Add to Watchlist

In-Memory Columnar Store for PostgreSQL

59 views

Citation of segment
Embed Code
Purchasing a DVD Cite video

Formal Metadata

Title In-Memory Columnar Store for PostgreSQL
Alternative Title In-Memory Columnar Store extension for PostgreSQL
Title of Series PGCon 2014
Number of Parts 31
Author Knizhnik, Konstantin
Contributors Crunchy Data Solutions (Support)
License CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/19081
Publisher PGCon - PostgreSQL Conference for Users and Developers, Andrea Ross
Release Date 2014
Language English
Production Place Ottawa, Canada

Content Metadata

Subject Area Computer Science
Abstract IMCS is In-Memory Columnar Store for PostgreSQL. Vertical data model is more efficient for analytic queries performing operations on entire column. IMCS provides 10-100 times improvement in performance comparing with standard SQL queries because of: data skipping: fetching only data needed for query execution parallel execution: using multiple threads to execute query vector operations: minimizing interpretation overhead and allowing SIMD instructions reduced locking overhead: simple array level locking no disk IO: all data is in memory IMCS is implemented as standard PostgreSQL extension. It provides set of function and operators for manipulations with timeseries. Some of them are analog of standard SQL operators (arithmetic, comparisons, sorting, aggregation...). But there are also complex analytic operators like calculation of ranks, percentiles, cross points and extended set of aggregates for financial application like split-adjusted price, volume-weighted average price, moving average... Columnar store manager stores data tables as sections of columns of data rather than as rows of data.In comparison, most relational DBMSs store data in rows. Such approach allows to load the whole record using one read operation which leads to better performance for OLTP queries. But OLAP queries are mostly performing operations on entire columns, for example calculating sum or average of some column. In this case vertical data representation is more efficient. Columnar store or vertical representation of data allows to achieve better performance in comparison with horizontal representation due to three factors: * Data skipping. Only columns involved in query are accessed. * Vector operations. Applying an operator to set of values minimize interpretation cost. Also SIMD instructions of modern processors accelerate execution of vector operations. Compression of data. For example such simple compression algorithm like RLE allows not only to reduce used space, but also minimize number of performed operations. IMCS is first of all oriented on work with timeseries. Timeseries is sequence of usually small fixed size elements ordered by some timestamp. Operations with timeseries rarely access some particular timeseries element, instead of it them operate either with whole timeseries either with some time interval. Such specific of timeseries operation requires special index for timeseries, which is different from traditional database indexes. Such index should not provide efficient way of locating arbitrary timeseries element. Instead of it this index should be able to efficiently extract range of timeseries elements. Advantages of IMCS approach: Fast execution based on vector operations Parallel execution of query No changes in PostgreSQL core (just standard extension) No MVCC overhead (MURSIW isolation level) No disk IO (in-memory store) Optimized for timeseries (massive operations with time slices)
Series
Annotations
Transcript
Loading...
