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

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

This booklet 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 awarded 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 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

Example text

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. Both problems discussed in the preceding sections present interesting possibilities in the design of solutions for generalized geometric range aggregate query problems.

All queries studied in the following sections are orthogonal and axis-parallel, unless explicitly specified otherwise. All results are in the pointer machine model. 1 Generalized Reporting in One Dimension Given a set of points in one dimension where each point has a color (not necessarily unique) associated with it, we want to preprocess the point-set such that given a query range we can efficiently report the distinct colors in that range. Gupta et al. [11] showed a transformation which reduces the generalized one dimensional range reporting problem into the standard grounded range reporting problem in two dimensions and solved the problem using a priority search tree (PST) [17].

Points whose y co-ordinate is less than ym in the remaining canonical nodes cannot lie on the maximal chain of the query region. So on the next canonical node, we do a three sided query [xm , ∃] × [ym , yh ], and so on. Each of these queries will return at most c colors. The time taken per canonical node will be O(log2 n + c log n). Since there are O(log n) canonical nodes, the total time per query will be O(log3 n + c log2 n). Note that even though the colors output by each canonical node will be distinct within themselves, the overall set may have duplicates.

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