CN108737185A - A kind of triangle count method and device in datagram stream based on random sampling - Google Patents
A kind of triangle count method and device in datagram stream based on random sampling Download PDFInfo
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Abstract
The present invention relates to technical field of data processing, the triangle count method and device in a kind of datagram stream based on random sampling is provided, this method includes：Side in the raw-data map stream of reception is sampled to obtain subgraph, and calculates and retains ratio；The quantity of the subgraph intermediate cam shape of sampling acquisition is counted；The quantity of the subgraph intermediate cam shape obtained according to statistics and the raw-data map stream intermediate cam figurate number amount retained than calculating reception.The present invention obtains subgraph by flowing into line sampling to raw-data map, and the triangle count for restoring artwork according to the triangle count result of subgraph shortens the execution time of algorithm as a result, to reduce the data volume of processing.
Description
Technical field
The present invention relates to the triangles in technical field of data processing more particularly to a kind of datagram stream based on random sampling
Shape method of counting and device.
Background technology
It is increasingly permeating to internet in our life, the generation speed and data volume of data are also growing day by day, very
To the increase for being all not enough to description data volume with " magnanimity ", " explosive increase " etc., however the speed that we handle data does not have but
The growth rate for the data that can coincide, the value information implied in big data are far from fully being excavated and being utilized by us.Closely
Over a little years, the research tendency of internet is developed towards the direction that can handle mass data.Also, as the weight of big data
The data flow of one of Deta bearer form is wanted, the concern of researcher and enterprise is increasingly caused.
In actual life, the data packet in website visiting request data stream, the image data stream of satellite backhaul, network monitor
Stream, share certificate many data of real-time fluctuations etc. be all to exist in the form of data flow, and it is universal with Internet of Things,
The data magnitude of data flow will improve several orders of magnitude, this is greatly to test to the requirement of data handled in real time.So
The research of data Mining stream can find many application scenarios in reality, can greatly be pushed to the research of data flow
The development of related industry improves enterprises production efficiency, scientific data analysis efficiency and the quality of life etc. of numerous residents.
Trigometric analysis is an interesting problem in diagram data analysis, while being also a more traditional problem,
Application on social networks is particularly extensive.For example, in social networks, A recognizes mutually with B, C, and B and C is also to recognize mutually
Two people known, then A, B and C three just constitute a triangle.Similar, if in a social networks, possess more
More triangle, then the contact of personnel is also closer in this social networks.The targeted abstract problem of the present invention is
Calculate the triangle number in a datagram stream.
Triangle count problem has many solutions, but both for the exact algorithm of small-scale data, for sea
The solution for measuring data flow is now also fewer and fewer, and count accuracy is to be improved.
Invention content
The technical problem to be solved in the present invention is, for the existing triangle count method lacked for mass data flow
Defect, provide the triangle count method and device in a kind of datagram stream based on random sampling.
In order to solve the above technical problem, the present invention provides the triangle counts in the datagram stream based on random sampling
Method, including：
1) side in the raw-data map stream of reception is sampled to obtain subgraph, and calculates and retains ratio；
2) quantity of the subgraph intermediate cam shape obtained to sampling counts；
3) quantity of the subgraph intermediate cam shape obtained according to statistics and the raw-data map stream retained than calculating reception
Intermediate cam figurate number amount.
Optionally, the step 1) includes：
After being sampled to the side in the raw-data map stream of reception using the cistern methods of sampling, pass through following formula meter
Calculation, which retains, compares α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is the subgraph that the cistern methods of sampling extracts
The quantity on middle side.
Optionally, the raw-data map stream intermediate cam figurate number amount N of reception is calculated by the following formula in the step 3)：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
Optionally, included the following steps using the quantity of multiple knot method statistic subgraph intermediate cam shape in the step 2)：
V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judge whether it is triangle and
vi<vj<vk, it is that triangle count adds 1；
For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot and vi<vj, then for viAny neighbour
Meet vertex uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count add 1.
Optionally, described retain than α is 4.