my name is Constantin unique I full Digital Equipment to give the soft borrowing cited the non Philip freelancer and CS is my 1st contribution for for this as quick as far as I
understand it yesterday and not everybody on finally is going to start paying most of the databases are storing data ongoing so each active attributes of which records are stored together which makes it possible to will fetch record to using just 1 party decorations which is optimal for most Aquarius but the form a lot of queries allow
queries used to the terrorists by the good where a large number of records but usually they need only some subset of columns for example of them are completing
the chemical collecting average cost price radical
data representation follows the tools fetched only as schools which are actually needed for execution of where but it is not the only advantage actually erected representation data-storage just as an eraser and become manipulate is that as his erased sequel compiler compiles quarry into some internal representation which then interpreted by sequel engine a cyclic engine that has to be performed each operation for each attribute of features and it certainly we can produce a local flood significant at interpretation of the phrase there are 2 ways of for solving this problem we can generate native code but as it was done for for example for the 2 but it is not portable and very complex approach vector operations is another approach we perform operation on just for a single event about for a set of values in this case interpretation costs can be significantly reduced also modern process of provides a set SIMD instructions which helps to perform better operation in fast fortunately it is not necessary at all you found convincing fashion all functions all right some of them they're called to use a standard the instructions modern compile the compiler Flag like efficiency are able to even meet SIMD instructions just for play in the cold for example if I read the arrival of each x component of the vector then it is build generate it indeed instruction from economics instructions so and lost their advantage of vertical model is the compression of the data certainly compression can be also done for horizontal representations about the the compression is based on redundancy and their that it is in the input data and you feel the elder speech that is viewed independently and then we can reach much better compression major here such simple a simple algorithm like earlier on Wednesday according poles tool significantly reduces memory footprint especially if available for the public radius although this has the
classical architecture for relational database system and is optimized for the Aquarius can execute or large number of requests concurrently but if we need to execute just single but very complex query and all this is not able to walk around in parallel also ponders use and this is the model of each year requires an additional significantly better record all the half space on the hard it's about 24 bytes if we don't deal this time serious in some cases the size of and fewer in the man all is small enough those bytes so in this case this better records space the compatible with the size of a lament itself salt storage is used very inefficiently I was have classical database system has to spend a lot of time in page management locking and conversion processing which are not always so needed for analytic queries so all
these so based on this idea so I decided to implement handsets extension for positive 1st of all it is a lot to our at way of storing data so data main storage of data that is still stored and all and says just create the in-memory copy of they so it has to deal with is the redundancy of consistency it is provided by positive it is learning memory is very cheap now so it's not computer visit about of memory is not something where exotic so we can lolled quite large sets of data and went to bleed them in memory of result buying significant she's I already have also I'm says provide parallel but properly but this an over some operations mostly aggregation filtering sorting can be done in parallel so i'm says used earlier compression and some other techniques that compression techniques which helps to reduce the memory footprint and incest is done by all this extension so it's not known to a change of the of the of course do you use this functionality
abscess is keeping its data in all this shared memory as well as all this internal shared waters well will for the main that the construction used by and says for storing and see is that it is the the q albeit that he is the i zone timestamp Pfizer element position in time series I'm serious can have over it into fires and the hash-table stable is
a user is used block a and C is by this and many dictionary is used to about dictionary will tell us later all I'm saying is
that of constructing pipeline over a period of the detect that internal results on never materialized in memory at the each of each apparatus producing some I call it dials all maybe uncovered call it a vector of some set of awareness which is transferred to the next level of my life size of the diol should be chosen to be a large enough to ordered use interpretation of course but to should be wary large to efficiently utilize this you cash right now default value is 128 bytes certainly gives is the much smaller than the size of modern gaseous but for the Please take in account that I wasn't 1 tile can be proceeded with at the same time and the more complex queries Furthermore tiles you need to access at the same time for most of the time since the apparatus on taken the time serious underdetermined also time serious and exception is the off aggregates reaches tones got where you a few words about the
