Asymptotically tight bounds on time-space trade-offs in a pebble game

Asymptotically Ught tune-space trade-offs for pebblmg three d~fferent classes of directed aeychc graphs are derived Let N be the size of the graph, S the number of avadable pebbles, and T the time necessary for pebbling the graph A time-space trade-off of the form ST = O(N 2) ls proved for pebbhng (usmg only black pebbles) a specml class of permutaaon graphs that tmplement the bR-reversal permutation. If we are allowed to use black and whtte pebbles~ the time-space trade-off is shown to be of the form (:) r = o T¢ +0(~ . A tune-space trade-off of the form /N\OIN/S~ T= S O I ~ ) ~s proved for pebbling a class of graphs constructed by stacking superconcentrators m series. This tunespace trade-off holds whether we use only black or black and white pebbles A tune-space trade-off of the form T -$2 2°~N/s) Is proved for the class of all directed acychc graphs This trade-off also holds whether we use only black or black and white pebbles

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