## Approximate covering detection among content-based subscriptions using space filling curves (2007)

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Venue: | in IEEE International Conference on Distributed Computing Systems |

Citations: | 4 - 0 self |

### BibTeX

@INPROCEEDINGS{Shen07approximatecovering,

author = {Zhenhui Shen and Srikanta Tirthapura},

title = {Approximate covering detection among content-based subscriptions using space filling curves},

booktitle = {in IEEE International Conference on Distributed Computing Systems},

year = {2007}

}

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### Abstract

We consider a problem that arises during the propagation of subscriptions in a content-based publish-subscribe system. Subscription covering is a promising optimization that reduces the number of subscriptions propagated, and hence the size of routing tables in a content-based publish-subscribe system. However, detecting covering relationships among subscriptions can be an expensive computational task that potentially reduces the utility of covering as an optimization. We introduce an alternate approach approximate subscription covering, which provide much of the benefits of subscription covering at a fraction of its cost. By forgoing an exhaustive search for covering subscriptions in favor of an approximate search, it is shown that the time complexity of covering detection can be dramatically reduced. The trade off between efficiency of covering detection and the approximation error is demonstrated through the analysis of indexes for multi-attribute subscriptions based on space filling curves. 1

### Citations

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Citation Context ... is a M × 1 rectangle, which is not efficiently handled by most popular SFCs. 1.3 Related Work From a worst-case time complexity perspective, the current best solution to point-dominance problem (see =-=[PS85]-=-[Ch. 8], [Wil84, WL85]) over a set of n of points in d dimensions has a query time of O(log d−1 n), insertion and deletion times of O(log d n). A serious limitation of this solution is the space compl... |

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Citation Context ...lifies the design of distributed applications. Since a centralized implementation of publish-subscribe may not scale to large networks, many existing systems like Gryphon [ZSB04], Siena [CRW04], JEDI =-=[CNF01]-=- and REBECA [MFB02] use a distributed network of routers to implement publish-subscribe. Subscription propagation is a key component in any distributed publish-subscribe system. A subscription registe... |

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Citation Context ...f indexing applications, including commercial data products such as Oracle [Ora01, GG98]. Other popularly used SFCs are the Hilbert curve [Hil91] and the Gray code curve [Fal86]. It has been observed =-=[MJFS01]-=- that the performance of the Z and Hilbert curves for many indexing applications are within a constant fraction of each other. 1.2 Our Contributions We introduce the notion of approximate covering to ... |

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Citation Context ...ar order on all 2 kd cells. Henceforth we use the term cube to refer to a cube in d dimensions and rectangle to refer to a rectangle in d dimensions. Most SFCs used for indexing including the Z curve =-=[Mor66]-=- and the Hilbert curve [Hil91], utilize a recursive partitioning of the universe. The universe is first divided into 2 d cubes, each of side length 2 k−1 , by bisecting along every dimension. Each res... |

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Citation Context ...e greatly simplifies the design of distributed applications. Since a centralized implementation of publish-subscribe may not scale to large networks, many existing systems like Gryphon [ZSB04], Siena =-=[CRW04]-=-, JEDI [CNF01] and REBECA [MFB02] use a distributed network of routers to implement publish-subscribe. Subscription propagation is a key component in any distributed publish-subscribe system. A subscr... |

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Citation Context ...f distributed applications. Since a centralized implementation of publish-subscribe may not scale to large networks, many existing systems like Gryphon [ZSB04], Siena [CRW04], JEDI [CNF01] and REBECA =-=[MFB02]-=- use a distributed network of routers to implement publish-subscribe. Subscription propagation is a key component in any distributed publish-subscribe system. A subscription registered at one router h... |

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Citation Context ...e has been used in a variety of indexing applications, including commercial data products such as Oracle [Ora01, GG98]. Other popularly used SFCs are the Hilbert curve [Hil91] and the Gray code curve =-=[Fal86]-=-. It has been observed [MJFS01] that the performance of the Z and Hilbert curves for many indexing applications are within a constant fraction of each other. 1.2 Our Contributions We introduce the not... |

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Citation Context ...nsion. SFCs are one of the most popular techniques for indexing high-dimensional data, and have been widely used for tasks such as nearest neighbor search and range queries in high-dimensional spaces =-=[Fal88]-=-, data partitioning in parallel computers [LAB + 02], and in scientific computing [WS93, NKV99]. However, as explained above, SFCs (or any other data structure, for that matter) do not provide worst-c... |

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Citation Context ...uting middleware greatly simplifies the design of distributed applications. Since a centralized implementation of publish-subscribe may not scale to large networks, many existing systems like Gryphon =-=[ZSB04]-=-, Siena [CRW04], JEDI [CNF01] and REBECA [MFB02] use a distributed network of routers to implement publish-subscribe. Subscription propagation is a key component in any distributed publish-subscribe s... |

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Citation Context ...isting subscription in S is equivalent to the problem of finding an existing rectangle that encloses the incoming rectangle. We apply the following well-known transformation (Edelsbrunner and Overmars=-=[EO82]-=-) to convert this into an equivalent point dominance problem in 2β-dimensional space. A β-dimensional rectangle (subscription) s = ([ℓ1, r1], [ℓ2, r2], . . . , [ℓβ, rβ]) is transformed into a 2β-dimen... |

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Citation Context ...utside the capacity of the main memory. Existing solutions to the problem of subscription covering [LHJ05, TE04] do not provide any formal analysis of the performance. In a recent work, Ouksel et. al.=-=[OJPA06]-=- consider a relaxed notion of subscription covering and give a probabilistic algorithm for covering detection. The complexity is O(nm), where n is the number of subscriptions and and m is the number o... |

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4 |
die stegie Abbildung einer Linie auf Flachenstuck
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Citation Context ... space filling curve. The Z curve has been used in a variety of indexing applications, including commercial data products such as Oracle [Ora01, GG98]. Other popularly used SFCs are the Hilbert curve =-=[Hil91]-=- and the Gray code curve [Fal86]. It has been observed [MJFS01] that the performance of the Z and Hilbert curves for many indexing applications are within a constant fraction of each other. 1.2 Our Co... |

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1 | A formal analysis of space filling curves for parallel domain decomposition
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(Show Context)
Citation Context ... clusters of points inside the rectangle is proportional to the surface area of the query rectangle. Their analysis considers exhaustive search while we consider approximate search. Tirthapura et. al.=-=[TSA06]-=- show a formal analysis of space filling curves for parallel domain decomposition. Roadmap. The rest of this paper is organized as follows. In Section 2 we review space filling curves. In Section 3, w... |