parallel execution In both and says has the set of whole so people will say that the number of sets can be here is explicitly specified all automatic chosen based on number of course in the system input data is splitted into 2 equal sized in there are also a number of with the walls is the same as number of so that each in the wall is indeed a precedent by which set and the partial results are produced is that this partial result that combined the combined to produce the final result so operators which can be executed in parallel should implement prepare methods which should do a 1st stage and the social the parliament environments which March partial results how
ancestors is you a is used so 1st step is the real is over just carried this extension the 2nd step is the 1 that is being since rate function is generating specialize functions in squared and a special type which can be used toaccess problem with daughter I will explain this model details the 1st
parameter is stable name is just the normal table in normal or stable and 2nd the 3rd parameters odd names of attributes in the stable the and serious should have a timestamp at the review data is ordered by these stump so timestamp can be considered as as a primary key but if the offender to be renewed and optional so its argument specifies the time series into 2 5 for example for 1 quarter we can use symbol name like IBM as metafile I'm serious if time series into the fire is not specified then all data from the table is placed in the single I'm own back
once the become he wants to reduce its functions and that's all I forgot the same or for what a table this function getting it generates quarter underscored time serious type this type has the same at an active uses the same name as a whole they will not dipoles is at the review is I'm serious once we complete the was functions are generated began in but data it can be adopted in explicitly using generated message it can be done implicitly when data is just accessed and I'm just understand that the call of stories and there is a and B also incrementally edit the call love story using 3 goes from data is placed in August quarter get is 1
of the main generated function into the that instances of work with a quarter time serious type as I already said at use all will resist that has the time serious and a is in the fire of time series it was sold to actually is is the function tone complex-type really reach encapsulate them serious and I'm since functions are manipulated into this and serious is is standout sequel aquaria and this is its I'm just another rich during the same things most of is
square apparatus but they contain serious as input and producing status as output so we have the vertical representations so all of the quarter execution blunt but sometimes it is now the more convenient to work and at the back door horizontal form a representative set of as normal positive staple it can be done using a projected functions so is this quiet takes vision all 4 both that URL for 10 time series and man is the maximal close right then we extracted elements a dispositions from all of the time series and the curve and stopped topples Serbia's responded elements the output is just the normal obvious table which can be used for any other such queries but this this was this
makes it possible to define a user defined parameter this feature is widely used by I'm serious to make or operations is the time series looks like a normal sequel expressions she Google's high lower you are tired old time series and the greater than minus divide up apparatus for time series as you can see that this looks like a normal sickle expression this is yet another example of aggregation it's calculate so cold or would emerge at price this is the concatenation operator which concatenates immense of 2 times serious and it is used as a group by body or he so this apparatus far more signal the correspondent for simple and other purposes but I'm still also
provides some of special apparatus which are widely used in for example international sphere for example of this is example of calculating what awaited at each price this is how it can be complicated in and that's equal and the and says has just the special apparatus for you a few words
about only the idea of an earlier study will be place a sequence of value of the same variance is just 1 window which is called by load and count how much that these values repeated Italy encoding health not only to reduce space used by data but also makes the increased speed all for grow quite execution for example if we multiply I'm serious at some other time series and we have over 100 same radius we don't need to repeat multiplication 100 times but can do it only once and reused 100 counter for that as well so this where is this case where can cutest 10 times faster 100 times
