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.
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01 Jan 1986
3 citations
16 Aug 1993
TL;DR: The main focus of the paper is on meshes of tree due to their importance as parallel architectures and shows that maximum level of system utilization can be obtained when each host node emulates an equal number of "busy" guest nodes for each step of computation.
Abstract: The ability to embed arbitrarily large graphs in smaller graphs has important applications in mapping problems which require more processors than is available in a parallel architecture. We address this problem with the main focus on balancing processor loads. We show that maximum level of system utilization can be obtained when each host node emulates an equal number of "busy" guest nodes for each step of computation. While the embedding methods used are applicable to a variety of guest graphs, the main focus of the paper is on meshes of tree due to their importance as parallel architectures. Methods are also developed for embedding arbitrarily large complete binary trees and grids.
3 citations
TL;DR: This work defines and illustrates edge grammars and analyzes them in the context of formal language theory and results include hierarchy and decidability properties.
3 citations
Dissertation•
14 Jun 2017
TL;DR: This thesis gives some new results on planar non-aligned drawings and the enumeration of planar Eulerian orientations, and proves that for every maximal planar graph, $G$ of order $n$, $gamma_P(G) leq frac{n-2}{4}$, and gives a constructive algorithm.
Abstract: In this thesis, we present results on three different problems concerning planar graphs.We first give some new results on planar non-aligned drawings, i.e. planar grid drawings where vertices are all on different rows and columns.We show that not every planar graph has a non-aligned drawing on an $n times n$-grid, but we present two algorithms generating a non-aligned polyline drawings on such a grid requiring either $n-3$ or $min(frac{2n-3}{5},$ $#{text{separating triangles}}+1)$ bends in total.Concerning non-minimal grids, we give two algorithms drawing a planar non-aligned drawing on grids with area of order $n^4$. We also give specific results for 4-connected graphs and nested-triangle graphs.The second topic is power domination in planar graphs. We present a family of graphs with power dominating number $gamma_P$ at least $frac{n}{6}$. We then prove that for every maximal planar graph $G$ of order $n$, $gamma_P(G) leq frac{n-2}{4}$, and we give a constructive algorithm.We also prove that for triangular grids $T_k$ of dimension $k$ with hexagonal-shape border, $frac{k}{3} - frac{1}{6} leq gamma_P(T_k) leq lceil frac{k}{3} rceil$.Finally, we focus on the enumeration of planar Eulerian orientations. After proposing a new decomposition for these maps, we define subsets and supersets of planar Eulerian orientations with parameter $k$, generated by looking at the orientations of the last $2k-1$ edges around the root vertex.For each set, we give a system of functional equations defining its generating function, and we prove that it is always algebraic.This way, we show that the growth rate of planar Eulerian orientations is between 11.56 and 13.005.
3 citations
TL;DR: This paper investigates the relative economies of extended and ordinary regular expressions and shows that there is a size n expression with Boolean variables which is not equivalent to any ordinary regular expression of size less than a double exponential function of n.
3 citations