By Darja Krushevskaja, S. Muthukrishnan (auth.), Leizhen Cai, Siu-Wing Cheng, Tak-Wah Lam (eds.)
This publication constitutes the refereed lawsuits of the twenty fourth overseas Symposium on Algorithms and Computation, ISAAC 2013, held in Hong Kong, China in December 2013. The sixty seven revised complete papers provided including 2 invited talks have been conscientiously reviewed and chosen from 177 submissions for inclusion within the booklet. the point of interest of the amount in at the following subject matters: computation geometry, trend matching, computational complexity, web and social community algorithms, graph conception and algorithms, scheduling algorithms, fixed-parameter tractable algorithms, algorithms and information buildings, algorithmic online game thought, approximation algorithms and community algorithms.
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Extra info for Algorithms and Computation: 24th International Symposium, ISAAC 2013, Hong Kong, China, December 16-18, 2013, Proceedings
Example text
In the j-th round for j ≥ 2, we only check triangles adjacent to at least one newly created edge corresponding to the ears removed in (j − 1)-th round (See Fig. 3 to get intuition, where colors indicate stages). We use the same skipping rule once we find a new ear. The following lemma justifies the strategy of the algorithm. Lemma 3. In the j-th round, no triangle that does not use an edge created in the (j − 1)-th round can be an ear. Proof. Suppose that a triangle formed by consecutive triple of vertices does not use an edge created in the (j − 1)-th round.
This implies a ∈ lens(c, d). (ii) It is easy to see that the angle between xy and cd is less than 30◦ . Since xy is perpendicular to ab, the lemma follows. Proof of Lemma 4: Suppose to the contrary that none of the three lenses contains two points of Q = {a, b, c, d, e, f } in its interior. Let us first consider two lenses, lens(a, b) and lens(c, d). By Lemmas 5 and 6, if c, d ∈ / lens(a, b), then a ∈ lens(c, d) or b ∈ lens(c, d) holds. This implies that at least one of c ∈ lens(a, b), d ∈ lens(a, b), a ∈ lens(c, d) or b ∈ lens(c, d) holds.
Geodesicpreserving polygon simplification. 3858 2. : Geodesic order types. Algorithmica (to appear, 2013) 3. : Extreme point and halving edge search in abstract order types. Computational Geometry: Theory and Applications 46(8), 970–978 (2013) 4. : On minimum-area hulls. Algorithmica 21(1), 119–136 (1998) 5. : On the geodesic Voronoi diagram of point sites in a simple polygon. In: SoCG, pp. 39–49 (1987) 6. : The furthest-site geodesic Voronoi diagram. Discrete and Computational Geometry 9, 217–255 (1993) Geodesic-Preserving Polygon Simplification 21 7.