A lower bound for area-universal graphs

We establish a lower bound on the efficiency of area--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 $c \leq \sqrt{A}/\log\log A$ satisfies the tradeoff $$A_u = \Omega ( A \log A / (c^2 \log (2d)) ).$$ In particular, if $A_u = O(A)$ then $\max(c,d) = \Omega(\sqrt{\log A} / \log\log A)$

A lower bound for area-universal graphs

We establish a lower bound on the efficiency of area-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#<=##sq root#A/loglog A satisfies the tradeoff A_u #OMEGA#(A log A/(c"2log(2d))). In particular, if A_u = O(A) then max(c,d) #OMEGA#(#sq root#(logA)/loglog A)SIGLEAvailable from TIB Hannover: RR 1912(93-144)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Forschung und Technologie (BMFT), Bonn (Germany)DEGerman

A Lower Bound for Area-Universal Graphs

We establish a lower bound on the efficiency of area-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 = \Omega\Gamma A log A=(c 2 log(2d))): In particular, if A u = O(A) then max(c; d) = \Omega\Gamma p log A= log log A)