Download e-book for iPad: Algorithms and Computation: 25th International Symposium, by Hee-Kap Ahn, Chan-Su Shin

By Hee-Kap Ahn, Chan-Su Shin

ISBN-10: 3319130749

ISBN-13: 9783319130743

ISBN-10: 3319130757

ISBN-13: 9783319130750

This booklet constitutes the refereed lawsuits 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 conscientiously reviewed and chosen from 171 submissions for inclusion within the booklet. the focal point of the quantity in at the following issues: computational geometry, combinatorial optimization, graph algorithms: enumeration, matching and project, info constructions 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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We prove that our vertical trapezoidal decomposition allows a divide-and-conquer algorithm and an expected time analysis. When the problem sub-instances are small enough, we propose two sub-algorithms. The first one combines the standard iterative approach [14] and the randomized incremental construction for the order-1 abstract Voronoi diagram [12] and computes the order-k abstract Voronoi diagram in expected O(k 2 n log n) operations. For the second one, we adopt Har-Peled’s method [9] and obtain an O(n2 2α(n) log n)-operation randomized algorithm, where α(·) is the inverse of the Ackermann function.

Figure 3(a-b) shows another example of two point sets with different order types but the same radial system U . In this case, a discussion later in the paper shows that |T (U )| = 2. In the preceeding examples, the labeled ordered types were distinct, but isomorphic in the sense they differ only by a relabeling of the points. Figure 3(cd) shows that this is not always the case: the two point sets have the same radial system and distinct and non-isomorphic order types (see [8]). This construction can be generalized to obtain examples with an arbitrary number of points.

In light of Lemma 10, we can apply the algorithms in [4,11,18] to solve the kmedian problem on P . The algorithms in [4,18] run in O(nk) time and the algorithm in [11] runs in O(τ log n) time and O(τ ) time for the unweighted case. Theorem 4. The L1 constrained k-median can be solved in O(min{nk, τ log n}) time and the unweighted case can be solved in O(min{nk, τ }) time. Line-Constrained k-Median, k-Means, and k-Center Problems 4 11 The Constrained k-Center This section presents our k-center algorithms.

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Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings by Hee-Kap Ahn, Chan-Su Shin

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