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Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park's Algorithms and Computation: 21st International Symposium, PDF

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. earlier variations 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 issues in algorithms and computation. the most function 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 examine group. according to the decision for papers, ISAAC 2010 obtained 182 papers. every one submission was once reviewed by way of a minimum of 3 application Committee participants with the help of exterior referees. on the grounds 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 authorised seventy seven of the submissions to be p- sented on the convention. particular matters, one in every of Algorithmica and one of many overseas 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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Additional resources for Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part II

Sample text

Initially, set i = 1 and s = 1. Then, iterate as follows. First, find the first occurrence k of Pi in T [s, n] by a PPM query. Next, if k does not exist, report that P does not occur in T . Otherwise, do the following: if i = m, report that P occurs in T ; and otherwise, increase i by one, set s = k +|Pi |, and then proceed to the next iteration. It is easy to see that the query time is O(|P1 |+|P2 |+. +|Pm |) = O(|P |). We obtain the following. Theorem 5. We can construct an O(n)-word index for a string T over an alphabet Σ of size O(polylog(n)), so that we can determine in O(p) time whether a pattern P over Σ ∪ {∗} occurs in T .

Next, for each internal node v of GT , construct the bridge structure of Lemma 6 from Av to Alef t(v) and Aright(v) , where lef t(v) and right(v) are, respectively, the left and right children of v. We also maintain the structure of Lemma 7 so that the position in Av of an element in Alef t(v) or Aright(v) can be found in O(1) time. Since GT is a binary tree and its height is O(log n), the structures of Lemmas 6 and 7 take O(n log n) bits of space. With the above constructed data structure, succ(L[i, j], s) is found as follows.

6 Concluding Remarks M¨ akinen and Navarro [14] had an O(n)-word index with O(p + log n) query time for the following problem: preprocess a text T , so that for any pattern P and integer k, the kth occurrence of P in T can be found efficiently. Using the result in [3], the query time can be improved to O(p + log n/ log log n). 2, the query time can be further improved to O(p). One direction for further study is to investigate more pattern matching problems which can be solved efficiently based on the idea in this paper.

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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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