Triangle count device in the present invention also provides a kind of datagram stream based on random sampling, includes at least：
Sampling unit, subgraph statistic unit and artwork evaluation unit；
The sampling unit is sampled to obtain subgraph for the side in the raw-data map stream to reception, and calculates and deposit
Stay ratio；
The quantity of the subgraph statistic unit, the subgraph intermediate cam shape for being obtained to sampling counts；
The artwork evaluation unit, the quantity of subgraph intermediate cam shape for being obtained according to statistics and described retains than calculating
The raw-data map stream intermediate cam figurate number amount of reception.
Optionally, the sampling unit takes out the side in the raw-data map stream of reception using the cistern methods of sampling
After sample, it is calculated by the following formula to retain and compares α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is the subgraph that the cistern methods of sampling extracts
The quantity on middle side.
Optionally, the raw-data map stream intermediate cam figurate number of reception is calculated by the following formula in the artwork evaluation unit
Measure N：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
Optionally, the quantity of multiple knot method statistic subgraph intermediate cam shape is used in the subgraph statistic unit, wherein：
V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judge whether it is triangle and
vi<vj<vk, it is that triangle count adds 1；
For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot and vi<vj, then for viAny neighbour
Meet vertex uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count add 1.
Optionally, described retain than α is 4.
Implement the triangle count method and device in the datagram stream provided in an embodiment of the present invention based on random sampling,
At least have the advantages that：
1, the present invention obtains subgraph by flowing into line sampling to raw-data map, and according to the triangle count result of subgraph
The triangle count of artwork is restored as a result, to reduce the data volume of processing, shortens the execution time of algorithm；
2, present invention selection is sampled the side of figure, rather than is sampled to the vertex of figure, avoids opposite vertexes
The integrally-built change for the figure that sampling is easy to cause；And the run time of algorithm is related to the quantity on side, is calculated after sampling
The execution time of method also greatly reduces；
3, the present invention calculates the number of triangles of subgraph using multiple knot method, first calculates the quantity of multiple knot triangle,
It counts the quantity of non-multiple knot triangle again, is the number of triangles of subgraph after the two, the computational methods efficiency and accurate
Property is relatively high.
Description of the drawings
Fig. 1 is the stream for the triangle count method that the embodiment of the present invention one is provided in the datagram stream based on random sampling
Cheng Tu；
Fig. 2 is that the embodiment of the present invention three provides showing for triangle count device in the datagram stream based on random sampling
It is intended to；
Fig. 3 a, 3b, 3c and 3d are respectively the quantity k on sampling side under different datagram stream size for triangle count standard
The influence of exactness；
Fig. 4 a, 4b and 4c are respectively approximation of the invention under different datagram stream size and the exact value that actually measures
Comparison figure.
In figure：201：Sampling unit；202：Subgraph statistic unit；203：Artwork evaluation unit.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill people
The every other embodiment that member is obtained without making creative work, shall fall within the protection scope of the present invention.
Embodiment one
As shown in Figure 1, the triangle count method in the datagram stream provided in an embodiment of the present invention based on random sampling,
It may comprise steps of：
Step S101：Side in the raw-data map stream of reception is sampled to obtain subgraph, and calculates and retains ratio.It is preferred that
Ground passes through following public affairs after being sampled to the side in the raw-data map stream of reception using the cistern methods of sampling in the step
Formula calculating, which retains, compares α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is the subgraph that the cistern methods of sampling extracts
The quantity on middle side.The present invention is not limited to use the cistern methods of sampling, other this field basic technology personnel can also be used
The known and applicable methods of sampling.
Step S102：The quantity n of the subgraph intermediate cam shape of sampling acquisition is counted.
Step S103：The quantity of the subgraph intermediate cam shape obtained according to statistics and the original number retained than calculating reception
Intermediate cam figurate number amount is flowed according to figure.Preferably, it is calculated by the following formula three in the raw-data map stream of reception in step S103
Angular quantity N：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
Due to huge datagram stream be likely to can not disposable loading enter memory, in order to ensure three for datagram stream
Angular method of counting normal operation, the present invention sacrifices accuracy to a certain extent, by the way of sampling, is estimated with subgraph
Whole number of triangles, and the precise results of subgraph triangle count can be calculated in a short time.
