Showing papers by "Gerth Stølting Brodal published in 2000"
01 Feb 2000
TL;DR: A data structure that supports insertions and deletions of characters and movements of arbitrary large blocks within a text in O(log~nloglognlog*n) time per operation and an ingredient in the solution is a data structure for the dynamic string equality problem introduced by Mehlhorn, Sundar and Uhrig.
Abstract: Pattern matching is the problem of finding all occurrences of a pattern in a text. In a dynamic setting the problem is to support pattern matching in a text which can be manipulated on-line, i.e., the usual situation in text editing. We present a data structure that supports insertions and deletions of characters and movements of arbitrary large blocks within a text in O(log~nloglognlog*n) time per operation. Furthermore a search for a pattern P in the text is supported in time O(lognloglogn + oct + [PI), where occ is the number of occurrences to be reported. An ingredient in our solution to the above main result is a data structure for the dynamic string equality problem introduced by Mehlhorn, Sundar and Uhrig. As a secondary result we give almost quadratic better time bounds for this problem which in addition to keeping polylogarithmic factors low for our main result also improves the complexity for several other problems.
84 citations
05 Jul 2000
TL;DR: An improved algorithm for the problem of computing a minimum spanning tree of a general graph is developed, as well as new algorithms for the single source shortest paths and the multi-way graph separation problems on planar graphs.
Abstract: Recently external memory graph algorithms have received considerable attention because massive graphs arise naturally in many applications involving massive data sets. Even though a large number of I/O-efficient graph algorithms have been developed, a number of fundamental problems still remain open. In this paper we develop an improved algorithm for the problem of computing a minimum spanning tree of a general graph, as well as new algorithms for the single source shortest paths and the multi-way graph separation problems on planar graphs.
78 citations
01 Jan 2000
TL;DR: In this article, the authors presented methods for finding all maximal pairs with gap in an upper and lower bounded interval in time O(n log n+z) where z is the number of reported pairs.
Abstract: A pair in a string is the occurrence of the same substring twice. A pair is maximal if the two occurrences of the substring cannot be extended to the left and right without making them different. The gap of a pair is the number of characters between the two occurrences of the substring. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length n we can find all maximal pairs with gap in an upper and lower bounded interval in time O(n log n+z) where z is the number of reported pairs. If the upper bound is removed the time reduces to O(n+z). Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats.
66 citations
21 Jun 2000
TL;DR: This paper gives an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log n) and space O( n).
Abstract: Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic substring and gave an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log2 n) In this paper we give an algorithm that finds all maximal quasiperiodic substrings in a string of length n in time O(n log n) and space O(n) Our algorithm uses the suffix tree as the fundamental data structure combined with efficient methods for merging and performing multiple searches in search trees Besides finding all maximal quasiperiodic substrings, our algorithm also marks the nodes in the suffix tree that have a superprimitive path-label
43 citations
TL;DR: A data structure is constructed for the case d=1, that requires space O (n log m) and has query time O (1) in a cell probe model with word size m .
32 citations
Proceedings Article•
05 Jul 2000
TL;DR: Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the redblue segment intersection problem where all red and all blue segments are connected.
Abstract: The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n ċ log log log n) time, point deletions in amortized O(log n ċ log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the redblue segment intersection problem where all red and all blue segments are connected.
31 citations
05 Jul 2000
TL;DR: In this paper, the authors present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions and various queries about the convex hull in optimal O (log n) worst-case time.
Abstract: The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log log n) time, point deletions in amortized O(log n · log log n) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requires O(n) space. Applications of the new dynamic convex hull data structure are improved deterministic algorithms for the k-level problem and the red-blue segment intersection problem where all red and all blue segments are connected.
15 citations