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 provided including three invited talks have been rigorously reviewed and chosen from sixty two submissions. The papers are geared up in topical sections on computational geometry, algorithms and approximations, allotted computing and networks, graph algorithms, complexity and limits, and graph embeddings and drawings.
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Extra info for Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings
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.
Consider the set of points in Pt that lie on a line segment of C. These points are already sorted by their x-coordinates in the preprocessing phase. Because of convexity of SDIST in Lemma 5, we sort them in the ascending order of SDIST in time linear to the number of points. We do this for the remaining points of Pt in a similar way, and get the final list of points in Pt sorted in the ascending order of SDIST in time O(|Pt |). Lemma 6. We can sort data points having the same distance from q in the ascending order of SDIST in time linear to the number of the points.
In general it takes O(m) time to compute SDIST(p) for a data point p and therefore O(nm) time for all data points of P . We propose another method that computes SDIST(p) for each data point p in O(log m) time after O(m log m) time preprocessing. Consider any two data points p and p∩ . y|) q≤Q (1) Equation (1) suggests that SDIST(p∩ ) can be computed immediately once we know the values of SDIST(p) and the last two terms. In the following we will show how to evaluate the second term of Equation (1) efficiently.
Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings by Kurt Mehlhorn (auth.), Sudebkumar Prasant Pal, Kunihiko Sadakane (eds.)