S. Shekhar, D.R. Liu, Partitioning similarity graphs: A framework for declustering problems, Information Systems 21 (6) (1996) 475--496.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Design Aids General Terms Algorithms, Experimentation Keywords Partitioning, Maximum degree, Placement, Congestion 1. INTRODUCTION Hypergraph partitioning is an important problem with extensive applications to many areas, including VLSI design [5] ecient storage of large databases on disks [23], information retrieval [28] and data mining [9, 15] The problem is to partition the vertices of a hypergraph into k equal size subdomains, such that the number of the hyperedges connecting vertices in di erent subdomains (called the cut) is minimized. This work was supported by NSF ....

S. Shekhar and D. R. Liu. Partitioning similarity graphs: A framework for declustering problmes. Information Systems Journal, 21(4), 1996.

.... University of Minnesota, Department of Computer Science, Minneapolis, MN 55455 karypis cs.umn.edu Introduction Hypergraph partitioning is an important problem with extensive application to many areas, including VLSI design [Alpert and Kahng, 1995] efficient storage of large databases on disks [Shekhar and Liu, 1996], and data mining [Mobasher et al. 1996, Karypis et al. 1999b] The problem is to partition the vertices of a hypergraph into k equal size parts, such that the number of hyperedges connecting vertices in different parts is minimized. During the course of VLSI circuit design and synthesis, it is ....

Shekhar, S. and Liu, D. R. (1996). Partitioning similarity graphs: A framework for declustering problmes. Information Systems Journal, 21(4).

....that the neighboring data in multi dimensional space are placed into different disks. Such methods apply only to spatial databases and specific indexing techniques. A promising declustering technique is based on max cut graph partitioning which outperformed all mapping function based strategies [34]. This method can be applied to any relational database system. However, this method have some deficiencies as a relational database system cannot be fully represented by a graph and the cost model of graph partitioning does not accurately represent the cost function of declustering. We show the ....

....have been many research on developing strategies to effectively decluster the data on several disks in order to achieve minimum I O cost. Many declustering strategies were developed on declustering multidimensional data structures such as cartesian product files, grid files, quad trees and R trees [7, 12, 26, 28, 30, 32, 34], multimedia databases [2, 5, 27, 31, 33] parallel web servers [20] signature files [8] spatial databases and geographic information systems (GIS) 34, 35] Most of the efforts on developing declustering strategies were based on mapping functions. These mapping function based strategies ....

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S. Shekhar and D. R. Liu. Partitioning similarity graphs: A framework for declustering problems. Information Systems, 21(6):475--496, 1996.

....declustering schemes that minimize the query response time. Various declustering schemes have been proposed for range queries, including those that are speci cally devised for uniform data [13, 23, 14, 37, 33, 34, 25, 17, 6, 7, 3, 35] and those that work for both uniform and non uniform data [28, 15, 27, 31, 8]. In most of the prior work, performance is evaluated through simulation with randomly chosen grid and query sizes. In contrast, we propose a scheme with (limited) analytical guarantees on its performance. The conference version of this paper [6] was the rst paper proving non trivial theoretical ....

....analytical guarantees on uniform data may not carry over to the case of non uniform data. There are specialized schemes speci cally designed to deal with non uniform data. Several of them are based on graph theory techniques. Examples include [15, 31] based on minimumspanning trees paths) and [27] (based on graph partition with max cut) To the best of our knowledge [27, 8, 25] even the best graph based algorithm, namely the max cut algorithm [27] does not outperform cyclic declustering schemes for uniform data. Because of the above reason and because our primary interest is in uniform ....

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D.R. Liu and S. Shekhar. Partitioning similarity graphs: a framework for declustering problems. Information Systems: An International Journal, 21(6):475-496, Sep. 1996.

....the gains 5 obtained from moving to a hyper graph model. The project led to exploration of graph partitioning for other problems in databases including declustering problems, and join index based join algorithms. Finally, the project led to several refereed journal and conference publications [32, 58, 59, 62, 63], as well as refereed conference papers [31, 39, 57, 60, 61] Impact: The project partially supported the Ph. D. thesis of Dr. Duen Ren Liu, Xuan Liu and C.T. Lu and the M. S. thesis of Mr. Rajat Aggarwal as well. Dr. Liu is currently with the faculty of Inst. of Info. Management at National ....

....Geographic Information and Analysis invited P.I. as an expert on navigable road map databases for advising California Dept. of Transportation center for interoperability. The project is leading to exploration of graph partitioning for other problems in databases including declustering problems [58, 60, 62, 63], and join index based join algorithms [61] It also lead to min cut hypergraph partitioning algorithms needed to optimize CCAM for get successors( operations. We developed a novel hyper graph partitioning algorithm, HMETIS [31, 32] in collaboration with Prof. V. Kumar, which benefits VLSI ....

