We introduce data-structural bootstrapping, a technique to design data structures recursively, and use it to design confluently persistent deques. Our data structure requires O(log 3 k) worstcase time and space per deletion, where k is the total number of deque operations, and constant worst-case time and space for other operations. Further, the data structure allows a purely functional implementation, with no side effects. This improves a previous result of Driscoll, Sleator, and Tarjan. 1 An extended abstract of this paper was presented at the 4th ACM-SIAM Symposium on Discrete Algorithms, 1993. 2 Supported by a Fannie and John Hertz Foundation fellowship, National Science Foundation Grant No. CCR-8920505, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) under NSF-STC88-09648. 3 Also affiliated with NEC Research Institute, 4 Independence Way, Princeton, NJ 08540. Research at Princeton University partially supported by the National Science Foundatio...

Let S be a set whose items are sorted with respect to d ? 1 total orders OE 1 ; : : : ; OE d , and which is subject to dynamic operations, such as insertions of a single item, deletions of a single item, split and concatenate operations performed according to any chosen order OE i (1 i d). This generalizes to dimension d ? 1 the notion of concatenable data structures, such as the 2-3-trees, which support splits and concatenates under a single total order. The main contribution of this paper is a general and novel technique for solving order decomposable problems on S, which yields new and efficient concatenable data structures for dimension d ? 1. By using our technique we maintain S with the following time bounds: O(log n) for the insertion or the deletion of a single item, where n is the number of items currently in S; O(n 1\Gamma1=d ) for splits and concatenates along any order, and for rectangular range queries. The space required is O(n). We provide several applications of ...

Abstract. The relative worst order ratio, a new measure for the quality of on-line algorithms, was recently defined and applied to two bin packing problems. Here, we apply it to the paging problem. Work in progress by various researchers shows that the measure gives interesting results and new separations for bin coloring, scheduling, and seat reservation problems as well. Using the relative worst order ratio, we obtain the following results: We devise a new deterministic paging algorithm, Retrospective-LRU, and show that it performs better than LRU. This is supported by experimental results, but contrasts with the competitive ratio. All deterministic marking algorithms have the same competitive ratio, but here we find that LRU is better than FWF. No deterministic marking algorithm can be significantly better than LRU, but the randomized algorithm MARK is better than LRU. Finally, look-ahead is shown to be a significant advantage, in contrast to the competitive ratio, which does not reflect that look-ahead can be helpful. 1

This paper provides a novel approach for optimal route planning making efficient use of the underlying geometrical structure. It combines classical AI exploration with computational geometry. Given a set

We shall focus on the following three problems in data structures 1. The Union-find problem. 2. Constructing optimal alphabetic binary trees. 3. The suffix tree. Depending upon the number of students participating we may touch other topics as well.

When reservations are made to for instance a train, it is an on-line problem to accept or reject, i.e., decide if a person can be fitted in given all earlier reservations. However, determining a seating arrangement, implying that it is safe to accept, is an off-line problem with the earlier reservations and the current one as input. We develop algorithms with optimal running time to handle problems of this nature.