faster yet another optimization done by time since it was moderated by real use case there was no application which collecting information from mobile devices this information includes name of operating system 1 name of Dubai's provide the name novel for different where this is not where the largest of from 100 to 1 thousand but for each of fires large analysis is just short forms of very alluded fires a much larger so if a them directly it will take a lot of space I says makes it possible to implicitly map existing installed integers it contains a dictionary and when data is loaded in I'm says storage of these things are replaced 3 is unique integer called depending on size of the dictionary if it is less than the 64 kilobytes them integer hold his dog bites precise Tobias otherwise it's the size for whites and later in the where it would can manipulate is is
er resist integers instead of students for example if the comparing 2 elements that can compare integers instead of comparing things which is always a significantly faster and and variations of each off strategic for example marching Zysset integer quarters are implicitly converted back to streams also it is done when the results operating so them operate and just in normal text for form I'm says is
optimized to work with time serious usually and fears group quarters are not existing just some individual elements of them are a there but the whole time series is taken from a range of and so 1 of the main goals of arms sales was to provide an efficient way of extracting some in the intervals of elements from time series this is most the a simple form it just extracts 1 simple element this is more popular form which extracts a range of romance it's also it's was these and this case so we use timestamps toward select and it's also possible to select elements by position position started from 0 or so to extract shows closely elements is specified you position equal tool to position can be also negative in this case it is a calculated from the end of time series so don't get them last elements we can specify from position as minus that and just fill up around in all these cases is the justifier of and serious it's also possible which to the final just single the the fire but the rate of the difference in this case immense from all this time series will be taken together I and
waters are used to perform some aggregation of the data this is why I'm says provides large number of these different aggregate function 1st of all it's a good and aggregates each copulate aggregates for the whole time series group by aggregates the has 2 2 parameters to utterances just 1 is time series which is actually aggregated there aggregated and 2nd appearance specifies the the group by I'm serious elements of system that serious is the same value of forming groups so this quiet locally what symbol for each week if you don't consider 1 week stuff of great abrogates are splitting time series in the same size in digitizing the wealth and aggregated circle collated for each share in the wealth moving are all window aggregates are also working with the 60 size and their walls but this window is more so number of elements in the result and Sears is the same as input time serious fresh aggregators are similar with the water followed edition is done in the sequel and that's equal unlike a group by adding dates it's they account all elements from 1 time serious knowledge subsequent ones and then finally cummulative aggregate's in this case the result depends on the values of all preceding elements this aggregate's
all president and that of course and Alex but I'm says also offers some I dig a specific of all financial applications for examples is where execute average to arrange Carter for 2 weeks I don't want to explain this formula it's quite complex I just want to comment some apparatus used here because this is a and C is concatenation operations in the big elements from all 1 time series and the apparent elements from 2nd I'm serious was this short period there is used to walk cut elements from time series by shifting and serious 1 position left we are cutting hospital and from time series what so what absolute values this seems to be obvious and others example is the collection of related stands index indicator here we are using CSV indoor yeah functions stands for exponential moving average it's a very popular for financial analysis I think soul and
since acquires additional memory it's requires additional time for loading data and there and Proc per and also provides some special set of functions so special set of parameters of each of it's not supported language but the room in any case index and little bit different is not sequel the question is why do we need all these things and then is the answer is the the all of the Ministries performance so i'm is the from 10 to 100 times faster than the respondent and that's equal Aquarius actually perform well on the radio performance radio depends on size of form and here's what I'm seriously is the cells and elements in use of performance is about 10 times and and the the 1st size of them seriously is the median more than a man so that I can get my environment up to 100 improvement in speech it is the poles of world in memory on access it's because of compression it's because of parallel and diffusion of candidates and they're like 0 for all their heads the transaction locking and other overhead you know
