The R-tree, one of the most popular access methods for rectangles, IS based on the heurlstlc optlmlzatlon of the area of the enclosmg rectangle m each mner node By running numerous experiments m a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which mcorporates a combined optlmlzatlon of area, margin and overlap of each enclosmg rectangle m the directory Using our standardized testbed m an exhaustive performance comparison, It turned out that the R*-tree clearly outperforms the exlstmg R-tree varmnts Guttman's linear and quadratic R-tree and Greene's variant of the R-tree This superlorlty of the R*-tree holds for different types of queries and operations, such as map overlay. for both rectangles and multldlmenslonal points m all experiments From a practical pomt of view the R*-tree 1s very attractive because of the followmg two reasons 1 It effrclently supports pomt and spattal data at the same time and 2 Its lmplementatlon cost 1s only slightly higher than that of other R-trees l.Introduction In this paper we will consider spatial access methods (SAMs) which are based on the approxlmatlon of a complex spatial object by the mmlmum boundmg rectangle with the sides of the rectangle parallel to the axes of the data space yIp---+ This work was supported by grant no Kr 670/4-3 from the Deutsche Forschun&iememschaft (German Research Society) and by the Mmlstry of Environmental and Urban Planning of Bremen Pemxss~on to copy wthout fee all or part of this maternal IS granted prowded that the copses are not made or dlstnbuted for dwzct commeraal advantage, the ACM copy&t notice and the title of the pubbcatlon and its date appear, and notw IS gwn that cqymg II by pemuwon of the Assoaatlon for Computmg Machmq To copy othemw, or to repubbsh requ,res a fee and/or speoflc pemllsslon 0 1990 ACM 089791365 5/!90/0@35/0322 $150The most important property of this simple approxlmatlon 1s that a complex object 1s represented by a limited number of bytes Although a lot of mformatlon 1s lost, mnumum bounding rectangles of spatial oblects preserve the most essential geometric properties of the object, 1 e the location of the oblect and the extension of the object in each axisIn [SK 881 we showed that known SAMs organlzmg (mmlmum bounding) rectangles are based on an underlymg point access method (PAM) using one of the followmg three techniques cllpplng, transformation and overlapping regionsThe most popular SAM for storing rectangles 1s the Rtree [Gut 841 Followmg our classlflcatlon, the R-tree 1s based on the PAM B+-tree [Knu 731 usmg the technique over-lapping regions Thus the R-tree can be easily implemented which considerably contributes to Its popularity The R-tree 1s based on a heurlstlc optlmlzatlon The optlmlzatton crlterlon which It persues, 1s to mmlmlze the area of each enclosing rectangle m the mner nodes This crlterlon IS taken for granted and not shown to be the best possible Questions arise such as Why not mnumlze the margin or the overlap of such mlnlmum...

The skyline of a d -dimensional dataset contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive methods that can quickly return the initial results without reading the entire database. All the existing algorithms, however, have some serious shortcomings which limit their applicability in practice. In this article we develop branch-andbound skyline (BBS), an algorithm based on nearest-neighbor search, which is I/O optimal, that is, it performs a single access only to those nodes that may contain skyline points. BBS is simple to implement and supports all types of progressive processing (e.g., user preferences, arbitrary dimensionality, etc). Furthermore, we propose several interesting variations of skyline computation, and show how BBS can be applied for their efficient processing.

The skyline of a set of d-dimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the first skyline points without having to read the entire data file. Currently, the most efficient algorithm is NN (nearest neighbors), which applies the divideand-conquer framework on datasets indexed by R-trees. Although NN has some desirable features (such as high speed for returning the initial skyline points, applicability to arbitrary data distributions and dimensions), it also presents several inherent disadvantages (need for duplicate elimination if d>2, multiple accesses of the same node, large space overhead). In this paper we develop BBS (branch-and-bound skyline), a progressive algorithm also based on nearest neighbor search, which is IO optimal, i.e., it performs a single access only to those R-tree nodes that may contain skyline points. Furthermore, it does not retrieve duplicates and its space overhead is significantly smaller than that of NN. Finally, BBS is simple to implement and can be efficiently applied to a variety of alternative skyline queries. An analytical and experimental comparison shows that BBS outperforms NN (usually by orders of magnitude) under all problem instances.

No abstract

The skyline of a set of d-dimensional points contains the points that are not dominated by any other point on all dimensions. Skyline computation has recently received considerable attention in the database community, especially for progressive (or online) algorithms that can quickly return the first skyline points without having to read the entire data file. Currently, the most efficient algorithm is NN (nearest neighbors), which applies the divideand-conquer framework on datasets indexed by R-trees. Although NN has some desirable features (such as high speed for returning the initial skyline points, applicability to arbitrary data distributions and dimensions), it also presents several inherent disadvantages (need for duplicate elimination if d>2, multiple accesses of the same node, large space overhead). In this paper we develop BBS (branch-and-bound skyline), a progressive algorithm also based on nearest neighbor search, which is IO optimal, i.e., it performs a single access only to those R-tree nodes that may contain skyline points. Furthermore, it does not retrieve duplicates and its space overhead is significantly smaller than that of NN. Finally, BBS is simple to implement and can be efficiently applied to a variety of alternative skyline queries. An analytical and experimental comparison shows that BBS outperforms NN (usually by orders of magnitude) under all problem instances.