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By Hee-Kap Ahn, Chan-Su Shin

This ebook constitutes the refereed complaints of the twenty fifth foreign Symposium on Algorithms and Computation, ISAAC 2014, held in Jeonju, Korea, in December 2014.
The 60 revised complete papers offered including 2 invited talks have been rigorously reviewed and chosen from 171 submissions for inclusion within the publication. the point of interest of the amount in at the following issues: computational geometry, combinatorial optimization, graph algorithms: enumeration, matching and task, information buildings and algorithms, fixed-parameter tractable algorithms, scheduling algorithms, computational complexity, computational complexity, approximation algorithms, graph concept and algorithms, on-line and approximation algorithms, and community and scheduling algorithms.

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Extra resources for Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings

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Recall that ∗ is the optimal objective value. Let S = {li ( ∗ ), ri ( ∗ ) | 1 ≤ i ≤ n}. If we know the sorted lists of the values of S, then we can use our decision algorithm to compute an optimal facility set in O(n) time. Although we do not know ∗ , we can still sort S by parametric search [12]. In the parametric search, we will need to compare two values of S. Although we do not know ∗ , we can resolve the comparison using our decision algorithm in Lemma 11. We omit the details. Theorem 5. The constrained k-center problem under the L2 metric can be solved in O(n log n) time, by using Cole’s parametric search.

COCOON 2000. LNCS, vol. 1858, pp. 299–309. Springer, Heidelberg (2000) 23. : A simple linear time (1 + )-approximation algorithm for k-means clustering in any dimensions. In: Proc. of the 45th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 454–462 (2004) 24. : The planar k-means problem is NP-hard. Theoretical Computer Science 442, 13–21 (2012) 25. : Linear-time algorithms for linear programming in R3 and related problems. SIAM Journal on Computing 12(4), 759–776 (1983) 26. : Linear programming in linear time when the dimension is fixed.

This bound is tight, as shown by the example of Figure 2(a)-2(b). For the sake of readability, the proofs involve Euclidean point sets, but we are careful to use only those properties of point sets that hold also for arbitrary order types (realizable or not). An easy way to verify this is to use the representation of abstract order types as generalized configurations, discussed in detail in [5]. A generalized configuration in general position is a pair (P, L) where P ⊂ R2 and L is a pseudoline arrangement such that every pseudoline in L contains exactly two points of P .

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