A parameter instantiation method for unary basis constraints

Abstract

The application discloses a parameter instantiation method for unary base constraint, comprising the following steps: step one, calculating corresponding unary probability constraint according to the base of the value range of a column and all related unary base constraints; step two, obtaining the cumulative distribution function of unary inequality base constraint according to all unary inequality probability constraints, and dividing the entire probability space into several disjoint intervals according to the obtained cumulative distribution function; step three, using a greedy algorithm to insert all unary equality probability constraints into the minimum interval meeting the constraints in sequence, and updating the interval data distribution information after each insertion; and step four, instantiating the parameters corresponding to all unary base constraints according to the probability distribution function and the interval data distribution information. The input information in the method does not contain specific data information of a database, so that data leakage is avoided, and the filtering ratio of the unary base constraint after parameter instantiation is the same as that of the original.

Description

Technical Field

[0001] This invention belongs to the fields of analytical databases and load generation technology, and relates to a parameter instantiation method for unary cardinality constraints. Background Technology

[0002] Currently, with the advent of the big data era, the scale of data is constantly expanding, and new application scenarios are emerging one after another. To address these new application scenarios, database performance evaluation has become increasingly important. Traditional benchmarking has been widely used in database system performance evaluation. However, if the application scenario represented by the benchmark is completely different from the application scenario in the actual production environment, the reliability of the basic evaluation will be greatly reduced. While the best approach is to evaluate the database system using the load of a real-world application scenario, this carries a serious risk of data leakage. Therefore, database instances that simulate the load characteristics of a real-world environment become crucial.

[0003] To address the above requirements, the Query-Aware Database Generator (QAG) is used. [1-7] This led to the development of query-aware database generators. These generators simulate specific application scenarios by generating simulated data and queries. The essence of application-oriented database generation is that when the simulated workload is executed on the simulated database, the input and output of each operator are as similar as possible to the original workload. In other words, the query execution cost obtained by executing the generated workload on the test database is as similar as possible to the query execution cost obtained by executing the original workload on the original database. In short, simulated databases have data distribution characteristics similar to real workloads and can be used for performance evaluation of database systems.

[0004] To implement a query-aware database generator, data security requires retrieving as little information as possible from the database. To prevent data leakage and avoid exposing the specific details of the original distribution of the test environment, all parameters of the original query need to be symbolized; this symbolized query is called a query template. In existing query-aware database generators, a key step in generating simulated queries and simulated databases is to re-instantiate these symbolized parameters, i.e., assign them new values; this process is called parameter instantiation.

[0005] When instantiating parameters for a unary cardinality constraint, only one attribute column that is not involved in the join and its parameters are considered. If you want to instantiate the parameters of a unary cardinality constraint and further generate the related attribute columns, you must consider the following: For a certain attribute column in a table, there are often multiple related unary cardinality constraints. These constraints are all related to the data distribution of that column. Therefore, to instantiate parameters for all unary cardinality constraints, you must consider all unary cardinality constraints involving the same column together. When the number of unary cardinality constraints increases, ensuring that a parameter instantiation solution can always be found becomes a problem.

[0006] Since all parameters have been symbolized, the key to finding a reasonable parameter instantiation scheme is to redetermine their magnitudes, that is, the relative positions of these univariate cardinal constraints in the probability space. This requires breaking the problem down into two parts: first, how to determine the relative positions of these symbolized parameters in the probability space; and second, how to instantiate them based on their relative positions in the probability space. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention aims to provide a method for instantiating query template parameters for univariate cardinality constraints. First, the probability space is divided into disjoint ranges using univariate non-equivalent cardinality constraints, determining the relative positions of all parameters involved in these constraints. Then, a greedy algorithm is used to insert the probabilities corresponding to univariate equivalent cardinality constraints into the smallest interval satisfying the constraints, thereby determining the position of the equivalent univariate cardinality constraints in the probability space and constructing the cumulative probability density model of the column (i.e., the set of univariate probability constraints converted from all univariate cardinality constraints related to that column). Finally, parameters for all univariate cardinality constraints are instantiated by assigning a cardinality range.

[0008] The parameter instantiation method for univariate cardinal constraints of the present invention includes the following steps:

[0009] Step 1: Obtain Unary Probability Constraints: For a given range of non-key columns that do not participate in the join and the unary cardinality constraints associated with that column, calculate the unary probability constraint corresponding to each unary cardinality constraint. For example, given attribute column A (the cardinality of the range is |A|) and k unary cardinality constraints UCC1, ..., UCC associated with that column. k (unary cardinality constraint), calculate the unary probability constraint UPC1, ..., UPC corresponding to each unary cardinality constraint. k (unaryprobability constraint).

[0010] Among them, a unary cardinality constraint consists of a database filtering predicate composed of a single column, a single relational symbol, and a single parameter, as well as the number of rows of the column obtained by filtering through this predicate. The form of the unary cardinality constraint is ${|A\Theta P|}=k$, where $A$ refers to the column name, $P$ k refers to the symbolized parameter, $\Theta$ refers to the symbol, including $=,\neq,\lt,\gt,\leq,\geq,(NOT)IN,(NOT)LIKE$ (all common symbols in database queries), $|A|$ is the cardinality of the value range of the column, and $k$ is the number of tuples satisfying the predicate condition $A\Theta P$ k . k

[0011] A unary probability constraint consists of the predicate of the unary cardinality constraint and the filtering ratio of the column corresponding to the unary cardinality constraint. The form of the unary probability constraint is $P(A\Theta P$ k ) = $p_b$, where $A\Theta P$ k is the above-mentioned unary cardinality constraint, and $p_b$ is the percentage of the tuples satisfying this cardinality constraint in the total number of tuples in the table (i.e., the filtering ratio).