I mean ready to answer questions you can also find information in internet only is this so it's possible to adorn bundles this extension that she had to come up and that it's so that they can be used to view the most of reasons of discretion starting from 9 3 and this it is not using some modern features like the moniker shared memory segments and it requires the preloading of this extension um we because it need to talk sense for place date and positive shared memory not credit answer the questions he since
they're all functions this she has underscored graphics I I'm says functions functions so that the user class table underscore is generated function for these functions are generated by the end of the 8 and these functions of adjusting disease and all the them all of yes if there but if a user defined function it takes the NCS that sort of argument of this function is the NCAA Quartet is Penzias and that it spread useless scholar where your hand in the light of the of life of the privacy of the years of that is exactly what it was singled out your normal and argument has years direct and serious is that compiled that a user defined types provided by the eye and say yes it's a encapsulate access to attend actually contains no data from and go back and
it'll be I think here so
option most 0 4 times its functions are not performing executions themselves so when we're have cold CS-MUX no executions heard is fusion is that it just constructs uh element of a pipeline again and execution has started by a top level function so in this case where this pipeline starts to roll and the date that is such a pulled so some operator asks for file from Marx that the ultimate marks and John is loading data from it the artists from 1 for all of the star and in this case it all these big procedures all of the time is that the tireless 120 so so we give you move for our multiple barriers between each apparatus but the thing multiple but if this is there is the main idea but about 15 so solo CLB 5 marks the moment 100 elements and so on z so much that the other is implemented just as the blue ridge iterates through 100 elements and find out marks and the same is true for all for most of all the answers operations if you propose additional they also have to just lay in a plants even cheer takes 1 that the and as a vector and the if a edition of its elements this is why up a seat compiler is able to work attitudes scored a very efficient very efficient and very efficient ways and he actually played no cost for interpreting what quarter of the 1 on the use of ah yes it's also more now all apparatus of overlooking the styles so input both dialect that is said to be in each they started in that column a story it's you just go 100 elements from the 3 page and bullshit into the pipeline so my and along similar lines mostly and just sort of the of the of the time series data and this effectively represents an automaton runs against time series data so that the a triple triple vertical bar operator this time series that agents that that effectively operating in the automaton and once that's done all the operators the actual execution yes that's right now we're saying it's all there you have the universe and know what are data can be only up and it and the digit has to be and in no time stamp increasing order so it's not possible to insert in the inside of it was a lot of or some its moment multiple learning a single right a model for the whole time serious so it's possible that executed several quarters in parallel the child the former quarters bought a film date and fears and it's not possible to do to perform quarters at this time during long yes all you're all year if you but it it is not intended that it's in the data is actually related 1 element by element it's a much more efficient to water data somewhere and then the energy of the yes I I tested it but the performance open and much more so than if you just look up and data for the whole day for example so all at time stamp is the and it's not that it has not been tied it's any integer fire why be is that it can be it on g is a sequence number so we know also I forgot to say that I'm sensor about types supported by and see right now all world cannot positive that's all the time of the day that then for the floating-point time for all staying still and the customs know of custom times on the support of the calls and tone it's just grow cold in the which implements at the author of this operation for the particular type the other functions of the let's yes so how do we know about the use of what was going to use the image of that you is that was the price of some of the problems with the people the for example you would like
program for a price the price you take
not to be in a lot of it is possible for the answers provided as of joy and so you can if you care for it to a different time seriously you grown much of them by timestamp and compare so you can compare prices for IBM for some data and price for for them before it in the fall the same the another short hand here when the ice age if you want to compare book yes there's some examples
