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1,309
A Catalog of Hanan Grid Problems
 Networks
, 2000
"... We present a general rectilinear Steiner tree problem in the plane and prove that it is solvable on the Hanan grid of the input points. This result is then used to show that several variants of the ordinary rectilinear Steiner tree problem are solvable on the Hanan grid, including  but not li ..."
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Cited by 11 (2 self)
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We present a general rectilinear Steiner tree problem in the plane and prove that it is solvable on the Hanan grid of the input points. This result is then used to show that several variants of the ordinary rectilinear Steiner tree problem are solvable on the Hanan grid, including
NonHanan Routing
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN
, 1998
"... This work presents a Steiner tree construction procedure, MVERT, to meet specified sink arrival time constraints. It is shown that the optimal tree requires the use of nonHanan points. The procedure works in two phases: a minimumdelay Steiner tree is first constructed using a minor variant of the S ..."
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Cited by 10 (6 self)
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This work presents a Steiner tree construction procedure, MVERT, to meet specified sink arrival time constraints. It is shown that the optimal tree requires the use of nonHanan points. The procedure works in two phases: a minimumdelay Steiner tree is first constructed using a minor variant
Distance Browsing in Spatial Databases
, 1999
"... Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is kn ..."
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Cited by 390 (20 self)
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Two different techniques of browsing through a collection of spatial objects stored in an Rtree spatial data structure on the basis of their distances from an arbitrary spatial query object are compared. The conventional approach is one that makes use of a knearest neighbor algorithm where k is known prior to the invocation of the algorithm. Thus if m#kneighbors are needed, the knearest neighbor algorithm needs to be reinvoked for m neighbors, thereby possibly performing some redundant computations. The second approach is incremental in the sense that having obtained the k nearest neighbors, the k +1 st neighbor can be obtained without having to calculate the k +1nearest neighbors from scratch. The incremental approach finds use when processing complex queries where one of the conditions involves spatial proximity (e.g., the nearest city to Chicago with population greater than a million), in which case a query engine can make use of a pipelined strategy. A general incremental nearest neighbor algorithm is presented that is applicable to a large class of hierarchical spatial data structures. This algorithm is adapted to the Rtree and its performance is compared to an existing knearest neighbor algorithm for Rtrees [45]. Experiments show that the incremental nearest neighbor algorithm significantly outperforms the knearest neighbor algorithm for distance browsing queries in a spatial database that uses the Rtree as a spatial index. Moreover, the incremental nearest neighbor algorithm also usually outperforms the knearest neighbor algorithm when applied to the knearest neighbor problem for the Rtree, although the improvement is not nearly as large as for distance browsing queries. In fact, we prove informally that, at any step in its execution, the incremental...
The R+Tree: A Dynamic Index For MultiDimensional Objects
, 1987
"... The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman's Rtrees (R trees) that avoids overlapping rectangles in ..."
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Cited by 343 (19 self)
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The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman's Rtrees (R trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R trees achieve up to 50% savings in disk accesses compared to an Rtree when searching files of thousands of rectangles. 1 Also with University of Maryland Systems Research Center. 2 Also with University of Maryland Institute for Advanced Computer Studies (UMIACS). This research was sponsored partialy by the National Science Foundation under Grant CDR8500108. 1. Introduction It has been recognized in the past that existing Database Management Systems (DBMSs) do not ...
Spatial Data Structures
, 1995
"... An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarch ..."
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Cited by 334 (13 self)
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An overview is presented of the use of spatial data structures in spatial databases. The focus is on hierarchical data structures, including a number of variants of quadtrees, which sort the data with respect to the space occupied by it. Suchtechniques are known as spatial indexing methods. Hierarchical data structures are based on the principle of recursive decomposition. They are attractive because they are compact and depending on the nature of the data they save space as well as time and also facilitate operations such as search. Examples are given of the use of these data structures in the representation of different data types such as regions, points, rectangles, lines, and volumes.
Hanane Mouawad (PhD in Food Economy)
"... Modernity and tradition of Lebanese food consumption between standardization and particularsims ..."
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Modernity and tradition of Lebanese food consumption between standardization and particularsims
Rectilinear Group Steiner Trees and Applications in VLSI Design
, 2000
"... Given a set of disjoint groups of points in the plane, the rectilinear group Steiner tree problem is the problem of finding a shortest interconnection (under the rectilinear metric) which includes at least one point from each group. This is an important generalization of the wellknown rectiline ..."
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Cited by 3 (0 self)
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algorithm for solving the rectilinear group Steiner tree problem (and related variants of the problem). The algorithm essentially constructs a subgraph of the corresponding Hanan grid on which existing algorithms for solving the Steiner tree problem in graphs are applied. The reductions of the Hanan
Algorithms for NonHananbased Optimization for VLSI Interconnect under a Higher Order AWE Model
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN
, 2000
"... To improve the performance of critical nets where both timing and wire resources are stringent, we integrate buffer insertion and driver sizing separately with nonHanan optimization and propose two algorithms: BINO (simultaneous Buffer Insertion and NonHanan Optimization) and FARDS (Fullplane A ..."
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Cited by 7 (3 self)
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To improve the performance of critical nets where both timing and wire resources are stringent, we integrate buffer insertion and driver sizing separately with nonHanan optimization and propose two algorithms: BINO (simultaneous Buffer Insertion and NonHanan Optimization) and FARDS (Full
Nontree routing for reliability and yield improvement
 In Proc. Int. Conf. on Computer Aided Design
, 2002
"... Abstract—We propose to introduce redundant interconnects for manufacturing yield and reliability improvement. By introducing redundant interconnects, the potential for open faults is reduced at the cost of increased potential for short faults. Overall, manufacturing yield and fault tolerance can be ..."
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Cited by 12 (0 self)
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such practical issues as wirelength increase budget, routing obstacles, and the use of Steiner points.2) We show that an optimum solution can always be found on the Hanan grid defined by the terminals and the corners of the feasible routing region. 3) We give a compact integer program formulation which is solved
Preferred Direction Steiner Trees
"... Interconnect optimization for VLSI circuits has received wide attention. To model routing surfaces, multiple circuit layers are frequently abstracted as a single rectilinear plane, ignoring via costs, layer dependent routing costs, and congestion impact for routing in a particular direction. In this ..."
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Cited by 11 (0 self)
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, obtaining reductions in tree cost of 11% to 37% on average for random problems. Our results include a proof that the performance bound of Minimum Spanning Tree cost to Steiner Minimal Tree cost under this model is 2:1 (in contrast to 1.5:1 for planar problems). We adapt the Hanan grid to this model
Results 1  10
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1,309