The optical bus based arrays have recently shown many applications. In this paper we use the pipelining ability of the LARPBS to solve the repetitions detection problem. We propose an algorithm that finds all kind of repetitions in a string including k-power repetitions, overlapping repetitions and non-contiguous repetitions. For a given distance, this operation is performed in O(1) communication cycle with a constant computation time processors on a O(n) processors LARPBS for a string of length n. For all the periods, it is O(n) bus cycle. No previous algorithms were known for this problem on the LARPBS.

The reconfigurable mesh is a processor array that consists processors arranged in 1-dimensional or 2dimensional grids with a reconfigurable bus system. The main contribution of this paper is to show initialization algorithms on the 1-dimensional reconfigurable mesh with Ò processors. We assume that processors are identical, and does not have unique IDs. Initialization is a task that assigns sequential IDs to processors in the reconfigurable mesh. We first show a simple deterministic initialization algorithm for the 1-dimensional reconfigurable mesh that runs in Ç´Òµ time. This deterministic algorithm is optimal, because no deterministic solution can perform initialization in less than Ç´Òµ time. Quite surprisingly, we show that expected sublinear-time initialization is possible if we use randomized techniques. Our initialization algorithm runs in Ç´´ÐÓ Ò· Ð Ó µ ÐÓ ÐÓ Òµ time with probability at least ½ ½ for every real number ½. It follows that the initialization algorithm runs in expected Ç´ÐÓ Ò ÐÓ ÐÓ Òµ time.We also proved that any randomized initialization need to run in ª´ÐÓ Òµ time. Thus, our randomized initialization algorithm running in Ç´ÐÓ Ò ÐÓ ÐÓ Òµ time is very close to a theoretical lower bound ª´ÐÓ Òµ time.

No abstract