Showing papers by "Gerth Stølting Brodal published in 2015"
TL;DR: A new randomized paging algorithm OnlineMin is presented that has optimal competitiveness and allows fast implementations and two implementations of OnlineMin are presented which use O(k) space, but only O(logk) worst case time and O( logk/log logk) best case time per page request respectively.
Abstract: In the field of online algorithms paging is one of the most studied problems. For randomized paging algorithms a tight bound of H k on the competitive ratio has been known for decades, yet existing algorithms matching this bound have high running times. We present a new randomized paging algorithm OnlineMin that has optimal competitiveness and allows fast implementations. In fact, if k pages fit in internal memory the best previous solution required O(k 2) time per request and O(k) space. We present two implementations of OnlineMin which use O(k) space, but only O(logk) worst case time and O(logk/loglogk) worst case time per page request respectively.
10 citations
TL;DR: A new overlay is presented, called the Deterministic Decentralized tree, which provides matching and better complexities, which are deterministic for the supported operations, and the management of nodes (peers) and elements are completely decoupled from each other.
Abstract: We present a new overlay, called the Deterministic Decentralized tree ($$D^2$$D2-tree). The $$D^2$$D2-tree compares favorably to other overlays for the following reasons: (a) it provides matching and better complexities, which are deterministic for the supported operations; (b) the management of nodes (peers) and elements are completely decoupled from each other; and (c) an efficient deterministic load-balancing mechanism is presented for the uniform distribution of elements into nodes, while at the same time probabilistic optimal bounds are provided for the congestion of operations at the nodes. The load-balancing scheme of elements into nodes is deterministic and general enough to be applied to other hierarchical tree-based overlays. This load-balancing mechanism is based on an innovative lazy weight-balancing mechanism, which is interesting in its own right.
4 citations
05 Aug 2015
TL;DR: The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue is introduced, which supports worst-case O(1) time Insert and \(O(\log n) time (and moves) ExtractMin operations.
Abstract: The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements n – here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized O(1) time Insert and \(O(\log n)\) time ExtractMin operations, where both operations require amortized O(1) element moves. No previous implicit heap with O(1) time Insert supports both operations with O(1) moves. The second structure supports worst-case O(1) time Insert and \(O(\log n)\) time (and moves) ExtractMin operations. Previous results were either amortized or needed \(O(\log n)\) bits of additional state information between operations.
1 citations
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TL;DR: In this paper, a strictly implicit priority queue with amortized $O(1)$ time Insert and O(log n) time ExtractMin operations was introduced. But this was not the case for the binary heap of Williams (1964).
Abstract: The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements $n$ - here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized $O(1)$ time Insert and $O(\log n)$ time ExtractMin operations, where both operations require amortized $O(1)$ element moves. No previous implicit heap with $O(1)$ time Insert supports both operations with $O(1)$ moves. The second structure supports worst-case $O(1)$ time Insert and $O(\log n)$ time (and moves) ExtractMin operations. Previous results were either amortized or needed $O(\log n)$ bits of additional state information between operations.
Posted Content•
TL;DR: The update bound is a significant factor $B^{1-\varepsilon}$ improvement over the previous best update bounds for the two query problems, while staying within the same query and space bounds.
Abstract: An external memory data structure is presented for maintaining a dynamic set of $N$ two-dimensional points under the insertion and deletion of points, and supporting 3-sided range reporting queries and top-$k$ queries, where top-$k$ queries report the $k$~points with highest $y$-value within a given $x$-range. For any constant $0<\varepsilon\leq \frac{1}{2}$, a data structure is constructed that supports updates in amortized $O(\frac{1}{\varepsilon B^{1-\varepsilon}}\log_B N)$ IOs and queries in amortized $O(\frac{1}{\varepsilon}\log_B N+K/B)$ IOs, where $B$ is the external memory block size, and $K$ is the size of the output to the query (for top-$k$ queries $K$ is the minimum of $k$ and the number of points in the query interval). The data structure uses linear space. The update bound is a significant factor $B^{1-\varepsilon}$ improvement over the previous best update bounds for the two query problems, while staying within the same query and space bounds.