Efficient graph algorithms on a linear array with a reconfigurable pipelined bus system

We present efficient algorithms for solving several fundamental graph theoretic problems on a Linear Array with a Reconfigurable Pipelined BUS System (LARPBS), one of the recently proposed models of computation based on optical buses. Our algorithms include finding connected components, minimum spanning forest, biconnected components, bridges and articulation points for an undirected graph. We complete the connected components and minimum spanning forest of a graph in O(log n) time using O(m+n) processors where m and n are the number of edges and vertices in the graph and m=O(n²) for a dense graph. Both the processor and time complexities of these two algorithms match the complexities of algorithms on the Arbitrary and Priority CRCW PRAM models which are two of the strongest PRAM models. The previous best algorithms by Li et al. for these two problems on the LARPBS require O(log n) time and O(n³/log n) processors. Our algorithms for computing biconnected components, bridges and articulation points of an undirected graph run in O(log n) time on an LARPBS with O(n²) processors. No previous algorithms were known for these latter problems on the LARPBS