Book•
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.
Citations
More filters
15 Jul 1985
TL;DR: This paper investigates the other two cases of intermediate-length keys and confirms the inherent validity of the bounds for short and long keys by exhibiting optimal or near-optimal VLSI networks.
Abstract: Recently discovered lower bounds for the area-time complexity of VLSI sorting of n k -bit keys exhibit a dependence upon the key length. On this basis, keys can be classified into short (k ≤logn), long (k ≥logn) and intermediate-length. Intermediate-length keys have been heretofore the object of investigation; this paper investigates the other two cases and confirms the inherent validity of the bounds for short and long keys by exhibiting optimal or near-optimal VLSI networks.
16 citations
01 Apr 1991
TL;DR: In this paper, the principles of inductive fault analysis (IFA), a technique for the determination of a list of the possible faults in an integrated circuit, ranked according to their probability of occurrence, are reviewed and criticised.
Abstract: The principles of inductive fault analysis (IFA), a technique for the determination of a list of the possible faults in an integrated circuit, ranked according to their probability of occurrence, are reviewed and criticised. It is pointed out that IFA should be upgraded to achieve reasonable flexibility in dealing with different MOS technologies and that the Monte Carlo approach, used for determination of fault probabilities, cannot practically provide reliable fault ranking. A possible approach to more algorithmic and less technology-dependent IFA and an alternative to the Monte Carlo method for evaluation of fault probabilities are discussed, together with a simple application example.
16 citations
TL;DR: Some efficient algorithms for the largest rectangle problem are presented that run in O ( nlogn + K ) time for all three problems and the worst-case running time is O (n 2 ) time.
16 citations
16 Jun 1994
TL;DR: A general lower bound on the book crossing number of any graph is derived and a second polynomial time algorithm is presented to generate a drawing of any graphs with O(m2/k2) many edge crossings.
Abstract: The paper introduces the book crossing number problem which can be viewed as a variant of the well-known plane and surface crossing number problem or as a generalization of the book embedding problem. The book crossing number of a graph G is defined as the minimum number of edge crossings when the vertices of G are placed on the spine of a k-page book and edges are drawn on pages, so that each edge is contained by one page. We present polynomial time algorithms for drawing graphs in books with small number of crossings. One algorithm is suitable for sparse graphs and gives a drawing in which the number of crossings is within a multiplicative factor of O(log2n) from the optimal one under certain conditions. Using these drawings we improve the best known upper bound on the rectilinear crossing number, provided that m≥4n. We also derive a general lower bound on the book crossing number of any graph and present a second polynomial time algorithm to generate a drawing of any graph with O(m2/k2) many edge crossings. This number of crossings is within a constant multiplicative factor from our general lower bound of Ω(m3/n2k2), provided that m=Θ(n2). For several classes of well-known graphs, we also sharpen our algorithmic upper bounds by giving specific drawings.
16 citations
TL;DR: An almost optimal bound is derived for the case of one-way communication when the functions function 1,....
Abstract: : we consider a situation where two processors P sub 1 and P sub 2 ar e to evaluate a collection of functions function 1,....,function 8 of two vector variables x, y, under the assumption that processor P sub 1 (respectively, P sub 2) has access only to the value of the variable x (respectively, y) and the functional form of function 1,....,function 8. We provide some new bounds on the communication complexity (the amount of information that has to be exchanged between the processors) for this problem. An almost optimal bound is derived for the case of one-way communication when the functions function 1,...., function 8 are polynomials. We also derive some new lower bounds for the case of two-way communication which improve on earlier bounds by Abelson A 80. As an application, we consider the case where x and y are n x n matrices and f(x,y) is a particular entry of the inverse of x + y. Under certain restriction on the class of allowed communication protocols, we obtain an omega(n squared) lower bound, in contrast to the omega(n) lower bound obtained by applying Abelson's results. Our results are based on certain tools from classical algebraic geometry and field extension theory.
16 citations
Cites methods from "Computational Aspects of Vlsi"
...A similar argument applies to computations using special purpose VLSI chips [U 84] in which communications capabilities are constrained by physical and topological considerations....
[...]