A bounded-space tree traversal algorithm
Information Processing Letters
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Backing up in singly linked lists
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Reducing sweep time for a nearly empty heap
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An efficient machine-independent procedure for garbage collection in various list structures
Communications of the ACM
Advances in Pebbling (Preliminary Version)
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Alias Types for Recursive Data Structures
TIC '00 Selected papers from the Third International Workshop on Types in Compilation
Backing up in singly linked lists
Journal of the ACM (JACM)
Efficient pebbling for list traversal synopses with application to program rollback
Theoretical Computer Science
LTS: the list-traversal synopses system
NGITS'06 Proceedings of the 6th international conference on Next Generation Information Technologies and Systems
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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(lg n) memory for a list of size n, the i'th back-step from the farthest point reached so far takes O(lg i) time worst case, while the overhead per forward step is at most epsilon for arbitrary small constant Ɛ 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 algorithm is based on a novel pebbling technique which moves pebbles on a "virtual binary tree" that can only be traversed in a pre-order fashion. The list traversal synopsis extends to general directed graphs, and has other interesting applications, including memory efficient hash-chain implementation. Perhaps the most surprising application is in showing that for any program, arbitrary rollback steps can be efficiently supported with small overhead in memory, and marginal overhead in its ordinary execution. More concretely: Let P be a program that runs for at most T steps, using memory of size M. Then, at the cost of recording the input used by the program, and increasing the memory by a factor of O(lg T) to O(M lg T), the program P can be extended to support an arbitrary sequence of forward execution and rollback steps, as follows. The i'th rollback step takes O(lg i) time in the worst case, while forward steps take O(1) time in the worst case, and 1 + Ɛ amortized time per step.