We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find... more We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find-min requires O(1) worst-case time, insert, meld and decrease-key require O(1) amortized time, and delete-min requires $O(\log n)$ amortized time. Our structure is simple and promises an efficient practical behavior when compared to other known Fibonacci-like heaps. The main idea behind our construction is to propagate rank updates instead of performing cascaded cuts following a decrease-key operation, allowing for a relaxed structure.
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is as... more We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of n items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n \cdot \lg n$. In particular, we give an almost-optimal algorithm for finding the closest pair among a set of $n$ points that runs in $O(n^2/s + n \cdot \lg s)$ time. We give a simple algorithm to enumerate the intersections of $n$ line segments whose running time is $O((n^2/s) \cdot \lg^2 s + k)$, where $k$ is the number of reported intersections. When the segments are axis-parallel, we give an $O(n^2/s + n \cdot \lg s)$-time algorithm for counting the intersections, and an algorithm for enumerating the intersections whose running time is $O((n^2/s) \cdot \lg s \cdot \lg \lg s + n \cdot \lg s + k)$. We also present space-efficient algorithms to calculate the measure of $n$ axis-parallel rectangles.
Google, Inc. (search). SIGN IN SIGN UP. Adaptive algorithms and structures. Authors: Amr Ahmed El... more Google, Inc. (search). SIGN IN SIGN UP. Adaptive algorithms and structures. Authors: Amr Ahmed Elmasry, Directors: Michael Fredman, Publication: · Doctoral Dissertation, ... top of page ABSTRACT. An abstract is not available. top of page AUTHORS. Amr Ahmed Elmasry No contac
We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find... more We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, find-min requires O(1) worst-case time, insert, meld and decrease-key require O(1) amortized time, and delete-min requires $O(\log n)$ amortized time. Our structure is simple and promises an efficient practical behavior when compared to other known Fibonacci-like heaps. The main idea behind our construction is to propagate rank updates instead of performing cascaded cuts following a decrease-key operation, allowing for a relaxed structure.
We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is as... more We introduce space-efficient plane-sweep algorithms for basic planar geometric problems. It is assumed that the input is in a read-only array of n items and that the available workspace is $\Theta(s)$ bits, where $\lg n \leq s \leq n \cdot \lg n$. In particular, we give an almost-optimal algorithm for finding the closest pair among a set of $n$ points that runs in $O(n^2/s + n \cdot \lg s)$ time. We give a simple algorithm to enumerate the intersections of $n$ line segments whose running time is $O((n^2/s) \cdot \lg^2 s + k)$, where $k$ is the number of reported intersections. When the segments are axis-parallel, we give an $O(n^2/s + n \cdot \lg s)$-time algorithm for counting the intersections, and an algorithm for enumerating the intersections whose running time is $O((n^2/s) \cdot \lg s \cdot \lg \lg s + n \cdot \lg s + k)$. We also present space-efficient algorithms to calculate the measure of $n$ axis-parallel rectangles.
Google, Inc. (search). SIGN IN SIGN UP. Adaptive algorithms and structures. Authors: Amr Ahmed El... more Google, Inc. (search). SIGN IN SIGN UP. Adaptive algorithms and structures. Authors: Amr Ahmed Elmasry, Directors: Michael Fredman, Publication: · Doctoral Dissertation, ... top of page ABSTRACT. An abstract is not available. top of page AUTHORS. Amr Ahmed Elmasry No contac
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