Max-Throughput for (Conservative) k-of-n Testing

We define a variant of $$k$$k-of-$$n$$n testing that we call conservative$$k$$k-of-$$n$$n testing. We present a polynomial-time, combinatorial algorithm for the problem of maximizing throughput of conservative $$k$$k-of-$$n$$n testing, in a parallel setting. This extends previous work of Condon et al. and Kodialam who presented combinatorial algorithms for parallel pipelined filter ordering, which is the special case where $$k=1$$k=1 (or $$k=n$$k=n). We also give a polynomial-time algorithm for maximizing throughput for standard$$k$$k-of-$$n$$n testing, based on the ellipsoid method, using previous techniques.