By Jeff Erickson (auth.), Frank Dehne, Jörg-Rüdiger Sack, Norbert Zeh (eds.)

ISBN-10: 3540739483

ISBN-13: 9783540739487

The papers during this quantity have been awarded on the tenth Workshop on Algorithms and information buildings (WADS 2005). The workshop came about August 15 - 17, 2007, at Dalhousie collage, Halifax, Canada. The workshop alternates with the Scandinavian Workshop on set of rules thought (SWAT), carrying on with the t- dition of SWAT and WADS beginning with SWAT 1988 and WADS 1989. From 142 submissions, this system Committee chosen fifty four papers for presentation on the workshop. additionally, invited lectures got by means of the subsequent dist- guished researchers: Je? Erickson (University of Illinois at Urbana-Champaign) and Mike Langston (University of Tennessee). On behalf of this system Committee, we want to precise our honest appreciation to the numerous folks whose e?ort contributed to creating WADS 2007 successful. those comprise the invited audio system, individuals of the steerage and ProgramCommittees, the authorswho submitted papers, andthe manyreferees who assisted this system Committee. we're indebted to Gerardo Reynaga for fitting and enhancing the submission software program, retaining the submission server and interacting with authors in addition to for assisting with the guidance of the program.

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**Additional info for Algorithms and Data Structures: 10th International Workshop, WADS 2007, Halifax, Canada, August 15-17, 2007. Proceedings**

**Example text**

Suppose that the total number of points in an interval [c, d] must be found. Using a standard searching data structure, we identify the predecessor td of d and the successor tc of c among the leaves of T . Let q be the lowest common ancestor of tc and td . Then a range sum query can be answered by answering at most two queries to internal nodes of T on each level l, 1 ≤ l ≤ lq , where lq is the level of the node q. Hence, a range sum query can be answered in O(log n/ log log n) time. When a new element is inserted into Cij we insert the new leaf u into T .

The penalty can be reduced to O(logε n) using the method described in [15], section 4. When a new point (x, y) is inserted into the dynamic data structure, we insert the v-labels of p into data structures Dv for O(log n/ log log n) nodes v1 , v2 , . . e. nodes whose ranges contain x). When a new v-label is inserted into the set of v-labels Yv , we may have to change the values of O(log2 n) other v-labels. This means that O(log2 n) elements must be removed from and re-inserted into Dv . Hence the cost of an insertion is O(log2 n log1/2 n log log n(log n/ log log n)) = 24 Y.

Hence, we can examine all Lf and compute the sum of values associated with points O( log n) points in √ p ∈ [a, b]×[c, d] in O( log n) time. If rf < rl , we ﬁnd q1 = p∈([a,b]×(rl−1 ,d]) g(p), q2 = p∈([a,b]×[c,rf )) g(p), and q3 = p∈([a,b]×[rf ,rl−1 ]) g(p). We can compute q1 √ and q2 in O( log n) time; q3 is computed with a range sum query [f, l] to Cab . Cij can be implemented as a B-tree TB with node degree O(logε n). Elements and their values are stored in the leaves of TB . In every internal node v we store a data structure Sv with O(logε n) elements.

### Algorithms and Data Structures: 10th International Workshop, WADS 2007, Halifax, Canada, August 15-17, 2007. Proceedings by Jeff Erickson (auth.), Frank Dehne, Jörg-Rüdiger Sack, Norbert Zeh (eds.)

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