An Optimal $O(\log \log N)$-Time Parallel Algorithm for Detecting all Squares in a String

An Optimal O(log log N)-Time Parallel Algorithm for Detecting All Squares in a String

An optimal O(loglogn) time concurrent-read concurrent-write parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm. When p processors are available the bounds become 0(fnl;gnl +loglogrl+p/n12p).

An Optimal O(log log n) Time Parallel String Matching Algorithm

An optimalO(log log n) time parallel algorithm for string matching on CRCWPRAM is presented. It improves previous results of [G] and [V].

An O(n log log n/ log n) Time Algorithm for the All-Pairs Shortest Path Problem

We design a faster algorithm for the all-pairs shortest path problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we improve the best known time complexity of O(n(log log n)/ logn) to O(n log log n/ log n). As an application, we show the k-maximum subarray problem can be solved in O(kn log log n/ log n) time for small k.

An O(log N) Parallel Time Exact Hidden-Line Algorithm

An O(n log log n)-Time Algorithm for Triangulating a Simple Polygon

Given a simple n-vertex polygon, the triangulation problem is to partition the interior of the polygon into n-2 triangles by adding n-3 nonintersecting diagonals. We propose an O(n log logn)-time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangu-lation is not as hard as sorting. Improved algorithms for several other computational geometry...