By Mohammad Ali Abam, Mark de Berg, Amirali Khosravi (auth.), Frank Dehne, John Iacono, Jörg-Rüdiger Sack (eds.)
This ebook constitutes the refereed complaints of the twelfth Algorithms and knowledge buildings Symposium, WADS 2011, held in manhattan, new york, united states, in August 2011.
The Algorithms and knowledge constructions Symposium - WADS (formerly "Workshop on Algorithms and knowledge Structures") is meant as a discussion board for researchers within the region of layout and research of algorithms and information constructions. The fifty nine revised complete papers offered during this quantity have been rigorously reviewed and chosen from 141 submissions. The papers current unique examine at the thought and alertness of algorithms and knowledge constructions in all parts, together with combinatorics, computational geometry, databases, snap shots, parallel and allotted computing.
Read or Download Algorithms and Data Structures: 12th International Symposium, WADS 2011, New York, NY, USA, August 15-17, 2011. Proceedings PDF
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Additional info for Algorithms and Data Structures: 12th International Symposium, WADS 2011, New York, NY, USA, August 15-17, 2011. Proceedings
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Then, the following statements hold: (i) for each pair of vertices u and v of T , d(u, v) ≥ |e|, for each edge e in the path connecting u and v in T ; (ii) any angle between two adjacent segments in Γ is at least 60◦ ; (iii) for any subtree T of T , Γ restricted to the vertices and edges of T is an MST embedding of T ; and (iv) Γ is planar. The next lemma bounds the length of an edge in an MST embedding in terms of the length of an adjacent edge and of the size of the angle between them. Lemma 2.
Next, we define an n-vertex tree T ∗ that requires Ω(2n ) area in any MST embedding. Let Tc be a complete tree of height six and degree five. Let r be the root of Tc . Augment Tc by inserting a degree-five caterpillar at each leaf of Tc . That is, for each leaf l of Tc , insert a caterpillar Cl whose every non-leaf vertex has degree five, such that l is an endvertex of the backbone of Cl , the parent of l in Tc is a leaf of Cl , and Cl and Tc do not share any other vertex. The resulting tree, shown in Fig.