616:
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169:, together with a scalable architecture. Another array database language, constrained to 2-D, has been presented by Marathe and Salem. Seminal theoretical work has been accomplished by Libkin et al.; in their model, called NCRA, they extend a nested relational calculus with multidimensional arrays; among the results are important contributions on array query complexity analysis. A map algebra, suitable for 2-D and 3-D spatial raster data, has been published by Mennis et al.
1568:
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value of an array resulting from the cell-wise addition of two input images is equivalent to adding the maximum values of each input array". By replacing the left-hand variant by the right-hand expression, costs shrink from three (costly) array traversals to two array traversals plus one (cheap) scalar operation (see Figure, which uses the SQL/MDA query standard).
368:
iteration sequence over the array cells during evaluation. Evaluation safety is achieved when every query terminates after a finite number of (finite-time) steps; again, avoiding general loops and recursion is a way of achieving this. At the same time, avoiding explicit loop sequences opens up manifold optimization opportunities.
623:
Due to the massive sizes of arrays in scientific/technical applications in combination with often complex queries, optimization plays a central role in making array queries efficient. Both hardware and software parallelization can be applied. An example for heuristic optimization is the rule "maximum
212:
data cubes are well established; they store cell values together with their location – an adequate compression technique in face of the few locations carrying valid information at all – and operate with SQL on them. As this technique does not scale in density, standard
367:
and safe in evaluation. As iteration over an array is at the heart of array processing, declarativeness very much centers on this aspect. The requirement, then, is that conceptually all cells should be inspected simultaneously – in other words, the query does not enforce any explicit
580:
Array storage has to accommodate arrays of different dimensions and typically large sizes. A core task is to maintain spatial proximity on disk so as to reduce the number of disk accesses during subsetting. Note that an emulation of multi-dimensional arrays as nested lists (or 1-D arrays) will not
71:
do on sets, Array DBMSs offer scalable, flexible storage and flexible retrieval/manipulation on arrays of (conceptually) unlimited size. As in practice arrays never appear standalone, such an array model normally is embedded into some overall data model, such as the relational model. Some systems
240:
When adding arrays to databases, all facets of database design need to be reconsidered – ranging from conceptual modeling (such as suitable operators) over storage management (such as management of arrays spanning multiple media) to query processing (such as efficient processing
632:
In many – if not most – cases where some phenomenon is sampled or simulated the result is a rasterized data set which can conveniently be stored, retrieved, and forwarded as an array. Typically, the array data are ornamented with metadata describing them further; for example,
213:
databases are not used today for dense data, like satellite images, where most cells carry meaningful information; rather, proprietary ad hoc implementations prevail in scientific data management and similar situations. Hence, this is where Array DBMSs can make a particular contribution.
474:, the query language offers all operations the cell type offers on array level, too. Hence, on numeric values all the usual unary and binary arithmetic, exponential, and trigonometric operations are available in a straightforward manner, plus the standard set of Boolean operators.
51:, with single objects frequently ranging into Terabyte and soon Petabyte sizes; for example, today's earth and space observation archives typically grow by Terabytes a day. Array databases aim at offering flexible, scalable storage and retrieval on this information category.
571:
Such languages allow formulating statistical and imaging operations which can be expressed analytically without using loops. It has been proven that the expressive power of such array languages in principle is equivalent to relational query languages with ranking.
130:
in business). The variety occurring can be observed, e.g., in geo data where 1-D environmental sensor time series, 2-D satellite images, 3-D x/y/t image time series and x/y/z geophysics data, as well as 4-D x/y/z/t climate and ocean data can be found.
595:
Compression of tiles can sometimes reduce substantially the amount of storage needed. Also for transmission of results compression is useful, as for the large amounts of data under consideration networks bandwidth often constitutes a limiting factor.
80: – while array objects easily can span several media. The prime task of the array storage manager is to give fast access to large arrays and sub-arrays. To this end, arrays get partitioned, during insertion, into so-called
75:
Management of arrays requires novel techniques, particularly due to the fact that traditional database tuples and objects tend to fit well into a single database page – a unit of disk access on server, typically
692:, a data transport architecture and protocol. While this is not a database specification, it offers important components that characterize a database system, such as a conceptual model and client/server implementations.
184:
is an open-source GIS software that extends object-relational DBMS technology to handle spatio-temporal data types; while main focus is on vector data, there is also some support for rasters. Starting with version 2.0,
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In June 2014, ISO/IEC JTC1 SC32 WG3, which maintains the SQL database standard, has decided to add multi-dimensional array support to SQL as a new column type, based on the initial array support available since the
380:
algebra and query language can serve, which establish an expression language over a minimal set of array primitives. We begin with the generic core operators and then present common special cases and shorthands.