there is that it gives a period by 5 different the out each share of stock the elements of 2 subsequent eleven-thirds produced a of differences and in this case you can actually use this in the company's during dynamic of the price and using she is due to appear at the end of the the year course of the the of the have no real search all of all of the all of these values of if if you what the only thing that you have the right kind of 1 of my or it's shoveling stood close you that's example low glosters at column names of the columns and so on it's er here you are using a different here not to what it here it's using different columns from a is just into 2 5 0 for all the time series it's and so it's not necessary to have a positive and citizens of 5 example it's possible to place all data in the single time serious and in this case single named build indicated as any other interview but usually international applications data analysis is performed for somebody to assume so we need to find the average price for a particular component the average prices for the whole day for yeah 4 of and other questions about the possible to use these standards and all the queries in the whole or on to do it it's necessary to implement that to change for this but at it positive of executive to support new low-pass about they're executed tool my program and that's equal expressions to the separation also
of some of the operations has no knowledge in sequel for example 1 on top of the
the for example I'm not sure how
you go commodity firm who do implement right what quality which implements community finding gettin standards equal and
the title you implement such kind of 4 quadrants then that's equal weights and uh not the role of all we circulate so for a possible to use to use or 0 this is why vector can be used to use
the uh at this stage you're
when we committed generate function so quartic character it to and it can use over view here instead of of 4 table and the combined result from more different bogus tables and also perform some grouping all Prepare testing on all 4 data the share has to be imported in almost all and the results of itemsets
quarters can be if you use a few projects and queries on the representation and you just just get normal set helpless which can be a movement related in standard way and if final
projection this performs and the result is just a set of world and serious you can use you can and then you can copper from 1 computer to another another question the aim of our own know what did directly adopted here might admitted it not so much time ago and then what i'm gonna continent at this moment I want to receive some feedback understand how it can be used for our can be improved how I need some real datasets because I'm testing at some data have bought this system is shown to be useful for where alleged data for small datasets for this is fast enough so you need to perform some kind of some analytic on very large volumes about words this is why I very interested in some feedbacks garments change requests and so also any more questions so that is that that is the thing you otherwise might have created this could influence difficult question to answer shortly will show that as it was in the thing for mall gulping sounds strike of some kind of a job offer and I just 1 title illustrates what kind of things I can do the use of just like in the hands of the people from all over the years and then actually was my so attempt for a dollar and I'm serious proposed this 1st was based on using arrays or just 4 bytes yet tools story parts of time series but unfortunately performance was much more so company just use the standard way of for storing elements and this is why I decided to to bypass most of all this the storage mechanism and implement item that is met in memory alternative for them now on north of and to compare the theaters and some other store but manner as the main difference here were suddenly my
fills the intention of also as a tool of my
1st intention was the tool of empowerment and coma story justice foreign data record In this case we can at this is is the issue and that also become
induces dataset by fetching owners articles which are needed for query execution but we cannot provide parallel execution and the move
cannot to provide the mean vector operations so if we execute crew or queries using standard sequel engine we can never achieve you're such high performance when we are using vector operations this is why I was thinking that using forward that the practice is not the best approach for almost all In fact this essentially means that we're all about using the memory of the system that kind controls on there in ensuring that data of readings is so in the world of of of the world and all of that I'm not using shared buffer so on reserve is I'm was using my old memories in configuration file specifies size of memory which can be used by storage and it's from with their independent his for this is the for the question of whether it
was 1 of them in there and the
answer is obvious here you get an
error had right we just say it's
just a just a generous kwacha 1 over the problem of have so I spent some the most significant amount of time to solve this and reporting in case all for using parallel that so if ever happen in parallel threat I can I should get used and then propagates to the main that's acute you
can look at a given to the user and the things that you're having only 1 that didn't release of 1 of these room in her
mind other people over here is
that the actual state of this is also the right you have the wrong and animal questions the
Raw image format
Query language
Division (mathematics)
Volume (thermodynamics)
Open set
Attribute grammar
Computer animation
Analog-to-digital converter
Database
Physical law
Representation (politics)
