Algorithm Theory – SWAT 2008: 11th Scandinavian Workshop on by Michael Mitzenmacher (auth.), Joachim Gudmundsson (eds.) PDF

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 rigorously reviewed and chosen from 111 submissions. Papers have been solicited for unique study on algorithms and information buildings in all components, together with yet now not constrained to: approximation algorithms, computational biology, computational geometry, dispensed algorithms, external-memory algorithms, graph algorithms, on-line algorithms, optimization algorithms, parallel algorithms, randomized algorithms, string algorithms and algorithmic video game idea.

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

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1 For technical reasons we include root(T ) in Ls [T ] ensuring that Ls [T ] is nonempty. Uniquely Represented Data Structures for Computational Geometry 23 Table 1. Some useful notation and definitions of various structures we maintain H Hv hash table mapping label i ∈ {0, 1}m to a pointer to the leader of T with label i hash table mapping k ∈ [q] to the tuple (if it exists) (min{u : u ∈ L[Tk ] ∧ (u, k) ∈ Tv }, max{u : u ∈ L[Tk ] ∧ (u, k) ∈ Tv }) number of descendants of node x of treap T weight s = Θ(log m) partition leaders of treap T the partition leader of x in T treap containing all elements of the ordered subset Sk , k ∈ [q] the treap on L the subtreap of T (D) on the weight s = Θ(log m) leaders of T (D) for x ∈ L[T (D)], a treap containing {u ∈ L : (u, T (D)) = x and ∃ i : u ∈ Si } w(x, T ) L[T ] (x, T ) Tk T (D) T (L[D]) Jx ˆ the set {(x, k) : x ∈ Sk } ∪ {(x, 0) : x ∈ L[T (D)]} L ˆ T a treap storing L Ix for x ∈ L, a fast ordered dictionary [4] mapping each k ∈ {i : x ∈ Si } to (x, k) in T Lemma 1.

The correctness of the query follows from the following observations. For each prefix p of q, I(p) is mapped to some node u on A. Therefore p is LP (u) unless some longer prefix is mapped to u. Furthermore, since for every v, LP (p(v)) is a prefix of LP (v), it follows that the longest prefix of q must be LP (w), where w is the last node on A for which LP (v) is not empty. 2 Inserting a New Prefix To insert a new prefix p we have to insert I(p) into T . We insert pL and pR into the appropriate height-1 nodes w and w , respectively, according to the lexicographic order of the endpoints.

In: Proc. SODA, pp. 531–540 (2004) 2. : New tight bounds on uniquely represented dictionaries. SIAM Journal of Computing 24(5), 1091–1103 (1995) 3. : Space-efficient dynamic orthogonal point location, segment intersection, and range reporting. In: Proc. SODA (2008) 4. : 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.

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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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