Graph pebbling with many free pebbles can be difficult

Abstract

The pebble game on directed acyclic graphs can be used to model the space-time tradeoff behavior of a straight-line algorithm (SLA). In this game, the maximum number of pebbles used at any one time corresponds to the number of temporary registers available and is called space. The number of moves made to reach the outputs of the graph, or the time, corresponds to the number of operations required by the SLA. In this paper, it is shown that there exist infinite families of constructible graphs on N nodes which possess an extreme time-space tradeoff. For a particular set of graphs, if space is restricted to fall in the range of T(log N) to T((