Internationalization and localization
Row (database)
Form (programming)
Complex (psychology)
Spacetime
Query language
Scientific modelling
WebDAV
Subset
Physical law
Internationalization and localization
Data compression
Algorithm
Process (computing)
Functional (mathematics)
Open set
Vector processor
Maxima and minima
Radical (chemistry)
Lattice (order)
Data compression
output
Absolute value
Representation (politics)
Pole (complex analysis)
Row (database)
Data compression
Read-only memory
Asynchronous Transfer Mode
Sequel
Algorithm
Set (mathematics)
Connectivity (graph theory)
Vector processor
Number
Attribute grammar
Average
Representation (politics)
Operations research
Standard deviation
Query language
Denial-of-service attack
Set (mathematics)
Compiler
Number
Database normalization
Radius
Computer animation
Intrusion detection system
Personal digital assistant
Analog-to-digital converter
Interpreter (computing)
Speech synthesis
Central processing unit
Classical physics
Web page
Standard deviation
Read-only memory
Query language
Spacetime
Implementation
Multiplication sign
Scientific modelling
Parallel computing
Computer
Number
Data model
Data management
Mathematics
Read-only memory
Database
Row (database)
Data conversion
Extension (kinesiology)
Data compression
Metropolitan area network
Computer architecture
Physical system
Overhead (computing)
Spacetime
Process (computing)
Database transaction
Relational database
Consistency
Query language
Complex (psychology)
Set (mathematics)
Functional (mathematics)
Causality
Database normalization
Computer animation
Data storage device
Personal digital assistant
Element (mathematics)
Data management
Resultant
Row (database)
Series (mathematics)
Data compression
Extension (kinesiology)
Time zone
Data dictionary
Block (periodic table)
Constructor (object-oriented programming)
Element (mathematics)
Shared memory
Time series
Water vapor
Data dictionary
Timestamp
Table (information)
Architecture
Computer animation
Buffer solution
Shared memory
Hash function
Position operator
Directed graph
Stability theory
Series (mathematics)
Read-only memory
Query language
Context awareness
Multiplication sign
Volume (thermodynamics)
Parallel computing
Vector processor
Number
Summation
Frequency
Finite element method
Video game
Energy level
Partial derivative
Exception handling
Physical system
Default (computer science)
Dialect
Parallel computing
Query language
Operator (mathematics)
Set (mathematics)
System call
Thread (computing)
Tessellation
Maxima and minima
Word
Computer animation
Integrated development environment
Interpreter (computing)
output
Resultant
Structural load
Scientific modelling
Time series
3 (number)
Parameter (computer programming)
Functional (mathematics)
Timestamp
Table (information)
Attribute grammar
Table (information)
Timestamp
Optical disc drive
Computer animation
Bit rate
Function (mathematics)
Special functions
Extension (kinesiology)
Data type
Extension (kinesiology)
Standard deviation
Query language
Sequel
Structural load
Multiplication sign
Time series
Instance (computer science)
System call
Functional (mathematics)
Table (information)
Message passing
Computer animation
Function (mathematics)
Data type
Sinc function
Extension (kinesiology)
Sequel
Correspondence (mathematics)
Time series
Function (mathematics)
Parameter (computer programming)
Axonometric projection
Maxima and minima
Representation (politics)
Position operator
Metropolitan area network
Form (programming)
Curve
Machine vision
Query language
Element (mathematics)
Expression
Operator (mathematics)
Set (mathematics)
Functional (mathematics)
Local Group
Table (information)
Maxima and minima
Computer animation
output
Normal (geometry)
Standard deviation
Multiplication
Spacetime
Observational study
Multiplication sign
Structural load
Volume (thermodynamics)
Operator (mathematics)
Counting
Time series
Variance
Sphere
Sequence
Word
Radius
Computer animation
Personal digital assistant
Window
Real number
Multiplication sign
Streaming media
Student's t-test
Integer
Physical system
Form (programming)
Mobile Web
Hidden surface determination
Data dictionary
Spacetime
Information
Element (mathematics)
Android (robot)
Mathematical analysis
Cartesian coordinate system
Computer animation
Personal digital assistant
Data storage device
String (computer science)
Normal (geometry)
Code
Integer
Mathematical optimization
Bounded variation
Resultant
Sequel
Multiplication sign
Equaliser (mathematics)
Range (statistics)
1 (number)
Time series
Water vapor
Parameter (computer programming)
Variance
Emulation
Number
Summation
Heegaard splitting
Bit rate
Selectivity (electronic)
Circle
Subtraction
Position operator
Form (programming)
Physical system
Metropolitan area network
Twin prime
Element (mathematics)
Shared memory
Timestamp
Functional (mathematics)
Element (mathematics)
Local Group
Maxima and minima
Computer animation
Personal digital assistant
Function (mathematics)
Uniform resource name
Computer cluster
output
Graphical user interface
Units of measurement
Resultant
Window
Series (mathematics)
Wide area network
Read-only memory
Database transaction
Query language
Overhead (computing)
Sequel
Multiplication sign
Equaliser (mathematics)
Time series
Parameter (computer programming)
Parallel computing
Average
Disk read-and-write head
Formal language
Summation
Frequency
Latent heat
Well-formed formula
Pressure volume diagram
Pairwise comparison
Absolute value
Data compression
