On time-space trade-offs in dynamic graph pebbling

Abstract

Pebble game on dynamic graphs is studied as an abstract model for the incremental computations. We investigate how the time T and/or the space S is changing according to the number m of insert-edge/delete-edge operations on directed acyclic graphs of size n. Time-space trade-off of the form T = Θ (n2/S+m) is given for standard pebble game on permutation graphs, In the case of the minimal space pebbling an extreme (superpolynomial) explosion of the time is related to the unit change of the graph size, If the space is from a small interval then a superpolynomial time increase is also achieved relative to the small (slowly increasing) change of the graph size.