Showing papers by "Richard Cole published in 2002"
19 May 2002
TL;DR: The crucial new idea underlying the first three results above is that of confirming matches by convolving vectors obtained by coding characters in the alphabet with non-boolean entries; in contrast, almost all previous pattern matching algorithms consider only boolean codes for the alphabet.
Abstract: (MATH) This paper obtains the following results on pattern matching problems in which the text has length n and the pattern has length mAn O(nlog m) time deterministic algorithm for the String Matching with Wildcards problems, even when the alphabet is large.An O(klog2 m) time Las Vegas algorithm for the Sparse String Matching with Wildcards problem, where k«n is the number of non-zeros in the text. We also give Las Vegas algorithms for the higher dimensional version of this problem.As an application of the above, an O(nlog2 m) time Las Vegas algorithm for the Subset Matching and Tree Pattern Matching problems, and a Las Vegas algorithm for the Geometric Pattern Matching problem.Finally, an O(nlog2 m) time deterministic algorithm for Subset Matching and Tree Pattern Matching..The crucial new idea underlying the first three results above is that of confirming matches by convolving vectors obtained by coding characters in the alphabet with non-boolean (i.e., rational or even complex) entries; in contrast, almost all previous pattern matching algorithms consider only boolean codes for the alphabet. The crucial new idea underlying the fourth result is a simpler method of shifting characters which ensures that each character occurs as a singleton in some shift.
159 citations
17 Sep 2002
TL;DR: In this paper, the authors present new algorithms that match the bounds of Dietz and Sleator, and present experimental evidence that suggests that their algorithms are superior in practice in practice.
Abstract: In the Order-Maintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.
153 citations
TL;DR: Two algorithms for finding all approximate matches of a pattern in a text, where the edit distance between the pattern and the matching text substring is at most k, are given.
Abstract: We give two algorithms for finding all approximate matches of a pattern in a text, where the edit distance between the pattern and the matching text substring is at most k. The first algorithm, which is quite simple, runs in time $O(\frac{nk^3}{m}+n+m)$ on all patterns except k-break periodic strings (defined later). The second algorithm runs in time $O(\frac{nk^4}{m}+n+m)$ on k-break periodic patterns. The two classes of patterns are easily distinguished in O(m)time.
126 citations
08 Jul 2002
TL;DR: A linear-space data structure for dynamic searching that supports searches and updates in optimal O(logB N) worst-case I/Os is given, eliminating amortization from the result of Bender, Demaine, and Farach-Colton (FOCS '00).
Abstract: We present cache-oblivious data structures based upon exponential structures. These data structures perform well on a hierarchical memory but do not depend on any parameters of the hierarchy, including the block sizes and number of blocks at each level. The problems we consider are searching, partial persistence and planar point location. On a hierarchical memory where data is transferred in blocks of size B, some of the results we achieve are: - We give a linear-space data structure for dynamic searching that supports searches and updates in optimal O(logB N) worst-case I/Os, eliminating amortization from the result of Bender, Demaine, and Farach-Colton (FOCS '00).We also consider finger searches and updates and batched searches. - We support partially-persistent operations on an ordered set, namely, we allow searches in any previous version of the set and updates to the latest version of the set (an update creates a new version of the set). All operations take an optimal O(logB(m+N)) amortized I/Os, where N is the size of the version being searched/updated, and m is the number of versions. - We solve the planar point location problem in linear space, taking optimal O(logB N) I/Os for point location queries, where N is the number of line segments specifying the partition of the plane. The pre-processing requires O((N/B) logM/B N) I/Os, where M is the size of the 'inner' memory.
58 citations
17 Sep 2002
TL;DR: This work explores the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements on more realistic memory models: the cache-oblivious model, which applies to unknown and multi-level memory hierarchies, and sequential-access models, where sequential block transfers are less expensive than random block transfers.
Abstract: We study the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements. This problem is trivially solved on a RAM and on a simple two-level memory hierarchy. We explore this traversal problem on more realistic memory models: the cache-oblivious model, which applies to unknown and multi-level memory hierarchies, and sequential-access models, where sequential block transfers are less expensive than random block transfers.
49 citations
Journal Article•
TL;DR: This work presents new algorithms that match the bounds of Dietz and Sleator, and presents experimental evidence that suggests that they are superior in practice.
Abstract: In the Order-Maintenance Problem, the objective is to maintain a total order subject to insertions, deletions, and precedence queries. Known optimal solutions, due to Dietz and Sleator, are complicated. We present new algorithms that match the bounds of Dietz and Sleator. Our solutions are simple, and we present experimental evidence that suggests that they are superior in practice.
11 citations