Position operator
Metropolitan area network
Form (programming)
Addition
Theory of relativity
Cellular automaton
Element (mathematics)
Mathematical analysis
Range (statistics)
Bit
Median
Price index
Set (mathematics)
Cartesian coordinate system
Functional (mathematics)
Subject indexing
Frequency
Computer animation
Integrated development environment
Personal digital assistant
Speech synthesis
Dependent and independent variables
Film editing
Pole (complex analysis)
Read-only memory
Information
Coma Berenices
Parameter (computer programming)
Discrete group
Information privacy
Functional (mathematics)
Table (information)
Summation
Video game
Computer animation
Internetworking
Information
Fiber bundle
Quicksort
Extension (kinesiology)
Pairwise comparison
Data type
Social class
Query language
Structural load
Euler angles
Multiplication sign
Scientific modelling
Water vapor
Food energy
Summation
Computer configuration
Position operator
Moment (mathematics)
Automaton
Functional (mathematics)
Sequence
Thread (computing)
Maxima and minima
Flow separation
output
Right angle
Code
Quicksort
Procedural programming
Data type
Digitizing
Web page
Vapor barrier
Computer file
Volume (thermodynamics)
Time series
Vector processor
Open set
Number
Authorization
Energy level
Integer
Dialect
Graph (mathematics)
Parallel computing
Element (mathematics)
Android (robot)
Operator (mathematics)
Line (geometry)
Timestamp
System call
Compiler
Computer animation
Scalar field
Personal digital assistant
String (computer science)
Function (mathematics)
Integer
Extension (kinesiology)
Standard deviation
Computer programming
Pairwise comparison
Query language
Overhead (computing)
Spacetime
Database transaction
Structural load
Multiplication sign
Complex (psychology)
Ext functor
Data management
Data model
Causality
Computer animation
Read-only memory
Iteration
Function (mathematics)
Element (mathematics)
Row (database)
Series (mathematics)
Data compression
Extension (kinesiology)
Standard deviation
Computer programming
Query language
Network operating system
Connectivity (graph theory)
Equaliser (mathematics)
Volume (thermodynamics)
Time series
Dynamical system
Data analysis
Average
Axonometric projection
Frequency
Average
Pressure volume diagram
Standard deviation
Element (mathematics)
Query language
Expression
Android (robot)
Shared memory
Operator (mathematics)
Range (statistics)
Cartesian coordinate system
Element (mathematics)
Frequency
Computer animation
Personal digital assistant
String (computer science)
Code
Queue (abstract data type)
Integer
Separation axiom
Series (mathematics)
Query language
Standard deviation
Torus
MUD
Sequel
Sine
Equaliser (mathematics)
Range (statistics)
Average
Vector processor
Weight
Cartesian coordinate system
Maxima and minima
Summation
Frequency
Computer animation
Pressure volume diagram
Computer cluster
Website
Standard deviation
Query language
Structural load
View (database)
Generating function
Axonometric projection
Representation (politics)
Software testing
Projective plane
Query language
Android (robot)
Shared memory
Operator (mathematics)
Set (mathematics)
Element (mathematics)
Table (information)
Maxima and minima
Computer animation
Function (mathematics)
String (computer science)
Code
Integer
Resultant
Series (mathematics)
Extension (kinesiology)
Read-only memory
Implementation
Structural load
Real number
Multiplication sign
Time series
Auto mechanic
Mereology
Axonometric projection
Computer
Table (information)
Timestamp
Array data structure
Software testing
Subtraction
Physical system
Projective plane
Feedback
Moment (mathematics)
Element (mathematics)
Volume (thermodynamics)
Set (mathematics)
Maxima and minima
Word
Process (computing)
Exterior algebra
Computer animation
Data storage device
Function (mathematics)
Resultant
Series (mathematics)
Extension (kinesiology)
Standard deviation
Read-only memory
Query language
Sequel
Computer file
Mathematical singularity
Home page
Angle
Coma Berenices
Vector processor
Plot (narrative)
Storage area network
Read-only memory
Physical system
Standard deviation
Parallel computing
Magneto-optical drive
Query language
Arithmetic mean
Computer animation
Continuous function
Personal digital assistant
Data storage device
Read-only memory
Buffer solution
Configuration space
Data logger
Reading (process)
Data compression
Extension (kinesiology)
Standard deviation
Spacetime
Query language
Asynchronous Transfer Mode
MUD
Algorithm
Structural load
Set (mathematics)
Multiplication sign
WebDAV
Volume (thermodynamics)
Parallel computing
Axonometric projection
Table (information)
Timestamp
Summation
Read-only memory
Error message
Operations research
Parallel computing
Operator (mathematics)
Ext functor
Open set
Thread (computing)
Vector processor
Maxima and minima
Number
Computer animation
Personal digital assistant
Analog-to-digital converter
Function (mathematics)
Data compression
Central processing unit
Representation (politics)
Data compression
Extension (kinesiology)
Series (mathematics)
Standard deviation
Query language
Data dictionary
State of matter
Network operating system
Android (robot)
Axonometric projection
Element (mathematics)
Maxima and minima
Computer animation
Function (mathematics)
String (computer science)
Right angle
Code
Integer
Uniform boundedness principle
Series (mathematics)
Loading...
Feedback

Timings

  862 ms - page object

Version

AV-Portal 3.8.0 (dec2fe8b0ce2e718d55d6f23ab68f0b2424a1f3f)