How to lay out arrays spared by rows and columns

Abstract

Perhaps the most common fault tolerant architecture configures a nominal t/spl times/at array using bt dedicated spare rows and ct dedicated spare columns. We counterexample an outstanding conjecture by constructively showing how dedicated sparing can be laid out in area proportional to the number of elements. However, we find that dedicated sparing is more costly than homogeneous extraction of a t/spl times/at array from a (1+b)t/spl times/(a+c)t array. i) In the presence of failures whose distribution is worst-case, iid, or clustered, the fault tolerance of either architecture is /spl Theta/(t/sup -1/). ii) At constant proportion of failures, the area of homogeneous arrays is /spl Theta/(exp t), while that of dedicated sparing is /spl Omega/(exp t). iii) The worst-case wirelength of either architecture is /spl Theta/(ct). iv) The best-case wirelength /spl Theta/(1) of homogeneous sparing is less than that /spl Theta/(t) of dedicated sparing. V) Probabilisticaily, homogeneous sparing has O(log t) wirelength, less than that /spl Theta/(t) of dedicated sparing. For large t, moreover, row-column sparing is more costly than local sparing.