Use With One-dimensional Data Structures For Range Searching
Although preserving locality well, for efficient range searches an algorithm is necessary for calculating, from a point encountered in the data structure, the next Z-value which is in the multidimensional search range:
In this example, the range being queried (x = 2, ..., 3, y = 2, ..., 6) is indicated by the dotted rectangle. Its highest Z-value (MAX) is 45. In this example, the value F = 19 is encountered when searching a data structure in increasing Z-value direction, so we would have to search in the interval between F and MAX (hatched area). To speed up the search, one would calculate the next Z-value which is in the search range, called BIGMIN (36 in the example) and only search in the interval between BIGMIN and MAX (bold values), thus skipping most of the hatched area. Searching in decreasing direction is analogous with LITMAX which is the highest Z-value in the query range lower than F. The BIGMIN problem has first been stated and its solution shown in Tropf and Herzog. This solution is also used in UB-trees ("GetNextZ-address"). As the approach does not depend on the one dimensional data structure chosen, there is still free choice of structuring the data, so well known methods such as balanced trees can be used to cope with dynamic data (in contrast for example to R-trees where special considerations are necessary). Similarly, this independence makes it easier to incorporate the method into existing databases.
Applying the method hierarchically (according to the data structure at hand), optionally in both increasing and decreasing direction, yields highly efficient multidimensional range search which is important in both commercial and technical applications, e.g. as a procedure underlying nearest neighbour searches. Z-order is one of the few multidimensional access methods that has found its way into commercial database systems (Oracle database 1995, Transbase 2000 ).
As long ago as 1966, G.M.Morton proposed Z-order for file sequencing of a static two dimensional geographical database. Areal data units are contained in one or a few quadratic frames represented by their sizes and lower right corner Z-values, the sizes complying with the Z-order hierarchy at the corner position. With high probability, changing to an adjacent frame is done with one or a few relatively small scanning steps.
Read more about this topic: Z-order Curve
Famous quotes containing the words data, structures, range and/or searching:
“Mental health data from the 1950’s on middle-aged women showed them to be a particularly distressed group, vulnerable to depression and feelings of uselessness. This isn’t surprising. If society tells you that your main role is to be attractive to men and you are getting crow’s feet, and to be a mother to children and yours are leaving home, no wonder you are distressed.”
—Grace Baruch (20th century)
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)
“I esteem it the happiness of this country that its settlers, whilst they were exploring their granted and natural rights and determining the power of the magistrate, were united by personal affection. Members of a church before whose searching covenant all rank was abolished, they stood in awe of each other, as religious men.”
—Ralph Waldo Emerson (1803–1882)