By Gerth Stølting Brodal, Spyros Sioutas, Kostas Tsichlas, Christos Zaroliagis (auth.), Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park (eds.)
This ebook constitutes the refereed complaints of the twenty first overseas Symposium on Algorithms and Computation, ISAAC 2010, held in Jeju, South Korea in December 2010. The seventy seven revised complete papers offered have been rigorously reviewed and chosen from 182 submissions for inclusion within the booklet. This quantity includes themes comparable to approximation set of rules; complexity; info 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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Extra resources for Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju, Korea, December 15-17, 2010, Proceedings, Part II
The total cost of re-building data structures and (pointers to) lists D and I in a sequence of B 4/3 update operations is O( rj=0 2r−j B) = O(B 4/3 ), where r = log2 B/6 + O(1) is the index of the last t-approximate boundary Vs . We can report all points that dominate an inward corner of Vi in O(22i ) I/Os as described above. Hence, dominance queries can k ) I/Os. This result is summarized in the following Lemma. be supported in O( B Lemma 1. Elements of a set S such that |S| = O(B 4/3 ) can be stored in a data structure that uses O( |S| B log2 |S|) blocks of space and supports dominance k ) I/O operations and updates in O(1) I/O operations amortized.
For each internal node v, denote by Sv the sorted sequence of all numbers associated in its descendant leaves. Then, we can construct a data structure so that the retrieval of an arbitrary element in a sequence Sv can be accomplished in (1) O(n log n) space and O(1) time; or (2) O(n) space and O(log n) time. In the indexes for short patterns and medium patterns, we explicitly store the sorted sequence Av at each node v in ST with d(v) ≤ log n, which requires O(n log n) space. Our intent is to apply the result in Lemma 8 to store the sequences Av .
Pinter  had a linear-time algorithm for determining whether P occurs in T . His algorithm is based upon the following observation: if P1 does not occur in T , then neither does P ; otherwise, P occurs in T if and only if P2 ∗ . . ∗Pm occurs in T [k1 + |P1 |, n], where k1 is the ﬁrst occurrence of P1 in T . Consider the example in Fig 3. The ﬁrst occurrence of P1 is at position 3. Thus, our problem reduces to determining whether P2 ∗P3 occurs in T [8, n]. Similarly, since the ﬁrst occurrence of P2 in T [8, n] is at position 11, the problem further reduces to determining whether P3 occurs in T [15, n].