Optimal Algorithms for Generalized Matrix Search Problem

We present a set of optimal and asymptotically optimal sequential and parallel algorith ms for the problem of searching on an m n sorted matrix m n Our two sequential algo rithms have a time complexity ofO m log n m which is shown to be optimal Our parallel algorithm runs in O log logm log logm log n m z time usingm log logm log logm processors on a COMMON CRCW PRAM where z is a monotonically decreasing function on m which is asymptotically work optimal The two sequential algorithms di er 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