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UnionFind with Constant Time Deletions
"... A unionfind data structure maintains a collection of disjoint sets under makeset, union and find operations. Kaplan, Shafrir and Tarjan [SODA 2002] designed data structures for an extension of the unionfind problem in which elements of the sets maintained may be deleted. The cost of a delete opera ..."
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Cited by 6 (1 self)
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A unionfind data structure maintains a collection of disjoint sets under makeset, union and find operations. Kaplan, Shafrir and Tarjan [SODA 2002] designed data structures for an extension of the unionfind problem in which elements of the sets maintained may be deleted. The cost of a delete
Upper Bounds for Maximally Greedy Binary Search Trees
, 2011
"... At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al. considered GreedyFuture, an offline BST algorithm that greedil ..."
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Cited by 1 (0 self)
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At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al. considered GreedyFuture, an offline BST algorithm
List update with locality of reference
 In Proceedings of the 8th Latin American Theoretical Informatics Symposium
, 2008
"... Abstract. It is known that in practice, request sequences for the list update problem exhibit a certain degree of locality of reference. Motivated by this observation we apply the locality of reference model for the paging problem due to Albers et al. [STOC 2002/JCSS 2005] in conjunction with biject ..."
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Cited by 7 (4 self)
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with bijective analysis [SODA 2007] to list update. Using this framework, we prove that MovetoFront (MTF) is the unique optimal algorithm for list update. This addresses the open question of defining an appropriate model for capturing locality of reference in the context of list update [Hester and Hirschberg
List Update with Locality of Reference: MTF Outperforms All Other Algorithms
"... It has been observed that in practice, typical request sequences for the list update problem exhibit a certain degree of locality of reference. We first extend the locality of reference model for the paging problem due to Albers et al [STOC 2002/JCSS 2005] to the domain of list update; this addresse ..."
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Cited by 2 (0 self)
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; this addresses the open question of defining an appropriate model for capturing locality of reference in the context of list update [Hester and Hirschberg ACM Comp. Surv. 1985]. We then apply this model in conjunction with a recent technique for comparing online algorithms, namely bijective analysis [SODA 2007
Range Minimum Queries: Simple and Optimal, At Last!
, 2008
"... For an array A of n objects from a totally ordered universe, a range minimum query rmqA(i, j) asks for the position of the minimum element in the subarray A[i, j]. This fundamental algorithmic problem has applications in string processing, text indexing, text compression, document retrieval, and gr ..."
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time preprocessing scheme for O(1)RMQs by reducing this problem to the computation of lowest common ancestors in trees (Harel and Tarjan, SICOMP 13(2): 1984). The drawback of this and most later schemes is their huge space consumption of O(n log n) bits, which is not optimal. We make the assumption that the input
Planarity allowing few error vertices in linear time
"... Abstract — We show that for every fixed k, there is a linear time algorithm that decides whether or not a given graph has a vertex set X of order at most k such that G − X is planar (we call this class of graphs kapex), and if this is the case, computes a drawing of the graph in the plane after del ..."
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Cited by 9 (1 self)
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the question posed by Cabello and Mohar in 2005, and by Kawarabayashi and Reed (STOC’07), respectively. Note that the case k = 0 is the planarity case. Thus our algorithm can be viewed as a generalization of the seminal result by Hopcroft and Tarjan (J. ACM 1974), which determines if a given graph is planar