a grid-based multi-layer, multi-terminal autorouter with the unique feature of diagonal routing. The router is suitable for routing memory boards and highly congested printed circuit boards. Diagonal routing is extremely useful in minimizing vias and in obtaining a high rate of completion with total route length reduced by up to 20% comparatively. The router employs an improved maze algorithm to incorporate multi-layer diagonal routing. The cost function used in the algorithm is complicated, but can be easily modified to meet specific needs. The algorithm models multi-terminal routing as a minimum spanning tree problem to use the least amount of wiring which is most desirable in the electronic industry. Intelligent net ordering and dynamic data structures reduce memory requirement and total route time by up to 30% compared to recently developed routers. The algorithm described in this paper was extensively tested against standard benchmarks and very inspiring results were achieved.
Consider a set A = {A1, A2,..., A(N)} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s1, s2,.., s(N)] and are to be arranged lexicogra...
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Consider a set A = {A1, A2,..., A(N)} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s1, s2,.., s(N)] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it is well known [10] that an optimal BST may be constructed using A and S. We consider the case when S is not known a priori. A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme the restructuring is performed only if it decreases the Weighted Path Length (WPL) of the overall resultant tree. An optimized version of the latter method which requires only one extra integer field per record has also been presented. Initial simulation results which compare our algorithm with various other static and dynamic schemes seem to indicate that this scheme asymptotically produces trees which are an order of magnitude closer to the optimal one than those produced by many of the other BST schemes reported in the literature.
The problem of maintaining the 3-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge and vertex insertions, is studied. This paper shows how to answer the question of whether o...
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The problem of maintaining the 3-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge and vertex insertions, is studied. This paper shows how to answer the question of whether or not two vertices belong to the same 3-edge-connected component of a connected graph that is undergoing only edge insertions. Any sequence of q query and updates on an n-vertex graph can be performed in O((n + q)alpha(q, n)) time.
Let P be a set of n points in the Euclidean plane and let C be a convex figure. In 1985, Chazelle and Edelsbrunner presented an algorithm, which preprocesses P such that for any query point q, the points of P in the t...
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Let P be a set of n points in the Euclidean plane and let C be a convex figure. In 1985, Chazelle and Edelsbrunner presented an algorithm, which preprocesses P such that for any query point q, the points of P in the translate C + q can be retrieved efficiently. Assuming that constant time suffices for deciding the inclusion of a point in C, they provided a space and query time optimal solution. Their algorithm uses O(n) space. A query with output size k can be solved in O(log n + k) time. The preprocessing step of their algorithm, however, has time complexity O(n(2)). We show that the usage of a new construction method for layers reduces the preprocessing time to O(nlog n). We thus provide the first space, query time and preprocessing time optimal solution for this class of point retrieval problems. Besides, we present two new dynamic data structures for these problems. The first dynamicdata structure allows on-line insertions and deletions of points in O ((log n)(2)) time. In this dynamicdata structure, a query with output size k can be solved in O(log n + k(log n)(2)) time. The second dynamicdata structure, which allows only semi-online updates, has O((log n)(2)) amortized update time and O(log n + k) query time.
This paper studies the problem of maintaining the 2-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge insertions and edge deletions. It is shown how to test at any time wheth...
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This paper studies the problem of maintaining the 2-edge-connected components of a graph undergoing repeated dynamic modifications, such as edge insertions and edge deletions. It is shown how to test at any time whether two vertices belong to the same 2-edge-connected component, and how to insert and delete an edge in O(m2/3) time in the worst case, where m is the current number of edges in the graph. This answers a question posed by Westbrook and Tarjan [Tech. Report CS-TR-229-89, Dept. of Computer Science, Princeton University, Princeton, NJ, August 1989;Algorithmica, to appear]. For planar graphs, the paper presents algorithms that support all these operations in O(square-root n log log n) worst-case time each, where n is the total number of vertices in the graph.
We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely t...
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We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m --> infinity asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.
The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of proble...
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The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In this paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key inn lists takes timeO(logN +n log logN) and an insertion or deletion takes timeO(log logN). HereN is the total size of all lists. If only insertions or deletions have to be supported theO(log logN) factor reduces toO(1). As an application we show that queries, insertions, and deletions into segment trees or range trees can be supported in timeO(logn log logn), whenn is the number of segments (points).
Point location is a fundamental primitive in Computational Geometry. In the plane it is stated as follows: Given a subdivision ℛ of the plane and a query point q , determine the region of ℛ containing q . We survey th...
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Point location is a fundamental primitive in Computational Geometry. In the plane it is stated as follows: Given a subdivision ℛ of the plane and a query point q , determine the region of ℛ containing q . We survey the work that has led to practical algorithms for the static version of the problem, and discuss current research on the corresponding dynamic algorithms.
Several center location problems on general networks and even on tree networks are nonconvex. Known solution procedures are based on decomposing the problem into subproblems, finding each one of the local solutions in...
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Several center location problems on general networks and even on tree networks are nonconvex. Known solution procedures are based on decomposing the problem into subproblems, finding each one of the local solutions independently, and then selecting among them the best solution. The purpose of this paper is to demonstrate that for some location models, it is possible to take advantage and use information that is common to certain subproblems in order to obtain better complexity bounds. The main tool implemented is a dynamicdata structure that is used to maintain the objective (dynamically) as we move from one subproblem to the next.
In this paper a dynamic technique for locating a point in a monotone planar subdivision, whose current number of vertices is n, is presented. The (complete set of) update operations are insertion of a point on an edge...
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