Algorithms and Computation: 21st International Symposium, by Gerth Stølting Brodal, Spyros Sioutas, Kostas Tsichlas,

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

This e-book constitutes the refereed court cases 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 awarded have been rigorously reviewed and chosen from 182 submissions for inclusion within the ebook. This quantity includes subject matters akin to approximation set of rules; complexity; facts constitution and set of rules; combinatorial optimization; graph set of rules; computational geometry; graph coloring; mounted parameter tractability; optimization; on-line set of rules; and scheduling.

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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

Similarly, if s2 > s1 , the finding of Av2 [kv2 ] can be ruled out. Therefore, with a bottom-up traversal on CT , we can compute min{succ(Av , s) | v ∈ C} in O(log n) time. Combining Theorem 1 and the above result, we obtain the following. Theorem 2. We can construct an O(n)-word index for a string T over a finite alphabet, so that a positional pattern matching query can be answered in O(p) time for any pattern P . Remark 1. Similar to the wavelet tree [8], our segment tree structure for long patterns is a complete binary tree augmented with binary rank and select indexes.

Insertions can be supported with a similar technique. Inserted points are stored in the list of new points I that may contain up to 22i−1 B points. When a point p is deleted, we add it to a list D of deleted points as described above. If a point p stored in I is deleted, we simply remove p from I. When I contains 22i−1 B points, we re-build the data structure for Vi . To k ) answer a query, we examine all points from T that do not belong to D in O( B I/Os as described in the previous paragraph.

The total space is O(n log n) and the query time is O(p + log n/ log log n + occ) = O(p + occ). An Index for Long Patterns. -C. -F. -C. Kuo segment tree GT . Let U be the sorted sequence of the occurrences of P in T [s, n]. Recall that to answer a PPM query, the interval [bμ(P ) , eμ(P ) ] is decomposed into O(log n) canonical pieces. Let C be the set of the O(log n) nodes that represent the pieces. Then, U can be obtained by merging the |C| sequences Av (succ−1 (Av , s), |Av |), where v ∈ C. Here, we use Willard’s Q∗ -heap [21] for the merge.

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