By Erik D. Demaine (auth.), Yossi Azar, Thomas Erlebach (eds.)

ISBN-10: 3540388753

ISBN-13: 9783540388753

This booklet constitutes the refereed complaints of the 14th Annual ecu Symposium on Algorithms, ESA 2006, held in Zurich, Switzerland, in September 2006, within the context of the mixed convention ALGO 2006.

The 70 revised complete papers awarded including abstracts of three invited lectures have been conscientiously reviewed and chosen from 287 submissions. The papers handle all present matters in algorithmics, achieving from layout and research problems with algorithms over to real-world purposes and engineering of algorithms in a number of fields.

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**Extra resources for Algorithms – ESA 2006: 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006. Proceedings**

**Example text**

Since ci was previously a part of j , we add an edge from ci to each vertex of H adjacent to j . We delete all the empty class vertices. , if a connected component c1 of a class vertex intersects s, then any other member c2 of intersects s as well. We consider two cases. The ﬁrst case is when s entirely contains c1 . Note that if c1 does not intersects any region then its cell must be contained by S since we have removed all the components from the special slabs of s. So we can assume c1 intersects at least one region.

Fix two regions ri and rj . Let c1 , . . , cm be the curves in Cij in clockwise order around ri . For m = 1, if ri and rj are in Q and all of the ≤ k regions intersecting c1 are not in Q, then add c1 to GQ as an edge between ri and rj . Observe that the probability that c1 is added is at least 1/k 2 (1 − 1/k)k = Ω(1/k 2 ). For m > 1, take each consecutive pair (ct , ct+1 ) and let r(ct , ct+1 ) be a region intersected by ct+1 but not ct , or a region intersected by ct but not ct+1 . Color the pair red in the former case, and blue otherwise.

We can obtain intersection-search structures for c1 , . . , cz from ˜ the structure for c by performing O(m) update operations in O(m) additional time. For each new class/component vertex created in this phase, we add an edge to each of the O(r) rectangle vertices it intersects. Since the total number of vertices created during the r updates is O(M + rn/q), the total cost of this ˜ ˜ + rn/q). step is O(rM + r2 n/q), which yields an amortized cost of O(M The size of each ci , 2 ≤ i ≤ z is at most half the size of c.

### Algorithms – ESA 2006: 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006. Proceedings by Erik D. Demaine (auth.), Yossi Azar, Thomas Erlebach (eds.)

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