S. Shekhar and D. R. Liu. Partitioning similarity graphs: A framework for declustering problems. An International Journal: Information Systems(Publisher: Pergamon Press), 21(6), September 1996.

....a partition thus have a higher probability of remaining in cache, yielding more reuse. Lexicographical sort is applied after partitioning to improve locality further. Partitioning algorithms were originally used for load balancing parallel computations [37] VLSI design [2] and database storage [65]. We adapt them for improving cache performance, where overhead of partitioning is much more important. Partitioning may be guided by either geometric location or the underlying graph structure. Recursive coordinate bisection (RCB) uses geometric coordinate information to recursively split ....

S. Shekhar and D.-R. Liu. Partitioning similarity graphs: A framework for declustering problems. Information Systems Journal, 21(4), 1996.

....all elements in a partition together in memory thus increases the probability they can remain in cache, yielding better reuse. Partitioning algorithms were originally developed for applications in such areas as load balancing parallel computations [27] VLSI design [2] and database storage [44]. We adapt them for improving cache performance for irregular codes, where overhead of partitioning is more important. In this section, we examine three partitioning algorithms: recursive coordinate bisection, multi level graph partitioning, and hierarchical graph clustering. 3.1 Recursive ....

S. Shekhar and D.-R. Liu. Partitioning similarity graphs: A framework for declustering problems. Information Systems Journal, 21(4), 1996.

....to facilitate testing [21] However the importance of the hypergraph partitioning problem goes beyond VLSI design. For example, electrical circuits with multiple pin nets are readily modeled as hypergraphs. Other applications include data mining [18] efficient storage of large databases on disks [19], clustering and partitioning of the roadmap database for routing applications [20] de clustering data in parallel databases [19] 1 2 3 4 5 6 7 f a b c e f d 1 2 3 4 5 6 7 a b c d e Figure 1. A hypergraph (left) and a concrete realization as electrical circuit (right) In the last years one has ....

....circuits with multiple pin nets are readily modeled as hypergraphs. Other applications include data mining [18] efficient storage of large databases on disks [19] clustering and partitioning of the roadmap database for routing applications [20] de clustering data in parallel databases [19]. 1 2 3 4 5 6 7 f a b c e f d 1 2 3 4 5 6 7 a b c d e Figure 1. A hypergraph (left) and a concrete realization as electrical circuit (right) In the last years one has observed a blossoming of graph and hypergraph partitioning algorithms and software packages (METIS, MELO, Paraboli, SCOTCH) The ....

S. Shekhar and R. Aggarwal, Partitioning similarity graphs: A framework for declustering problems, Tech. Report TR-94-18, University of Minnesota, Department of Computer Science, 1994.

....Furthermore, our algorithm is significantly faster, requiring 4 to 5 times less time than that required by K PM LR. 1 Introduction Hypergraph partitioning is an important problem with extensive application to many areas, including VLSI design [10] efficient storage of large databases on disks [14], and data mining [13] The problem is to partition the vertices of a hypergraph into k roughly equal parts, such that a certain objective function defined over the hyperedges is optimized. A commonly used objective function is to minimize the number of hyperedges that span different partitions; ....

S. Shekhar and D. R. Liu. Partitioning similarity graphs: A framework for declustering problmes. Information Systems Journal, 21(4), 1996.

....constitutes its partition domain. Three strategies were used to partition data among processors. These strategies are: 1) Contiguous Row Blocking(CRB) 2) Round Robin(RR) and (3) Mirror Image Round Robin(MIRR) The reader can find a survey of other partitioning techniques for GIS data in [SL95, SRT 95, ISS86, KGGK94] In all of our strategies, the basin is represented as an npt Theta npt grid space. 13 Computes bounds for consecutive rows assigned to a processor. getrows1(int P i , int npt, int P, int lower bound, int upper bound ) f compute upper and lower bound ....

S. Shekhar and D. R. Liu. Partitioning Similarity Graphs: A Framework for Declustring Problems. In IEEE Intl. conf. Data Eng., 1995.

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S. Shekhar, D.R. Liu, Partitioning similarity graphs: A framework for declustering problems, Information Systems 21 (6) (1996) 475--496.

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D.R. Liu and S. Shekhar. Partitioning Similarity Graphs: A Framework for Declustering Problems, Information Systems, 1996, volume 21,6, pages 475--496

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