By Gerth Stølting Brodal, Spyros Sioutas, Kostas Tsichlas, Christos Zaroliagis (auth.), Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park (eds.)

ISBN-10: 3642175139

ISBN-13: 9783642175138

ISBN-10: 3642175147

ISBN-13: 9783642175145

This ebook constitutes the refereed complaints of the twenty first foreign Symposium on Algorithms and Computation, ISAAC 2010, held in Jeju, South Korea in December 2010. The seventy seven revised complete papers provided have been conscientiously reviewed and chosen from 182 submissions for inclusion within the publication. This quantity includes issues similar to approximation set of rules; complexity; info constitution and set of rules; combinatorial optimization; graph set of rules; computational geometry; graph coloring; fastened parameter tractability; optimization; on-line set of rules; and scheduling.

**Read or Download Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju, Korea, December 15-17, 2010, Proceedings, Part II PDF**

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**Additional info for Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju, Korea, December 15-17, 2010, Proceedings, Part II**

**Example text**

In summary, we have the following. Theorem 3. We can construct an O(n)-word index for a string T over an alphabet of size O(polylog(n)), so that a positional pattern matching query can be answered in O(p) time for any pattern P . 4 The Position-Restricted Pattern Matching Problem For ease of exposition, we only present indexes for T that report all occurrences of P in T [s, n] in sorted order for any pattern P and position s given later. It is easy to modify our solutions to report all occurrences of P in T in sorted order within a given query interval [s, t].

Let π = πa ∪ πb denote the set of all nodes of T that belong to πa or πb . x ∈ [a, b] is stored in some set Sv such that either v belongs to π or v is a descendant of a node that belongs to π. We can visit all nodes v ∈ π and report all points in Sv ∩Q in O(logB N ) I/Os using data structures Ev (we ignore the time needed to output points). Points in descendants of v ∈ π can be found using the following property. Fact 1. Let v , v ∈ π, be a child of a node v ∈ π, and let w be a descendant of v .

Lemma 2 ([9, 11]). Given a string T over an alphabet Σ, the suﬃx tree ST occupies O(|T |) space. For any pattern P , μ(P ) can be determined in O(|P |) time, and all occurrences of P in T can be found in O(|P | + occ) time, where occ is the number of occurrences. The segment tree GT of interval [1, n] is an ordered balanced binary tree with n leaves, where the ith leaf represents the elementary interval [i, i], and each internal node v represents the union of the intervals represented by its descendant leaves.