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Download Algorithms and Computation: 24th International Symposium, by Darja Krushevskaja, S. Muthukrishnan (auth.), Leizhen Cai, PDF

By Darja Krushevskaja, S. Muthukrishnan (auth.), Leizhen Cai, Siu-Wing Cheng, Tak-Wah Lam (eds.)

This e-book constitutes the refereed court cases of the twenty fourth foreign Symposium on Algorithms and Computation, ISAAC 2013, held in Hong Kong, China in December 2013. The sixty seven revised complete papers awarded including 2 invited talks have been conscientiously reviewed and chosen from 177 submissions for inclusion within the ebook. the focal point of the amount in at the following themes: computation geometry, development matching, computational complexity, web and social community algorithms, graph concept and algorithms, scheduling algorithms, fixed-parameter tractable algorithms, algorithms and knowledge constructions, algorithmic video game conception, approximation algorithms and community algorithms.

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Additional resources for Algorithms and Computation: 24th International Symposium, ISAAC 2013, Hong Kong, China, December 16-18, 2013, Proceedings

Example text

G. if P is a convex polygon) to store, and the dynamic programing algorithms need quadratic space even if the visibility graph has a small size. Indeed, there is no way to improve O(n2 ) time and space complexity given by Chen and Wang [4]l if we explicitly construct the visibility graph. However, it seems to be overkill to compute the visibility graph in order to find the shape of the polygon. In this paper, we give a different idea to reconstruct the polygon. Instead of using a visibility graph, we find a triangulation of P .

Given a simple polygon P of n vertices out of which r > 0 are reflex, and two sets R and B of m points each, we can determine whether or not R and B are separable by a geodesic (and find a separating geodesic, if any exists) in O(n + (m + r) log(m + r)) time using O(n + m) space. , a ternary predicate p(a, b, c). In analogy to unconstrained point sets, the orientation of a point triple inside a simple polygon is defined via the order in which the points appear on the geodesic hull of the triple [2].

Our main theorem, proved in Section 4, affirmatively answers this question. Theorem 2. (6-planarity) Let P be a semi-generic set of points in the plane. For every edge ab ∈ MLG(P ), the number of edges crossing ab is at most six. Moreover, we prove the following theorem in Section 3. Theorem 3. (Quasi-planarity Theorem) Let P be a semi-generic set of points in the plane. No three edges of MLG(P ) pairwise cross. It is known that there is a point set P for which 1-GG(P ) contains three edges that mutually cross each other [3, Figure 4].

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