By Kurt Mehlhorn (auth.), Sudebkumar Prasant Pal, Kunihiko Sadakane (eds.)
This publication 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 offered including three invited talks have been conscientiously reviewed and chosen from sixty two submissions. The papers are prepared in topical sections on computational geometry, algorithms and approximations, disbursed 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
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, pp. 1576–1585 (2012) 20. : A note on the prize collecting traveling salesman problem. de Abstract. Efficiently retrieving relevant data from a huge spatial database is and has been the subject of research in fields like database systems, geographic information systems and also computational geometry for many years. In this context, we study the retrieval of relevant points with respect to a query and a scoring function: let P and Q be point sets in the plane, the skyline of P with respect to Q consists of points P for which no other point of P is closer to all points of Q.
Let Tx be a one dimensional range tree on the x co-ordinates of all points in P . Let S(v) be the subtree of an internal node v in Tx . 2 for three sided On Generalized Planar Skyline and Convex Hull Range Queries 39 queries, using the points in S(v) as the input. This takes O(|S(v)|) space and O(|S(v)| log |S(v)|) time per internal node v. Now consider the set Sd of all nodes lying at depth d in the primary tree Tx . The total time required to preprocess all nodes in Sd will be: O(|S(v)| log |S(v)|) ≤ v∈Sd O(|S(v)| log n) = O(log n v∈Sd |S(v)|) = O(n log n) v∈Sd (1) Likewise, the total space required to store the preprocessed data structures on each node in Sd will be: O(|S(v)|) = O( v∈Sd |S(v)|) = O(n) (2) v∈Sd There will be O(log n) levels in the tree Tx .
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. 3 Analysis We outline our algorithm as follows. 2. For the sorted list we can find top-k skyline points by using Algorithm Top-kMSSQ in Section 4. Let us analyze the running time of the algorithm. In the preprocessing phase, we spend O(n log n) time to compute two lists of points in P , one sorted along the line y = x and the other sorted along the line y = −x. For Algorithm Top-k-MSSQ, the time complexity is as follows.