161:
First significant work in going beyond BLOBs has been established with PICDMS. This system offers the precursor of a 2-D array query language, albeit still procedural and without suitable storage support.
444:
indicates that the current boundary of the array is to be used; note that arrays where dimension boundaries are left open at definition time may change size in that dimensions over the array's lifetime.
158:("binary large objects") which are the equivalent to files: byte strings of (conceptually) unlimited length, but again without any query language functionality, such as multi-dimensional subsetting.
103:, expressions of arbitrary complexity can be built on top of a set of core array operations. Due to the extensions made in the data and query model, Array DBMSs sometimes are subsumed under the
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Commonly arrays are partitioned into sub-arrays which form the unit of access. Regular partitioning where all partitions have the same size (except possibly for boundaries) is referred to as
592:. Array partitioning can improve access to array subsets significantly: by adjusting tiling to the access pattern, the server ideally can fetch all required data with only one disk access.
232:, and scalability issues in general. Besides, scientific communities still appear reluctant in taking up array database technology and tend to favor specialized, proprietary technology.
819:
Libkin, L., Machlin, R., Wong, L.: A query language for multidimensional arrays: design, implementation and optimization techniques. Proc. ACM SIGMOD'96, Montreal, Canada, pp. 228–239
612:). A large class of practically relevant queries can be evaluated by loading tile after tile, thereby allowing servers to process arrays orders of magnitude beyond their main memory.
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is a more recent initiative to establish array database support. Like SciQL, arrays are seen as an equivalent to tables, rather than a new attribute type as in rasdaman and PostGIS.
47:, etc.), sitting on a regular grid of one, two, or more dimensions. Often arrays are used to represent sensor, simulation, image, or statistics data. Such arrays tend to be
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These are but examples; generally, arrays frequently represent sensor, simulation, image, and statistics data. More and more spatial and time dimensions are combined with
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In the same manner and in analogy to SQL aggregates, a number of further shorthands are provided, including counting, average, minimum, maximum, and
Boolean quantifiers.
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Chock, M., Cardenas, A., Klinger, A.: Database structure and manipulation capabilities of a picture database management system (PICDMS). IEEE ToPAMI, 6(4):484–492, 1984
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Mennis, J., Viger, R., Tomlin, C.D.: Cubic Map
Algebra Functions for Spatio-Temporal Analysis. Cartography and Geographic Information Science 32(1)2005, pp. 17–32
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This subsetting keeps the dimension of the array; to reduce dimension by extracting slices, a single slicepoint value is indicated in the slicing dimension.
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specifies the domain to be iterated over and binds an iteration variable to it – again, without specifying iteration sequence. Likewise,
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Important application domains of Array DBMSs include Earth, Space, Life, and Social sciences, as well as the related commercial applications (such as
1161:
1173:
837:
Ritter, G. and Wilson, J. and
Davidson, J.: Image Algebra: An Overview. Computer Vision, Graphics, and Image Processing, 49(1)1994, 297-336
228:, there are still many open research questions, including query language design and formalization, query optimization, parallelization and
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Machlin, R.: Index-Based
Multidimensional Array Queries: Safety and Equivalence. Proc. ACM PODS'07, Beijing, China, June 2007, pp. 175–184
119:; actually, many array operators lend themselves well towards parallel evaluation, by processing each tile on separate nodes or cores.
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geographically referenced imagery will carry its geographic position and the coordinate reference system in which it is expressed.
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lists an array-valued attribute type, but this is only one-dimensional, with almost no operational support, and not usable for the
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A first declarative query language suitable for multiple dimensions and with an algebra-based semantics has been published by
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operator aggregates cell values into one scalar result, similar to SQL aggregates. Its application has the general form:
588:. A generalization which removes the restriction to equally sized partitions by supporting any kind of partitioning is
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Space sciences: Planetary sciences, astrophysics (optical and radio telescope observations, cosmological simulations)
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Marathe, A., Salem, K.: A language for manipulating arrays. Proc. VLDB'97, Athens, Greece, August 1997, pp. 46–55
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143:, which is prevailing today, does not directly support the array paradigm to the same extent as sets and tuples.
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axes, such as sales and products; one example where such abstract axes are explicitly foreseen is the (OGC)
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clause specifies the aggregating operation used to combine the cell value expressions into one single value.
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defines the result domain and binds an iteration variable to it, without specifying iteration sequence. The
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862:: Efficient Organization of Large Multidimensional Arrays. Proc. ICDE'94, Houston, USA, 1994, pp. 328-336
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embeds raster support for 2-D rasters; a special function offers declarative raster query functionality.
