 We settle this question by proving that computing \lambda_\infty is indeed NP-hard . Additionally, we use our techniques to prove NP-hardness of computing the spread constant (of a graph) \emph{  , a geometric measure  introduced by Alon, Boppana, and Spencer, in the context of deriving an asymptotic isoperimetric inequality on cartesian products of graphs.
<meaning-changed>  We settle this question by proving that computing \lambda_\infty is indeed NP-hard . Additionally, we use our techniques to prove NP-hardness of computing the spread constant (of a graph) \emph{  , a geometric measure  introduced by Alon, Boppana, and Spencer, in the context of deriving an asymptotic isoperimetric inequality on cartesian products of graphs.
 We settle this question by proving that computing \lambda_\infty is indeed NP-hard , even for weighted trees. Our gadget further proves NP-hardness of computing the spread constant (of a graph) \emph{ , a geometric measure introduced by Alon, Boppana, and Spencer, in the context of deriving an asymptotic isoperimetric inequality on cartesian products of graphs.