Upper and lower bounds on time-space tradeoffs

This paper derives asymptotically tight hounds on the time-space tradeoffs for pebbling tnree different classes of directed acyclic graphs. Let N be the size of the graph, S the number of available pebbles, and T the time necessary for pebbling the graph. (a) A time space tradeoff of the form ST = 9(N2) is proved for a special class of permutation graphs which implement the bit reversal permutation. (b) A time-space tradeoff of the form T = s e(N/s)8N/s is proved for a class of graphs constructed by stacking superconcentrators in series. (c) A time-space tradeoff of the form 2e(w/s) T = S-2 is proved for pebbling general directed acyclic graphs.