By Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park

ISBN-10: 3642175139

ISBN-13: 9783642175138

This quantity comprises the court cases of the twenty first Annual foreign S- posium on Algorithms and Computations (ISAAC 2010), held in Jeju, Korea in the course of December 15-17, 2010. prior versions were held in Tokyo, Taipei, Nagoya,HongKong,Beijing,Cairns,Osaka,Singapore,Taejon,Chennai,Taipei, Christchurch, Vancouver, Kyoto, Hong Kong, Hainan, Kolkata, Sendai, Gold Coast, and Hawaii through the years 1990-2009. ISAACis anannualinternationalsymposiumthatcoversthe verywide diversity of subject matters in algorithms and computation. the most goal of the symposium is to supply a discussion board for researchers operating in algorithms and the speculation of computation the place they could trade rules during this energetic learn neighborhood. based on the decision for papers, ISAAC 2010 acquired 182 papers. every one submission used to be reviewed by means of no less than 3 software Committee participants with the help of exterior referees. considering the fact that there have been many fine quality papers, this system Committee's job was once tremendous di?cult. via an in depth dialogue, this system Committee accredited seventy seven of the submissions to be p- sented on the convention. unique matters, one in every of Algorithmica and one of many foreign magazine of Computational Geometry and Applications,were ready with chosen papers from ISAAC 2010. the easiest paper award was once given to "From Holant to #CSP and again: c DichotomyforHolant Problems"byJin-YiCai,SangxiaHuangandPinyanLu, and the simplest pupil paper award to "Satis?ability with Index Dependency" by way of Hongyu Liang and Jing He. eminent invited speakers,David Eppstein from UniversityofCalifornia,Irvine,andMattFranklinfromUniversityofCalifornia, Davis, additionally contributed to this quantity

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

**Example text**

For a pattern P , its locus μ(P ) is the node v, nearest from the root, whose path label has the preﬁx P . Let Lv be the set of leaf labels in the subtree of ST rooted at v. We have the following. Lemma 1 ([15]). If μ(P ) exists, all occurrences of P in T are those in Lμ(P ) . The set Lv is not explicitly stored. -C. -F. -C. Kuo bv and ev , so that Lv is equal to the set of numbers in L[bv , ev ]. The maximum out-degree of each internal node v in ST is |Σ|. To facilitate the traversal of the tree, hash tables [9] can be used to achieve the following result.

Indexes for the Positional Pattern Matching Problem and Related Problems A 2 5 6 8 B 2 6 10 13 10 17 13 Fig. 1. 1 An Index for Short Patterns Given a text T , we ﬁrst construct a suﬃx tree ST of T . For ease of discussion, we assume that ST is a binary tree. In case it is not true, since the out-degree of each internal node is a constant, we simply transform ST into a binary tree. Recall that the set of all occurrences of a given pattern P in T is Lμ(P ) . For each node v, deﬁne Av to be the sequence obtained by sorting the labels in Lv increasingly.

In this paper, we also consider the indexing version of the variable-length don’t care pattern matching problem. For |Σ| = O(polylog(n)), we give an O(n)word index with O(p) query time. Table 3 summarizes the above results. Table 3. Indexes for pattern matching with variable-length don’t care symbols [10] [6] Ours 2 Space Query time Remarks O(n2 ) O(n1+ε ) O(n) O(p) O(p) O(p) |Σ| = O(polylog(n)) Preliminaries Let X be a string over an alphabet Σ. The length of X is denoted by |X|. The substring of X containing X[i], X[i + 1], .

### Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part II by Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park

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