## Compact Data Structures with Fast Queries (2005)

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Citations: | 4 - 0 self |

### BibTeX

@TECHREPORT{Blandford05compactdata,

author = {Daniel K. Blandford and Christos Faloutsos and Danny Sleator},

title = {Compact Data Structures with Fast Queries},

institution = {},

year = {2005}

}

### OpenURL

### Abstract

Many applications dealing with large data structures can benefit from keeping them in compressed form. Compression has many benefits: it can allow a representation to fit in main memory rather than swapping out to disk, and it improves cache performance since it allows more data to fit into the cache. However, a data structure is only useful if it allows the application to perform fast queries (and updates) to the data.

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Citation Context ...onds. a factor of 7.5 averaged over all the graphs (assuming the vertices are labeled with the separator ordering). The effect of insertion order has been previously reported (e.g. [84, page 268] and =-=[36]-=-) but the magnitude of the difference was surprising to us—the largest factor we have previously seen reported is about 4. We note that the magnitude is significantly less on the Pentium III with its ... |

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Citation Context ...ne a graph to be separable if it is a member of a class that satisfies an nc-separator theorem. A class of graphs has bounded density if every n-vertex member has O(n) edges. Lipton, Rose, and Tarjan =-=[80]-=- prove that any class of graphs that satisfies a n/(log n) 1+ǫ -separator theorem with ǫ > 0 has bounded density. Hence separable graphs have bounded density. Another type of graph separator is an edg... |

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Citation Context ...128, 7, 124, 5], these algorithms can be much more complicated than their main-memory counterparts, and can be significantly slower. The field of compressed meshes has received considerable attention =-=[44, 61, 121, 98, 105, 120, 70, 66, 53]-=-. In three dimensions, for example, these methods can compress a tetrahedral mesh to less than a byte per tetrahedron [120]—about 6 bytes/vertex (not including vertex coordinates). These techniques, h... |

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Citation Context ...he cache. However, a data structure is only useful if it allows the application to perform fast queries (and updates) to the data. There has been considerable previous work on compact data structures =-=[68, 91, 29, 46]-=-. However, most of the previous work has been exclusively theoretical, in that the structures are too complex to implement or suffer from very high associated constant factors. Further, the compressio... |

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Citation Context ...ent data structures for representing two and three dimensional simplicial meshes. (By a d simplicial mesh we mean a pure simplicial complex of dimension d, which is a manifold, possibly with boundary =-=[49]-=-.) The data structures support standard operations on meshes including traversing among neighboring simplices, inserting and deleting simplices, and the ability to store data on simplices. For a class... |

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Citation Context ...nd point distributions. We present experiments based on using our representation as part of incremental Delaunay algorithms in both 2D and 3D. We use a variant of the standard Bowyer-Watson algorithm =-=[25, 131]-=- and the exact arithmetic predicates of Shewchuk [111] for all geometric tests. We also present experiments based on a Delaunay refinement algorithm that removes triangles with small angles by adding ... |

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Citation Context ...ompression is better for denser sets (as predicted by the space bound given above). Separable Graphs (Chapter 5). Recently there has been a great deal of interest in compact representations of graphs =-=[125, 72, 65, 82, 64, 105, 92, 68, 91, 40, 46, 65, 28, 1, 119, 22]-=-. Using difference coding 3sit is possible to create several different compact representations for separable graphs. (A graph is defined to be separable if it and all its subgraphs can be partitioned ... |

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152 |
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Citation Context ...h on the current mesh. When a point p is inserted, the cavity is determined by a search starting from the face that contained p. To achieve optimal runtime bounds we use the idea of Clarkson and Shor =-=[41]-=- and maintain an association of every point p not yet inserted into the mesh with the face tp that contains p. The search for the cavity of p will start at tp. Their algorithm keeps the history of the... |

