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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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Journal ArticleDOI
TL;DR: A randomised approximation scheme for the permanent of a 0–1s presented, demonstrating that the matchings chain is rapidly mixing, apparently the first such result for a Markov chain with genuinely c...
Abstract: A randomised approximation scheme for the permanent of a 0–1s presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the graph. For a wide class of 0–1 matrices the approximation scheme is fully-polynomial, i.e., runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output. This class includes all dense matrices (those that contain sufficiently many 1’s) and almost all sparse matrices in some reasonable probabilistic model for 0–1 matrices of given density.For the approach sketched above to be computationally efficient, the Markov chain must be rapidly mixing: informally, it must converge in a short time to its stationary distribution. A major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing, apparently the first such result for a Markov chain with genuinely c...

878 citations

Journal ArticleDOI
David S. Johnson1
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.

857 citations


Cites background from "Computational Aspects of Vlsi"

  • ...Readers interested in learning more about area-time trade-offs in VLSI are directed to the substantial literature that now exists on the subject; for a start, see [18,19,26,27, 30 ,33,35]....

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Journal ArticleDOI
TL;DR: It is shown that any setF, which can support a Fáry embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.
Abstract: Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fary embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide anO(n) space,O(n logn) time algorithm to effect this embedding. The grid size is asymptotically optimal and it had been previously unknown whether one can always find a polynomial sized grid to support such an embedding. On the other hand we show that any setF, which can support a Fary embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.

755 citations

Book
Selim G. Akl1
01 Jan 1985
TL;DR: Kurskod av teknisk-naturvetenskapliga fakultetsnämnden Kursplan giltig från: 2012, vecka 10 Ansvarig enhet: Inst för datavetenskap SCB-ämnesrubrik: Informatik/Dataoch systemvetenskapskap Huvudområden och successiv fördjupning.
Abstract: Kurskod: 5DV050 Inrättad: 2008-03-31 Inrättad av: teknisk-naturvetenskapliga fakultetsnämnden Reviderad: 2012-02-29 Reviderad av: teknisk-naturvetenskapliga fakultetsnämnden Kursplan giltig från: 2012, vecka 10 Ansvarig enhet: Inst för datavetenskap SCB-ämnesrubrik: Informatik/Dataoch systemvetenskap Huvudområden och successiv fördjupning: Beräkningsteknik: Avancerad nivå, har endast kurs/er på grundnivå som förkunskapskrav (A1N) , Datavetenskap: Avancerad nivå, har endast kurs/er på grundnivå som förkunskapskrav (A1N) Betygsskala: För denna kurs ges betygen 5 Med beröm godkänd, 4 Icke utan beröm godkänd, 3 Godkänd, VG Väl godkänd, G Godkänd, U Underkänd Utbildningsnivå: Avancerad nivå

712 citations

Journal ArticleDOI
TL;DR: It is shown that the same technique used to prove that any VLSI implementation of a single output Boolean function has area-time complexity AT/sup 2/= Omega (n/Sup 2/) also proves that any OBDD representation of the function has Omega (c/sup n/) vertices for some c>1 but that the converse is not true.
Abstract: Lower-bound results on Boolean-function complexity under two different models are discussed. The first is an abstraction of tradeoffs between chip area and speed in very-large-scale-integrated (VLSI) circuits. The second is the ordered binary decision diagram (OBDD) representation used as a data structure for symbolically representing and manipulating Boolean functions. The lower bounds demonstrate the fundamental limitations of VLSI as an implementation medium, and that of the OBDD as a data structure. It is shown that the same technique used to prove that any VLSI implementation of a single output Boolean function has area-time complexity AT/sup 2/= Omega (n/sup 2/) also proves that any OBDD representation of the function has Omega (c/sup n/) vertices for some c>1 but that the converse is not true. An integer multiplier for word size n with outputs numbered 0 (least significant) through 2n-1 (most significant) is described. For the Boolean function representing either output i-1 or output 2n-i-1, where 1 >

566 citations


Cites background or methods from "Computational Aspects of Vlsi"

  • ...On a practical note, the area-time complexity could be reduced considerably by using carrysave adders and an H-tree layout [12]....

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  • ...In this model, and its various re nements [7, 9, 12], computation is viewed as the task of evaluating a Boolean function on a set of Boolean input values....

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