Graph-based seed scheduling for out-of-core FTLE and pathline computation

As the size of scientific data sets continues to increase, performing effective data analysis and visualization becomes increasingly difficult. Desktop machines, still the scientists´ favorite platform to perform analysis and visualization computation, usually do not have enough memory to load the entire data set all at once. For time-varying flow visualization, the Finite-Time Lyapunov Exponent (FTLE) allows one to glean insight into the existence of the Lagrangian Coherence Structures (LCS) by quantifying the separation of flows. To obtain high resolution FTLE fields, the computation of FTLE requires tracing particles from every grid point and at every time step. Because the size of the time-varying flow data can easily exceed the amount of available memory in the desktop machines, efficient out-of-core FTLE computation algorithms that minimize the I/O overhead are very much needed. To tackle this problem, one can perform a batch mode computation of particle tracing where the particles are organized into different groups, and at any time only one group of particles are advected in the time-varying field. Since tracing particles requires loading the necessary data blocks on demand along the flow paths, to maximize the usage of the data and minimize the I/O cost, an effective scheduling of particles becomes essential. The main challenge is to avoid reloading the same data blocks that were previously processed. In this paper, to solve the problem we model the flow as a directed weighted graph and predict the access dependency among the data blocks, i.e., the path of particles, using Markov chain. With the predicted path we devise an optimization method that groups the particles into different processing batches to minimize the total number of block accesses from the disk. Experimental results show that our scheduling algorithm performs better than algorithms based on a general space-filling ordering.