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By Mohammad Ali Abam, Mark de Berg, Amirali Khosravi (auth.), Frank Dehne, John Iacono, Jörg-Rüdiger Sack (eds.)

This e-book constitutes the refereed court cases of the twelfth Algorithms and information constructions Symposium, WADS 2011, held in manhattan, new york, united states, in August 2011.
The Algorithms and information constructions Symposium - WADS (formerly "Workshop on Algorithms and information Structures") is meant as a discussion board for researchers within the sector of layout and research of algorithms and knowledge buildings. The fifty nine revised complete papers provided during this quantity have been rigorously reviewed and chosen from 141 submissions. The papers current unique learn at the idea and alertness of algorithms and knowledge buildings in all components, together with combinatorics, computational geometry, databases, snap shots, parallel and dispensed computing.

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Additional resources for Algorithms and Data Structures: 12th International Symposium, WADS 2011, New York, NY, USA, August 15-17, 2011. Proceedings

Example text

Al [4] came up with some further results. A consolidation of the related results can be found in [4]. The following intermediate structural result in our paper becomes interesting in this context: 16 A. Adiga, J. Babu, and L. Sunil Chandran (d) In Lemma 4, we observe that if H is a bipartite graph whose complement is a CA graph, then H ∗ is a comparability graph. This is a generalization of similar results for convex bipartite graphs and interval bigraphs already known in literature [1,25]. This observation helps us in reducing the complexity of our polynomial time algorithms.

We can suppose that q is to the left of the vertical line lv through v, since otherwise β ≥ 90◦ ≥ 120◦ − α/2, where the last inequality holds by Lemma 1(ii), and there is nothing to prove. By Lemma 1(i), d(q, u) ≥ d(u, v) holds. Then, q is outside k(u, |e|). Still by Lemma 1(i), d(p, q) ≥ d(p, u) and d(p, q) ≥ d(u, v) hold. Then, q is outside k(p, m), where m = max{|e|, |e1 |}. Again by Lemma 1(i), | d(p, q) ≥ d(v, q) holds. Denote by lpv the line orthogonal to pv passing through the | midpoint of pv; then, q is in the half-plane delimited by lpv and not containing p.

The additive 2-factor algorithm directly works for any Proper Circular Arc graph, since computing an NCA model for it can be done in polynomial time. Keywords: Boxicity, Circular Arc Graphs, Approximation Algorithm. 1 Introduction Boxicity: Let G(V, E) be a graph. If I1 , I2 , · · ·, Ik are interval graphs on the vertex set V with E(G) = E(I1 ) ∩ E(I2 ) ∩ · · · ∩ E(Ik ), then {I1 , I2 , · · ·, Ik } is called a box representation of G of dimension k. Boxicity of G is defined as the minimum number k such that G has a box representation of dimension k.

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