Abstract
We present a set of optimal and asymptotically optimal sequential and parallel algorithms for the problem of searching on an m × n sorted matrix in the general case when m⩽ n. Our two sequential algorithms have a time complexity of O(m log( 2n m )) which is shown to be optimal. Our parallel algorithm runs in O( log( log m log log m ) log ( 2n m 1−z )) time using m/ log( log m log log m ) processors on a COMMON CRCW PRAM, where 0 ⩽ z < 1 is a monotonically decreasing function on m, which is asymptotically work-optimal. The two sequential algorithms differ mainly in the ways of matrix partitioning: one uses row-searching and the other applies diagonal-searching. The parallel algorithm is based on some non-trivial matrix partitioning and processor allocation schemes. All the proposed algorithms can be easily generalized for searching on a set of sorted matrices.
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