Due to the real-time arrival of data flow data, data flow total length can not be predicted in advance, but be known that by the end of
Until receiving window, the data total number that receives.Since the sampling of opposite vertexes can lead to the integrally-built change of figure, so
Selection is sampled the side in figure in the present invention.It will also realize that by above-mentioned analysis, the run time of the method for the present invention and side
Related, so, once reducing the quantity on side in figure, the execution time of algorithm can also greatly reduce.
Therefore, the classical cistern methods of sampling may be used in the present embodiment, it is assumed that want to preserve side in memory
Integrate as k, is m by the end of receiving window to have the total quantity on the side received altogether.After carrying out cistern sampling, it is known that in figure stream
Any a line, the probability that finally can be able to retain in memory are
Since each edge probability present in subgraph is in artworkAnd the selection on each side is random independent
, then probability of the three sides of a triangle all in subgraph is exactly in artworkSo, it is only necessary to by subgraph
In information carry out triangle statistics and calculate, so that it may to estimate artwork intermediate cam shape by the quantity for counting subgraph intermediate cam shape
Quantity.It enablesTo retain ratio, then the number of triangles in artwork can be multiplied by α with the number of triangles in subgraph3Come
Estimated.
Embodiment two
On the basis of embodiment one provides the triangle count method in the datagram stream based on random sampling, wherein
The process that the quantity n of the subgraph intermediate cam shape obtained to sampling in step S102 is counted, specifically can be in the following way
It realizes：
The triangle number purpose method of calculating subgraph employed in step S102 is multiple knot method, so-called multiple knot,
Refer to if the degree on a vertex is not less thanSo this vertex is multiple knot, can according to the quantitative relation on vertex and side
Multiple knot number is obtained to be no more thanAs soon as if three vertex of triangle are all multiple knots, then this triangle claims
Make multiple knot triangle.This method is divided into three steps：
1, preprocessing part：Firstly the need of the degree and preservation for calculating each vertex；And two vertex of each edge are established
Index so that can determine whether there is side between two vertex by index later；Each vertex is established and is indexed, i.e., given top
Point returns to the adjacent vertex on the vertex.
2, the statistics of multiple knot triangle：The degree that vertex is calculated from subgraph is not less thanVertex be multiple knot, and
Constitute the multiple knot set of the subgraph.V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judgement is
No triangle and vi<vj<vk, it is that triangle count adds 1.The heavy triangle can energy level be O (m3/2).In the present invention
Vertex size relatively refer to first comparing the number of degrees, number is compared if the number of degrees are identical.
3, the statistics of non-multiple knot triangle：For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot
And vi<vj, then for viAny adjacent vertex uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count
Add 1.
In one embodiment of the invention, each edge (v can also be first considered in the stepi,vj), if vi,vjAll it is
Multiple knot, then ignoring this edge；If viIt is not multiple knot, and vi<vj, then, it is found using index before and viIt is adjacent
All vertex u1, u2..., uk, whereinTo each adjacent vertex ui, i=1,2 ..., k judge side using index
(ui,vj) whether there is, if in the presence of and vi<uiThen to triangle (vi,ui,vj)) carry out statistical counting.
The number of triangles in subgraph is calculated by multiple knot method, it, can be also by being multiplied by a proportionality coefficient
Original goes out the quantity survey of artwork intermediate cam shape.
The pseudocode of figure sampling algorithm is as follows：
Input：Scheme G (V, E), parameter k
Output：Figure G ' (V ', E ') after sampling, total number of edges m
The purpose of above-mentioned figure sampling algorithm is the triangle statistics after facilitating in order to sample artwork at a subgraph,
The input of algorithm is artwork and requires the quantity k on side finally retained, the side in subgraph and artwork after exporting as sampling it is total
Quantity.Counter is counter, and can reflect current screening is which side of data flow.
