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A lower bound for area-universal graphs

MPG-Autoren

Bilardi,  Gianfranco
Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44233

Chaudhuri,  Shiva
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Dubhashi,  Devdatt
Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Zitation

Bilardi, G., Chaudhuri, S., Dubhashi, D., & Mehlhorn, K. (1994). A lower bound for area-universal graphs. Information Processing Letters, 51, 101-105.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0014-AD3C-6
Zusammenfassung
We establish a lower bound on the efficiency of rea--universal circuits. The area A u of every graph H that can host any graph G of area (at most) A with dilation d, and congestion c p A= log log A satisfies the tradeoff A u = OmegaGamma A log A=(c 2 log(2d))): In particular, if A u = O(A) then max(c; d) = OmegaGamma p log A= log log A). 1 Introduction Bay and Bilardi [2] showed that there is a graph H which can be laid out in area O(A) and into which any graph G of area at most A can be embedded with load 1, and dilation and congestion O(log A). As a consequence, they showed the existence of an area O(A) VLSI circuit that can simulate any area A circuit with a slowdown of O(log A). This note explores the feasibility of more efficient embeddings. Our main result is Theorem 5 which establishes a limitation relating the area of a universal graph to the parameters of the embedding. Informally, it asserts that any circuit which is universal for a family of graphs of area A, a...