Download Algorithms and Computation: 8th International Workshop, by Kurt Mehlhorn (auth.), Sudebkumar Prasant Pal, Kunihiko PDF

By Kurt Mehlhorn (auth.), Sudebkumar Prasant Pal, Kunihiko Sadakane (eds.)

This ebook constitutes the revised chosen papers of the eighth overseas Workshop on Algorithms and Computation, WALCOM 2014, held in Chennai, India, in February 2014. The 29 complete papers awarded including three invited talks have been rigorously reviewed and chosen from sixty two submissions. The papers are equipped in topical sections on computational geometry, algorithms and approximations, disbursed computing and networks, graph algorithms, complexity and boundaries, and graph embeddings and drawings.

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Additional resources for Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings

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1). We then do the query [l, r] on the preprocessed generalized reporting data structure D. For each of the O(log n) candidate nodes, the corresponding instance of D outputs the distinct colors present in the points which that node contributes to the convex hull of P ∪ q. The set of colors returned by querying each candidate node can at most be of size c, where c is the total number of distinct colors in the convex hull of P ∪ q. However, the same color can be output by more than one candidate node.

Hence our method requires O(log2 n + c log n) time per query. Thus we have the following result: 42 N. Moidu et al. Theorem 4. Let P be a set of colored points in two dimensions. P can be preprocessed into a O(n log2 n) space and O(n log3 n) preprocessing time data structure such that given an orthogonal range query q, the c distinct colors in the convex hull of P ∪ q can be reported in O(log2 n + c log n) time. 6 Future Work Designing output sensitive algorithms for generalized intersection searching problems is an challenging problem since the query time must depend on the number of colors and not on the number of points in the result.

Proof. The preprocessing stage involves: 38 N. Moidu et al. 1. The building of the tree Tx , which is a one dimensional range tree. It takes O(n) space and can be built in O(n log n) time. 2. The building of the tree T , which takes O(n log n) time. The number of nodes in T is the same as the number of points in P , therefore T has size O(n). 1. If the length of a heavy path is lh , it takes O(lh ) space and O(lh log lh ) time to build the required data structure. Clearly the overall space requirement is O(n) while the time required is O(n log n).

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