Upper and lower bounds on time-space tradeoffs
Thomas Lengauer, Robert Endre Tarjan · 1979
This paper derives asymptotically tight bounds on the time-space tradeoffs for pebbling three 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 = t(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 t(N/S)t(N/S) is proved for a class of graphs constructed by stacking superconcentrators in series. (c) A time-space tradeoff of the form T = S.22t(N/S)is proved for pebbling general directed acyclic graphs.