A parallel algorithm to compute the correlation dimension

A parallel algorithm is presented for computing the Correlation Dimension (D_2) from a time series generated by a dynamical system. The algorithm simultaneously gives the various correlation integrals needed to estimate the D_2. The parallelization is suitable for coarse-grained multiprocessor systems with distributed memory and is accomplished using a master-slave configuration. Two versions are implemented: the first for a message-passing environment and the second for a virtual shared memory environment. The algorithm is tested on a homogeneous cluster of workstations, consisting of four DEC Alpha 4/233 (233 MHz), interconnected by Ethernet. The Parasoft Express tool is used for version one, while version two is implemented using Network Linda. The algorithm is well balanced, gives a linear speed-up and allows efficient computation of D_2, even with a very high number of points.