Efficient pebbling for list traversal synopses with application to program rollback |
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Authors: | Yossi Matias Ely Porat |
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Affiliation: | 1. School of Computer Science, Tel Aviv University and Google Inc, Tel Aviv, Israel;2. Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel |
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Abstract: | We show how to support efficient back traversal in a unidirectional list, using small memory and with essentially no slowdown in forward steps. Using O(lgn) memory for a list of size n, the i’th back-step from the farthest point reached so far takes O(lgi) time in the worst case, while the overhead per forward step is at most ? for arbitrary small constant ?>0. An arbitrary sequence of forward and back steps is allowed. A full trade-off between memory usage and time per back-step is presented: k vs. kn1/k and vice versa. Our algorithms are based on a novel pebbling technique which moves pebbles on a virtual binary, or n1/k-ary, tree that can only be traversed in a pre-order fashion. |
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