By Michael Mitzenmacher (auth.), Joachim Gudmundsson (eds.)

ISBN-10: 3540699007

ISBN-13: 9783540699002

ISBN-10: 3540699031

ISBN-13: 9783540699033

This ebook constitutes the refereed lawsuits of the eleventh Scandinavian Workshop on set of rules concept, SWAT 2008, held in Gothenborg, Sweden, in July 2008.

The 36 revised complete papers awarded including 2 invited lectures have been conscientiously reviewed and chosen from 111 submissions. Papers have been solicited for unique examine on algorithms and knowledge constructions in all parts, together with yet no longer constrained to: approximation algorithms, computational biology, computational geometry, allotted algorithms, external-memory algorithms, graph algorithms, on-line algorithms, optimization algorithms, parallel algorithms, randomized algorithms, string algorithms and algorithmic online game idea.

**Read Online or Download Algorithm Theory – SWAT 2008: 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 2-4, 2008. Proceedings PDF**

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**Extra resources for Algorithm Theory – SWAT 2008: 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 2-4, 2008. Proceedings**

**Sample text**

Unless otherwise stated, all treaps in this paper use 8-wise independent hash functions to generate priorities. We use the following properties of treaps. Theorem 1 (Selected Treap Properties [22]). Let T be a random treap on n nodes with priorities generated by an 8-wise independent hash function from nodes to [p], where p ≥ n3 . Then for any x ∈ T , (1) E[depth(x)] ≤ 2 ln(n) + 1, so access and update times are expected O(log n) (2) Pr[|Tx | = k] = O(1/k 2 ) for all 1 ≤ k < n (3) Given a predecessor handle, the expected insertion or deletion time is O(1) (4) If the time to rotate a subtree of size k is f (k) for some f : N → R≥1 , the total f (k) time due to rotations to insert or delete an element is O f (n) 0

Strongly history-independent hashing with applications. In: Proc. FOCS, pp. 272–282 (2007) 5. : Uniquely represented data structures for computational geometry. Technical Report CMU-CS-08-115, Carnegie Mellon University (April 2008) 6. : Dynamic planar convex hull. In: Proc. FOCS, pp. 617–626 (2002) 7. : Lower and upper bounds on obtaining history independence. In: Boneh, D. ) CRYPTO 2003. LNCS, vol. 2729, pp. 445–462. Springer, Heidelberg (2003) 8. : Fractional cascading. Algorithmica 1, 133–196 (1986) 9.

If there isn’t a child u of v1 such that span(v1 ) ⊂ I(LP (u)) then LP (v1 ) is equal LP (v). Proof. We claim that there exists a child u of v1 that LP (u) is empty. From this claim the lemma follows since if there is a preﬁx q longer than LP (v) such that I(q) is mapped to v1 , then q is mapped to u before the split and LP (u) couldn’t have been empty. We prove this claim as follows. Assume to the contrary that LP (u) is not empty for every child u of v1 . Let w be a child of v1 such that I(LP (w)) is not contained in I(LP (w )) for any other child w of v (w exists since segments do not overlap).

### Algorithm Theory – SWAT 2008: 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 2-4, 2008. Proceedings by Michael Mitzenmacher (auth.), Joachim Gudmundsson (eds.)

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