We introduce and analyze a method to reduce the search cost in tries. Traditional trie structures use branching factors at the nodes that are either fixed or a function of the number of elements. Instead, we let the distribution of the elements guide the choice of branching factors. This is accomplished in a strikingly simple way: in a binary trie, the i highest complete levels are replaced by a single node of degree 2i; the compression is repeated in the subtries. This structure, the level-compressed trie, inherits the good properties of binary tries with respect to neighbour and range searches, while the external path length is significantly decreased. It also has the advantage of being easy to implement. Our analysis shows that the expected depth of a stored element is \Theta (log \Lambda n) for uniformly distributed data.

We consider the 2-dimensional range searching problem in the case where all point lie on an integer grid. A new data structure is preented that solves range queries on a U U grid in O(k + loglog U) time using O(n log n) storage, where n is the number of points and k the number of reported answers. Although the query

fast pattern matching queries. The scheme provides a general framework for representing information about repetitions, i.e., multiple occurrences of the same string in the text, and for using the information in pattern matching. Well-known text indexes, such as suffix trees, suffix arrays, DAWGs and their variations, which we collectively call suffix indexes, can be seen as instances of the scheme.

In this paper we consider solutions to the dictionary problem on AC RAMs, i.e.

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...

In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N) space [E77].

) Paolo Ferragina 1 and S. Muthukrishnan 2 1 Dipartimento di Informatica, Universit`a di Pisa, Italy. ferragin@di.unipi.it 2 Dept. of Computer Science, Univ. of Warwick, UK. muthu@dcs.warwick.ac.uk 1 Introduction We consider the following dynamic data structural problem. We are given a rooted tree of n nodes and a set f1; 2; : : :; Cg of colors. Each node u has a subset of these colors, say of size d u , and P u du = D. Note D C. The problem is to dynamically maintain this tree under updates, that is, insert(p; c) and delete(p; c) operations, and answer find(p; c) queries. The operations insert(p; c) and delete(p; c) respectively add and remove the color c from the node pointed to by pointer p (the tree does not change topology under these dynamic operations). The find(p; c) query returns the nearest ancestor, if any, of the node pointed to by p (possibly that node itself) which has the color c, 1 c C. If no such ancestor exists, Find(p; c) returns Null. We call this the...

Abstract. In this paper, we present an experimental study of the spacetime tradeoffs for the dictionary problem, where we design a data structure to represent set data, which consist of a subset S of n items out of a universe U = {0, 1,...,u − 1} supporting various queries on S. Our primary goal is to reduce the space required for such a dictionary data structure. Many compression schemes have been developed for dictionaries, which fall generally in the categories of combinatorial encodings and data-aware methods and still support queries efficiently. We show that for many (real-world) datasets, data-aware methods lead to a worthwhile compression over combinatorial methods. Additionally, we design a new data-aware building block structure called BSGAP that presents improvements over other data-aware methods. 1

Some previously proposed algorithms are re-examined. They were designed to find all sets in a collection that have no subset in the collection, but are easily modified to find all sets that have no supersets. One is shown to have a worst-case running-time of O(N 2 = log N ), where N is the sum of the sizes of all the sets. This is lower than the only previously known sub-quadratic worst-case upper bound for this problem. Key words: Analysis of algorithms, set-theoretic algorithms, extremal sets. 1 Introduction Yellin and Jutla [3] tackled the following fundamental problem, for some applications of which see [2]. Given is a collection F = fS 1 ; : : : ; S k g, where each S i is a set over the same domain. A set is a minimal (resp. maximal) set of F iff it has no strict subset (resp. superset) in F . Find the extremal sets of F , i.e., those that are minimal or maximal. With the problem size chosen as N = P i S i , Yellin and Jutla presented an abstract algorithm that requires O(N ...

We consider a problem that arises during the propagation of subscriptions in a content-based publish-subscribe system. Subscription covering is a promising optimization that reduces the number of subscriptions propagated, and hence the size of routing tables in a content-based publish-subscribe system. However, detecting covering relationships among subscriptions can be an expensive computational task that potentially reduces the utility of covering as an optimization. We introduce an alternate approach approximate subscription covering, which provide much of the benefits of subscription covering at a fraction of its cost. By forgoing an exhaustive search for covering subscriptions in favor of an approximate search, it is shown that the time complexity of covering detection can be dramatically reduced. The trade off between efficiency of covering detection and the approximation error is demonstrated through the analysis of indexes for multi-attribute subscriptions based on space filling curves. 1