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

By Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park

This quantity includes the complaints of the twenty first Annual overseas S- posium on Algorithms and Computations (ISAAC 2010), held in Jeju, Korea in the course of December 15-17, 2010. prior 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 themes in algorithms and computation. the most objective of the symposium is to supply a discussion board for researchers operating in algorithms and the speculation of computation the place they could alternate rules during this energetic study neighborhood. based on the decision for papers, ISAAC 2010 bought 182 papers. every one submission used to be reviewed through not less than 3 application Committee individuals with the help of exterior referees. when you consider that there have been many high quality papers, this system Committee's activity was once tremendous di?cult. via an intensive dialogue, this system Committee approved seventy seven of the submissions to be p- sented on the convention. unique matters, considered one 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 used to be 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" via 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 info for Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part II

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Lemma 2. Let 1 ≤ bx , by , bz ≤ 2 and m = bx + by + bz − 3. Elements of a set S such that |S| = O(B 4/3 ) can be stored in a data structure that uses m+1 k O( |S| |S|) blocks of space and supports (bx , by , bz )-sided queries in O( B ) B log2 m I/O operations and updates in O(log2 (|S|)) I/O operations amortized. k In particular, we can support (2, 1, 2)-sided queries in O( B ) I/Os and updates in 2 4/3 O(log2 B) I/Os on a set S that contains Θ(B ) points using a data structure that needs O(B 1/3 log32 B) blocks of space.

C. -F. -C. Kuo A0 B 0 1 0 1 1 0 0 A 2 5 6 8 10 11 13 2 6 11 13 A1 5 8 10 Fig. 2. An illustration of bit-vector B Lemma 6. Let A0 and A1 be two sorted sequences and let A be the sorted sequence obtained by merging A0 and A1 . The bridges from A to A0 and A1 can be maintained using O(|A|) bits of space. Proof. Rather than storing a pointer from each element of A to its successor in A0 , we employ binary rank query to serve the function of bridges. The details are as follows. We create a bit-vector B of size |A| to indicate whether each element of A belongs to A0 or A1 .

Vk , we replace v and its children by a weight-balanced binary search tree with root v and leaves v1 , v2 , . . , vk , in which node vi has weight equal to its number of descendant leaves. The above transformation increases the tree height by O(log n) [18]. Thus, we can apply Chazelle’s data structures on BT to store the sorted sequences Av , where v is a node in ST with d(v) ≤ log n. For long patterns, Chazelle’s data structures can be directly applied on GT to store the sorted sequences Av .

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