Linear-time algorithms for computing a maximal increasing subsequence

The longest increasing subsequence is a fundamental problem which has been studied for a long time in computer science. In this paper, we consider the maximal increasing subsequence problem where the constraint is released from the longest to the maximal. For two kinds of increasing (monotone increasing and strictly increasing), we propose linear-time algorithms computing a maximal increasing subsequence of an input sequence from an alphabet . Our algorithm for computing a maximal monotone increasing subsequence requires space and our algorithm for computing a maximal strictly increasing subsequence requires space.