Dynamic rectangular intersection with priorities

Kaplan, Haim; Molad, Eyal; Tarjan, Robert E.

doi:10.1145/780542.780635

Cited by 23 publications

(13 citation statements)

References 12 publications

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“…Aggregation over arbitrary trees would require traversing the ST-tree in a top-down fashion, which is impossible because nodes do not maintain pointers to their (potentially numerous) middle children. A solution is to apply ternarization to the underlying forest, which replaces each high-degree vertex by a chain of low-degree ones [Goldberg et al 1991;Kaplan et al 2003;Klein 2005;Langerman 2000;Radzik 1998]. …”

Section: St-treesmentioning

confidence: 99%

“…Typical operations include finding the minimum-cost edge on a path, adding a constant to the costs of all edges on a path, and finding the maximum-cost vertex in a tree. The dynamic tree problem has applications in network flows [Goldberg et al 1991;Tarjan 1997], dynamic graphs [Cattaneo et al 2002;Frederickson 1985Frederickson , 1997aHenzinger and King 1997;Radzik 1998;Zaroliagis 2002], and other combinatorial problems [Kaplan et al 2003;Klein 2005;Langerman 2000]. …”

Section: Introductionmentioning

confidence: 99%

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Dynamic trees in practice

Tarjan

Werneck

2009

ACM J. Exp. Algorithmics

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Dynamic tree data structures maintain forests that change over time through edge insertions and deletions. Besides maintaining connectivity information in logarithmic time, they can support aggregation of information over paths, trees, or both. We perform an experimental comparison of several versions of dynamic trees: ST-trees, ET-trees, RC-trees, and two variants of top trees (self-adjusting and worst-case). We quantify their strengths and weaknesses through tests with various workloads, most stemming from practical applications. We observe that a simple, lineartime implementation is remarkably fast for graphs of small diameter, and that worst-case and randomized data structures are best when queries are very frequent. The best overall performance, however, is achieved by self-adjusting ST-trees.

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Section: St-treesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic trees in practice

Tarjan

Werneck

2009

ACM J. Exp. Algorithmics

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“…This is called the geometric (or locus) view as opposed to the previous string view. The geometric approach has been proposed in Warkhede et al [2004] and Lampson et al [1999]; it has been extended in Feldmann and Muthukrishnan [2000] and in several recent papers [Thorup 2003;Kaplan et al 2003]. It has been used in Buchsbaum et al [2003] to formally prove the equivalence among several different problems.…”

Section: Our Contributionmentioning

confidence: 99%

“…We notice that for the multidimensional packet filtering problem, the multidimensional FIS tree [Feldmann and Muthukrishnan 2000], which follows the geometric view, has already established itself as a benchmark, not only for the asymptotic bounds, but also for empirical performance. 1 Since our objective is practical, we chose for the moment not to rely on the sophisticated techniques that have lead to the recent improvements in worst-case bounds (e.g., those in Feldmann and Muthukrishnan [2000], Thorup [2003], and Kaplan et al [2003]). 2 Instead, we ask ourselves whether simpler search trees built with the help of local optimization routines could lead to the stated goal.…”

Section: Our Contributionmentioning

confidence: 99%

“…Thorup [2003] improves the dynamic FIS tree: the storage becomes linear in n and any sequence of dynamic operations is supported efficiently (a detailed discussion of the FIS tree approach is postponed to Section 8). Kaplan et al [2003] give new algorithms for maintaining sets of intervals on a line that can be used for solving the IP lookup problem efficiently in the pointer model.…”

Section: Previous Workmentioning

confidence: 99%

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Efficient IP table lookup via adaptive stratified trees with selective reconstructions

Pellegrini

Fusco

2008

ACM J. Exp. Algorithmics

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IP address lookup is a critical operation for high-bandwidth routers in packet-switching networks, such as Internet. The lookup is a nontrivial operation, since it requires searching for the longest prefix, among those stored in a (large) given table, matching the IP address. Ever increasing routing table size, traffic volume, and links speed demand new and more efficient algorithms. Moreover, the imminent move to IPv6 128-bit addresses will soon require a rethinking of previous technical choices. This article describes a the new data structure for solving the IP table lookup problem christened the adaptive stratified tree (AST). The proposed solution is based on casting the problem in geometric terms and on repeated application of efficient local geometric optimization routines. Experiments with this approach have shown that in terms of storage, query time, and update time the AST is at a par with state of the art algorithms based on data compression or string manipulations (and often it is better on some of the measured quantities). ACM Reference Format:Pellegrini, M. and Fusco, G. 2007. Efficient IP table lookup via adaptive stratified trees with selective reconstructions. ACM J.

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Implementing the Link‐Cut Tree

Russo

2024

Softw Pract Exp

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We consider the challenge of implementing the link‐cut tree data structure. This data structure is well known and has had a wide impact on several theoretical results. However, there is a gap in mixed practical applications. We have recently used this data structure to generate uniform spanning trees and to compute a feedback vertex set. In this kind of application, the theoretical performance of the data structure is relevant but only when verified in practice. We thus present two implementations. One implementation is based on pointers and obtains good experimental performance for small problems. The other implementation is based on splay trees and provides amortized worst‐case guarantees. We use a simple API that allows us to explain the expected functionality. Moreover, it is designed to extract full functionality from the data structure while at the same time being as simple and compact as possible, in particular, it provides support for the cycle processing required by our applications. We give an experimental evaluation of both implementations. For completeness, we also review the theoretical analysis of this structure and obtain entropy and static finger bounds.

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Dynamic rectangular intersection with priorities

Cited by 23 publications

References 12 publications

Dynamic trees in practice

Dynamic trees in practice

Efficient IP table lookup via adaptive stratified trees with selective reconstructions

Implementing the Link‐Cut Tree

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