New PDF release: Algorithms and Computation: 8th International Workshop,
By Kurt Mehlhorn (auth.), Sudebkumar Prasant Pal, Kunihiko Sadakane (eds.)
This e-book constitutes the revised chosen papers of the eighth foreign 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 prepared in topical sections on computational geometry, algorithms and approximations, allotted computing and networks, graph algorithms, complexity and boundaries, and graph embeddings and drawings.
Read or Download Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings PDF
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Additional info for Algorithms and Computation: 8th International Workshop, WALCOM 2014, Chennai, India, February 13-15, 2014, Proceedings
For these SDIST values, the following lemma holds. Lemma 5. The function SDIST is a convex along a line. Proof. Consider any line σ. Clearly the distance function from a query point q is convex along σ. Since SDIST is the sum of these convex distance functions, SDIST is also convex . 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.
This can be done using a binary search algorithm. Then we scan the list LI starting from p in the ascending order of I and report each data point in LI if it lies in the top left quadrant. This gives us the list of data points contained the top left quadrant sorted in the order of the distance from q. We also compute the sorted lists for the other three quadrants analogously, and merge the four sorted lists into one to get Lq . Lemma 3. We can sort n data points in P in the ascending order of distance from a query point q ≥ Q in O(n) time after O(n log n) time preprocessing.
The top-k Manhattan spatial skyline problem can be formalized as Problem 1 (Top-k Manhattan Spatial Skyline Query). , qm } a set of query points f : P ⊗ R+ a monotone scoring function k > 0 a parameter Task: Compute a set Sk ≈ P of k points in the plane, so that the points of Sk are the ksmallest (with respect to f ) skyline points of P with respect to Q. 3 Related Work Skyline Computation. The problem of computing the skyline was known as the maximal vector problem [2,3] where the goal is to find the subset of the vectors that are not dominated by any of the vectors from the set.
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.)