The pseudocode that the triangle approximation counts is as follows：
Input：Figure G ' after sampling, parameter k, m
Output：The estimation Δ G ' that figure G intermediate cam shapes are counted
The last output result of the algorithm is the finally quantity survey to artwork intermediate cam shape, and input is after sampling
Subgraph, first cyclic part are statistics multiple knot triangles, and the second part is the non-multiple knot triangle of statistics, Rule of judgment
In the comparison of node size refer to the number of degrees of node, if the number of degrees are identical, the number of comparison node, in order to last
The result of statistics does not repeat, some counting of also not leaking down.
Embodiment three
As shown in Fig. 2, the triangle count device in the datagram stream provided in an embodiment of the present invention based on random sampling,
May include：Sampling unit 201, subgraph statistic unit 202 and artwork evaluation unit 203；
Sampling unit 201 obtains subgraph for being sampled for the side in the raw-data map stream to reception, and calculates
Retain ratio.The operation that the sampling unit 201 executes is identical as abovementioned steps S101；
The quantity of subgraph statistic unit 202, the subgraph intermediate cam shape for being obtained to sampling counts.The subgraph counts
The operation that unit 202 executes is identical as abovementioned steps S102；
Artwork evaluation unit 203, the quantity of subgraph intermediate cam shape for being obtained according to statistics and described retains than calculating
The raw-data map stream intermediate cam figurate number amount of reception.The operation that the artwork evaluation unit 203 executes is identical as abovementioned steps S103.
Preferably, sampling unit 201 takes out the side in the raw-data map stream of reception using the cistern methods of sampling
After sample, it is calculated by the following formula to retain and compares α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is the subgraph that the cistern methods of sampling extracts
The quantity on middle side.
Preferably, the raw-data map stream intermediate cam figurate number of reception is calculated by the following formula in artwork evaluation unit 203
Measure N：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
Preferably, the quantity of multiple knot method statistic subgraph intermediate cam shape is used in subgraph statistic unit 202, wherein：
V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judge whether it is triangle and
vi<vj<vk, it is that triangle count adds 1；
For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot and vi<vj, then for viAny neighbour
Meet vertex uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count add 1.
It is further to note that the triangle meter in the datagram stream provided in an embodiment of the present invention based on random sampling
Counting apparatus can also be realized by software realization by way of hardware or software and hardware combining.It is implemented in software to be
Example, as shown in Fig. 2, as the device on a logical meaning, being will be in nonvolatile memory by the CPU of equipment where it
Corresponding computer program instructions read what operation in memory was formed.
The time complexity of the present invention is analyzed as follows：
For multiple knot method：First, it is that (m refers to the number of edges of subgraph to O (m) that preprocessing part, which establishes index time complexity,
Amount)；Multiple knot triangle count, since multiple knot number is no more thanTherefore the combination of all multiple knot triangles is total
There are O (m3/2) kind, i.e. time complexity is O (m3/2)；Other triangle count parts, number of edges are up to m, and Therefore judge that all possibilities need O (m3/2)；Therefore total time complexity of multiple knot algorithm
For O (m3/2)。
The quantity on the side of subgraph is determined by sampling algorithm, and sampling process synchronous with the reading of data flow can carry out,
So being not counted in time complexity here, it is assumed that the quantity on the side retained in memory after sampling is k, then brings k into epimeres and answer
Miscellaneous degree, the final time complexity that can obtain this algorithm are O (k3/2)。
The present invention also verifies effect by experiment.In experiment, n indicates the vertex quantity of figure in datagram stream, m
Indicate the quantity on side in datagram stream.Experimental data is based on random self-generating data.If Fig. 3 a, 3b, 3c and 3d are respectively difference
Datagram stream size under sampling side influences of the quantity k for triangle count accuracy.Wherein horizontal axis is the number on sampling side
K is measured, the longitudinal axis is triangle count accuracy.It can be seen from upper curve in varied situations, as parameter k is to the approach of m
In the process, the accuracy rate of algorithm gradually rises, also, figure is denser, and curve climbing speed is faster.
