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Computational Aspects of Vlsi
01 Jan 1984-
About: The article was published on 1984-01-01 and is currently open access. It has received 862 citations till now. The article focuses on the topics: Very-large-scale integration.
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TL;DR: For each of the heuristics described, there exist classes of n-vertex, m-edge graphs which force it to obtain a number of crossings which is a function of n or m when the optimal number is a small constant.
Abstract: The worst-case performances of some heuristics for the fixed linear crossing number problem (FLCNP) are analyzed. FLCNP is similar to the 2-page book crossing number problem in which the vertices of a graph are optimally placed on a horizontal "node line" in the plane, each edge is drawn as an arc in one half-plane (page), and the objective is to minimize the number of edge crossings. In FLCNP, the order of the vertices along the node line is predetermined and fixed. FLCNP belongs to the class of NP-hard optimization problems Masuda et al., 1990. In this paper we show that for each of the heuristics described, there exist classes of n-vertex, m-edge graphs which force it to obtain a number of crossings which is a function of n or m when the optimal number is a small constant. This leaves open the problem of finding a heuristic with a constant error bound for the problem.
12 citations
Cites background from "Computational Aspects of Vlsi"
...Some examples of linear layout problems are the bandwith problem (Chinn et al., 1982), the book thickness problem (Bernhart and Kainen, 1979; Kainen, 1990), the pagenumber problem (Chung, Leighton, and Rosenberg, 1987; Malitz, 1994), the boundary VLSI layout problem ( Ullman, 1984 ), and the single row routing problem (Raghavan and Sahni, 1983)....
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TL;DR: In this article, a brief description of these problems are made in terms of their denitions, followed by a comparative study of them, using both approaches: matrix geometry and graph theory.
Abstract: The bandwidth, average bandwidth, envelope, prole and antibandwidth of the matrices have been the subjects of study for at least 45 years. These problems have generated considerable interest over the years because of them practical relevance in ar- eas like: solving the system of equations, nite element methods, circuit design, hypertext layout, chemical kinetics, numerical geo- physics etc. In this paper a brief description of these problems are made in terms of their denitions, followed by a comparative study of them, using both approaches: matrix geometry and graph theory. Time evolution of the corresponding algorithms as well as a short description of them are made. The work also contains concrete real applications for which a large part of presented al- gorithms were developed.
12 citations
TL;DR: Bounded broadcast is explored whereby an element of a processor array can broadcast to a bounded number of other processors, resulting in time complexities that are smaller than those reported previously.
Abstract: Much work has been done on the problem of synthesizing a processor array from a system of recurrence equations. Some researchers limit communication to nearest neighbors in the array; others use broadcast. In many cases, neither of the above approaches result in an optimal execution time. In this paper a technique called bounded broadcast is explored whereby an element of a processor array can broadcast to a bounded number of other processors. This technique is applied to the problems of transitive closure and all-pairs shortest distance, resulting in time complexities that are smaller than those reported previously. In general, the technique can be used to design bounded broadcast systolic arrays for algorithms whose implementation can benefit from broadcasting.
11 citations
TL;DR: The notion of communication slowdown as a measure of the total communication overhead incurred by a parallel computation is introduced and concluded that significant performance gains can be realized when the mapping is sensitive to the flow control scheme of the target architecture.
Abstract: We address the problem of mapping divide-and-conquer programs to mesh connected multicomputers with wormhole or store-and-forward routing. We propose the binomial tree as an efficient model of parallel divide-and-conquer and present two mappings of the binomial tree to the 2D mesh. Our mappings exploit regularity in the communication structure of the divide-and-conquer computation and are also sensitive to the underlying flow control scheme of the target architecture. We evaluate these mappings using new metrics which are extensions of the classical notions of dilation and contention. We introduce the notion of communication slowdown as a measure of the total communication overhead incurred by a parallel computation. We conclude that significant performance gains can be realized when the mapping is sensitive to the flow control scheme of the target architecture.
11 citations
TL;DR: O(kv/) algorithms are obtained for the case that one matrix is a general sparse matrix with at most kn nonzero elements and the other matrix has at most k non zero elements in every row or in every column.
Abstract: Algorithms for multiplying several types of sparse n x n-matrices on dynamically reconfigurable n n-arrays are presented. For some classes of sparse matrices constant time algorithms are given, e.g., when the first matrix has at most kn elements in each column or in each row and the second matrix has at most kn nonzero elements in each row, where k is a constant. Moreover, O(kv/) algorithms are obtained for the case that one matrix is a general sparse matrix with at most kn nonzero elements and the other matrix has at most k nonzero elements in every row or in every column. Also a lower bound off(x/) is proved for thisand other cases which shows that the algorithms are close to the optimum.
11 citations