How to lay out arrays spared by rows and columns

Perhaps the most common fault tolerant architecture configures a nominal t×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×at array from a (1+b)t×(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 Θ(t^-1). ii) At constant proportion of failures, the area of homogeneous arrays is Θ(exp t), while that of dedicated sparing is Ω(exp t). iii) The worst-case wirelength of either architecture is Θ(ct). iv) The best-case wirelength Θ(1) of homogeneous sparing is less than that Θ(t) of dedicated sparing. V) Probabilisticaily, homogeneous sparing has O(log t) wirelength, less than that Θ(t) of dedicated sparing. For large t, moreover, row-column sparing is more costly than local sparing