145 | Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates
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Citation Context ...ing our representation as part of incremental Delaunay algorithms in both 2D and 3D. We use a variant of the standard Bowyer-Watson algorithm [25, 131] and the exact arithmetic predicates of Shewchuk =-=[111]-=- for all geometric tests. We also present experiments based on a Delaunay refinement algorithm that removes triangles with small angles by adding new points at their circumcenters. All space is report... |

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Citation Context ...he cache. However, a data structure is only useful if it allows the application to perform fast queries (and updates) to the data. There has been considerable previous work on compact data structures =-=[68, 91, 29, 46]-=-. However, most of the previous work has been exclusively theoretical, in that the structures are too complex to implement or suffer from very high associated constant factors. Further, the compressio... |

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Citation Context ...ves experimental results for the second representation. To show the versatility of the compression technique, we applied it to two separate data structures: red-black trees [60] and functional treaps =-=[6]-=-. 4.2 Representation With Dictionaries Here we describe a representation for ordered sets based on our variable-bit-length dictionary from Section 3.3. We would like to represent ordered sets S of int... |

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Citation Context ...ertex, it may be 51sMax Graph Vtxs Edges Degree Source auto 448695 6629222 37 3D mesh [130] feocean 143437 819186 6 3D mesh [130] m14b 214765 3358036 40 3D mesh [130] ibm17 185495 4471432 150 circuit =-=[3]-=- ibm18 210613 4443720 173 circuit [3] CA 1971281 5533214 12 street map [127] PA 1090920 3083796 9 street map [127] googleI 916428 5105039 6326 web links [56] googleO 916428 5105039 456 web links [56] ... |

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Citation Context ...nd therefore close together in the numbering. This is similar to the graph-reordering algorithm of Chapter 5. We have implemented this idea and tested it on indexing data from the TREC-8 ad hoc track =-=[129]-=- (disks 4 and 5, excluding the Congressional Record). We tested a variety of codes in combination with difference coding. Our algorithm was able to improve the performance of the best compression tech... |

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Citation Context ...external memory. To avoid thrashing, this requires designing algorithms for which the access to the mesh is carefully orchestrated. Although several such external memory algorithms have been designed =-=[55, 45, 43, 83, 128, 7, 124, 5]-=-, these algorithms can be much more complicated than their main-memory counterparts, and can be significantly slower. The field of compressed meshes has received considerable attention [44, 61, 121, 9... |

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Citation Context ...tely they have to be laid out in two dimensions with only a small constant number of layers of connections. It is well understood that the size of the layout depends critically on the separator sizes =-=[126]-=-. Clearly certain graphs do not have good separators. Expander graphs by their very definition cannot have small separators. 5.2 Static Representation We will consider three kinds of queries: degree q... |

103 |
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Citation Context ...acent faces rotating around its 3 edges, and 3 to the corner vertices). This corresponds to 18 pointers per tetrahedron. Weiler’s radial-edge representation [134], Brisson’s cell-tuple representation =-=[26]-=-, and Lienhardt’s G-map representation [79] all take more space. In summary, the most efficient standard data structures of simplicial meshes use 6 pointers per triangle in 2D and 8 pointers per tetra... |

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Citation Context ...on system used for this must be capable of allocating or freeing |s| bits of memory in time O(|s|/w), and may use O(|s|) space to keep track of each allocation. It is well known how to do this (e.g., =-=[8]-=-). Overview. We begin with an overview of our array structure. We partition the strings ai into blocks of contiguous elements, containing on average Θ(w) bits of data per block. We maintain the blocks... |

92 |
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Citation Context ...imized to 9 pointers per face (6 to the adjacent faces rotating around its 3 edges, and 3 to the corner vertices). This corresponds to 18 pointers per tetrahedron. Weiler’s radial-edge representation =-=[134]-=-, Brisson’s cell-tuple representation [26], and Lienhardt’s G-map representation [79] all take more space. In summary, the most efficient standard data structures of simplicial meshes use 6 pointers p... |

90 | Face Fixer: Compressing Polygon Meshes with
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