An Efficient Parallel Algorithm for the Longest Increasing Subsequence Problem on a LARPBS

In this paper, we give a parallel algorithm for the longest increasing subsequence problem on a LARPBS, one of the recently proposed parallel model based on optical bus. For a sequence of n integers, we solve the longest increasing subsequence problem in O(k) time using n processors where k is the length of the solution. Then, we give an algorithm for the maximal layers problem that runs in O(k+log(n)) time for a set of n points where k is the number of layers on a n-processor array. To our knowledge, this is the fastest algorithm for that problem.