Brief Announcement: Approximating the I/O Complexity of One-Shot Red-Blue Pebbling

Abstract

Red-blue pebbling is a model of computation that captures the complexity of I/O operations in systems with external memory access. We focus on one-shot pebbling strategies, that is without re-computation. Prior work on this model has focused on finding upper and lower bounds on the I/O complexity of certain families of graphs. We give a polynomial-time bi-criteria approximation algorithm for this problem for graphs with bounded out-degree. More precisely, given a n-vertex DAG that admits a pebbling strategy with R red pebbles and I/O complexity opt, our algorithm outputs a strategy using O(R ⋅ log3/2 n) red pebbles, and I/O complexity O(opt ⋅ log3/2 n). We further extend our result to the generalization of red-blue pebble games that correspond to multi-level memory hierarchies. Finally, we complement our theoretical analysis with an experimental evaluation of our algorithm for red-blue pebbling.