Fig. 4 a, 4b and 4c are respectively approximation of the invention under different datagram stream size and the exact value that actually measures
Comparison.It is 4 that order, which is retained than α,.Horizontal axis is the quantity on the side of figure in figure, and the longitudinal axis is number of triangles.At each location point, the left side
For the exact value (also referred to as actual value) obtained by accurate metering algorithm counts, the right is three calculated according to the method for the present invention
Angular count value (also referred to as approximation).It is fine in the propinquity effect of small-scale data that algorithm is can be seen that from the above chart,
Accuracy rate can averagely reach 99% or more.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, it will be understood by those of ordinary skill in the art that：It still may be used
With technical scheme described in the above embodiments is modified or equivalent replacement of some of the technical features；
And these modifications or replacements, various embodiments of the present invention technical solution that it does not separate the essence of the corresponding technical solution spirit and
Range.
Claims (10)
1. a kind of triangle count method in datagram stream based on random sampling, which is characterized in that including：
1) side in the raw-data map stream of reception is sampled to obtain subgraph, and calculates and retains ratio；
2) quantity of the subgraph intermediate cam shape obtained to sampling counts；
3) it the quantity of subgraph intermediate cam shape that is obtained according to statistics and described retains than calculating three in the raw-data map stream received
Angular quantity.
2. according to the method described in claim 1, it is characterized in that, the step 1) includes：
After being sampled to the side in the raw-data map stream of reception using the cistern methods of sampling, it is calculated by the following formula and deposits
It stays and compares α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is side in the subgraph that the cistern methods of sampling extracts
Quantity.
3. according to the method described in claim 2, it is characterized in that, being calculated by the following formula the original of reception in the step 3)
Beginning datagram stream intermediate cam figurate number amount N：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
4. according to the method described in claim 1, it is characterized in that, using in multiple knot method statistic subgraph in the step 2)
The quantity of triangle, includes the following steps：
V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judge whether triangle and vi<vj<
vk, it is that triangle count adds 1；
For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot and vi<vj, then for viAny adjacent top
Point uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count add 1.
5. according to the method described in claim 1, it is characterized in that, described retain than α is 4.
6. the triangle count device in a kind of datagram stream based on random sampling, which is characterized in that include at least：Sampling is single
Member, subgraph statistic unit and artwork evaluation unit；
The sampling unit is sampled to obtain subgraph for the side in the raw-data map stream to reception, and calculates and retain ratio；
The quantity of the subgraph statistic unit, the subgraph intermediate cam shape for being obtained to sampling counts；
The artwork evaluation unit, the quantity of the subgraph intermediate cam shape for being obtained according to statistics and described retain receive than calculating
Raw-data map stream intermediate cam figurate number amount.
7. device according to claim 6, which is characterized in that the sampling unit is using the cistern methods of sampling to receiving
Raw-data map stream in side be sampled after, be calculated by the following formula to retain and compare α：
Wherein m is by the end of the total quantity for receiving the side that window receives altogether, and k is side in the subgraph that the cistern methods of sampling extracts
Quantity.
8. device according to claim 7, which is characterized in that be calculated by the following formula and connect in the artwork evaluation unit
The raw-data map stream intermediate cam figurate number amount N of receipts：
N=n α3
Wherein, n is the quantity for the subgraph intermediate cam shape that statistics obtains.
9. device according to claim 6, which is characterized in that use multiple knot method statistic in the subgraph statistic unit
The quantity of subgraph intermediate cam shape, wherein：
V is combined for arbitrary three vertex in the multiple knot set of subgraphi,vj,vk, judge whether triangle and vi<vj<
vk, it is that triangle count adds 1；
For the arbitrary a line (v in subgraphi,vj), if viIt is not multiple knot and vi<vj, then for viAny adjacent top
Point uiIf triangle (vi,ui,vj) exist and vi<ui<vj, then triangle count add 1.
10. device according to claim 6, which is characterized in that described retain than α is 4.
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| CN114389961A (en) * | 2022-01-14 | 2022-04-22 | 北京睿芯高通量科技有限公司 | Graph flow triangle counting method and device based on node heat sampling |
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| CN113448732A (en) * | 2021-07-09 | 2021-09-28 | 北京睿芯高通量科技有限公司 | Triangle counting method and device for large-scale flow graph online self-adaptive sampling space |
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