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The following are representative domains in which large-scale multi-dimensional array data are handled:
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Transformation of a query to a more efficient, but equivalent version during array query optimization
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The above examples have simply copied the original values; instead, these values may be manipulated.
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Generally, Array DBMSs are an emerging technology. While operationally deployed systems exist, like
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432:"A slice through an x/y/t timeseries at position t=100, retrieving all available data in x and y."
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access to such arrays, allowing to create, manipulate, search, and delete them. Like with, e.g.,
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implement arrays as an analogy to tables, some introduce arrays as an additional attribute type.
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include {0..255} for 8-bit greyscale images and {0..255} × {0..255} × {0..255} for standard
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per se accomplish this and, therefore, in general will not lead to scalable architectures.
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system has the longest implementation track record of n-D arrays with full query support.
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operator creates an array over some given domain extent and initializes its cells:
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condense condense-op over index-range-specification using cell-value-expression
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788:. VLDB Journal 4(3)1994, Special Issue on Spatial Database Systems, pp. 401–444
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A tile-based storage structure suggests a tile-by-tile processing strategy (in
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of convenient size which then act as units of access during query evaluation.
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Following established database practice, an array query language should be
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offers chunked storage of 2-D raster maps, albeit without SQL integration.
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875:. Proc. ICDE'99, March 23–26, 1999, Sydney, Australia, pp. 328–336
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Many communities have established data exchange formats, such as
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39:), that is: homogeneous collections of data items (often called
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SQL fights back against NoSQL's big data cred with SQL/MDA spec
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marray index-range-specification values cell-value-expression
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System that provides database services specifically for arrays
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A Database Array
Algebra for Spatio-Temporal Data and Beyond
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688:. A de facto standard in the Earth Science communities is
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This special case, pure subsetting, can be abbreviated as
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Life sciences: gene data, confocal microscopy, CAT scans
560:. The aggregation operator counts the occurrences of
801:. Proc. NGITS'99, LNCS 1649, Springer 1999, pp.76-93
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ISO 9075 SQL Part 15: MDA (Multi-Dimensional Arrays)
556:, establishes a Boolean array of the same extent as
454:"Array A, with a log() applied to each cell value."
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On the
Management of Multidimensional Discrete Data
711:. The new standard, adopted in Fall 2018, is named
548:marray bucket in values count_cells( A = bucket )
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107:category, in the sense of "not only SQL". Query
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154:of Array DBMSs. Another option is to resort to
193:is an array query language being added to the
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530:The next example demonstrates combination of
404:is evaluated at each location of the domain.
544:"A histogram over 8-bit greyscale image A."
376:As an example for array query operators the
172:In terms of Array DBMS implementations, the
58:Euclidean neighborhood of elements in arrays
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501:is evaluated at each domain location. The
253:is given by a (total or partial) function
695:A declarative geo raster query language,
336:, and following common notation we write
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653:Social sciences: statistical data cubes
277:-dimensional integer interval for some
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458:marray p in domain(A) values log( A )
244:
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699:(WCPS), has been standardized by the
515:condense + over p in sdom(A) using A
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640:Earth sciences: geodesy / mapping,
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538:operators by deriving a histogram.
519:A shorthand for this operation is:
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67:In the same style as standard
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462:This can be abbreviated as:
352:sized images), examples for
332:denotes an array element or
115:are important for achieving
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1613:Database management systems
1143:Database management systems
888:, The Register, 26 Jun 2014
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470:Through a principle called
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701:Open Geospatial Consortium
31:services specifically for
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552:The induced comparison,
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124:hydrocarbon exploration
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987:Entity–attribute–value
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440:The wildcard operator
414:marray p in values A
230:distributed processing
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1417:Concurrency control
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719:List of array DBMSs
709:2003 version of SQL
628:Application domains
249:Formally, an array
245:Conceptual modeling
152:application domains
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135:History and status
91:Array DBMSs offer
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1240:Multi-model
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1018:Star schema
950:Dimensional
503:condense-op
365:declarative
222:PostGIS 2.0
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117:scalability
97:declarative
37:raster data
1607:Categories
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960:Relational
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288:, called
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1273:Database
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662:abstract
606:rasdaman
586:chunking
554:A=bucket
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536:condense
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489:As with
479:condense
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430:Example:
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378:rasdaman
320:. Each (
236:Concepts
226:rasdaman
182:TerraLib
174:rasdaman
63:Overview
49:Big Data
29:database
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1381:Trigger
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690:OPeNDAP
608:called
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684:, and
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1233:list
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