[0012] Step 2. Obtain the cumulative distribution function of the unary non-equality probability constraint: The unary probability constraint obtained from the unary equality cardinality constraint in Step 1 is called the unary equality probability constraint, and the unary probability constraint obtained from the unary non-equality cardinality constraint in Step 1 is called the unary non-equality probability constraint. Equality and non-equality are divided according to whether the symbol $\Theta$ in the unary cardinality constraint is an equality symbol or a non-equality symbol. For all the unary non-equality probability constraints obtained in Step 1, convert them into the form of cumulative distribution functions $F_x(P_1),\cdots,F_x(P$ k ), and divide the entire probability space into several non-overlapping intervals $(p$ i ,p$ j ), where $0\lt i\leq j - 1,j\leq k$. Moreover, the several intervals obtained by the division are non-overlapping and their union is equal to the entire probability space.

[0013] The unary non-equality probability constraint refers to the unary probability constraint obtained from the unary non-equality cardinality constraint in Step 1, and its form is $P(A\Theta P$ k ) = $p_b$, and the corresponding symbol $\Theta$ is a non-equality symbol, i.e., $\neq,\lt,\gt,\leq,\geq$.

[0014] The cumulative distribution function refers to the probability that the value of the column is less than a certain value, and its form is $F_x(P$ k ) = $P(x\leq P$ k ), where $P_k$ is the parameter corresponding to the unary cardinality constraint, and $F_x(P$ k ) is the probability that the value of the column is less than or equal to this parameter.

[0015] ​Step 3: Obtain the cumulative distribution function of the univariate equivalence probability constraints: Given all the univariate equivalence probability constraints obtained in Step 1 and the interval data distribution information in the probability space obtained in Step 2, insert the probabilities of the univariate equivalence probability constraints into the intervals obtained in Step 2 in ascending order using a greedy algorithm. Update the interval data distribution information after each insertion, and finally obtain the cumulative distribution function of all univariate equivalence probability constraints and the final interval data distribution information.

[0016] The univariate equivalence probability constraint refers to the univariate probability constraint obtained from the univariate equivalence cardinal constraint through step one, and its form is P(AΘP). k =pb, and the corresponding symbol Θ is the equivalence symbol, that is, =, IN, LIKE, NOT IN, NOT LIKE.

[0017] Greedy algorithms are commonly used to solve the knapsack problem, aiming to find the minimum range that can accommodate equal probabilities, ensuring that all equal probabilities can be successfully inserted. Specifically, in this invention, to ensure that all unary equal probability constraints can be successfully inserted into the interval, if two unary equal probability constraints have the same probability, they are considered to have the same parameters and will be inserted into the same position in the same interval during insertion, so as to ensure that all unary probability constraints can find an insertion position.

[0018] Step 4, Parameter Instantiation: Based on all the cumulative distribution functions obtained in Steps 2 and 3, the last updated interval data distribution information, and the column's value range, the cardinality of the column's value range is assigned to all intervals. Finally, all parameters are instantiated according to the cardinality assigned to each interval. Specifically, for all intervals represented by univariate equivalence constraints, only one cardinality is assigned to it from the cardinality of the value range. For the remaining intervals (i.e., the intervals representing unequal constraints remaining after inserting equivalence probability constraints), the remaining cardinality of the value range is randomly assigned.

[0019] The beneficial effects of this invention include: ensuring data security: all input information in this invention does not contain specific data information from the database, thus preventing data leakage. Simulating the data distribution of non-key columns not involved in the join in the original database: after parameter instantiation, the unary cardinality constraint only changes its parameters; its filtering ratio remains the same as the original unary cardinality constraint, meaning the filtering ratio of each operator remains unchanged. Attached Figure Description

[0020] Figure 1 These are schematic diagrams of steps two, three, and four of a specific embodiment of the present invention.

[0021] Figure 2 This is a flowchart of the parameter template instantiation method of the present invention. Detailed Implementation

[0022] The present invention will be further described in detail below with reference to the specific embodiments and accompanying drawings. Except for the contents specifically mentioned below, the processes, conditions, and experimental methods for implementing the present invention are all common knowledge and general knowledge in the art, and the present invention does not have any particular limitations.

[0023] The present invention implements a query template parameter instantiation method for unary cardinality constraints, comprising the following steps:

[0024] Step 1: Obtain unary probability constraints: For a given range of values ​​of a non-key column that does not participate in the join and the unary cardinality constraints associated with that column, calculate the unary probability constraints corresponding to each unary cardinality constraint.

[0025] Step 2: Obtain the cumulative distribution function of the univariate non-equivalent probability constraints: For all the univariate non-equivalent probability constraints obtained in Step 1, convert them into the form of cumulative distribution functions, and divide the entire probability space into several non-overlapping intervals based on all the cumulative distribution functions.

[0026] Step 3: Obtain the cumulative distribution function of the univariate equivalence probability constraints: For all the univariate equivalence probability constraints obtained in Step 1 and the interval data distribution information in the probability space obtained in Step 2, the greedy algorithm is used to sequentially insert all the univariate equivalence probability constraints into the smallest interval that satisfies the constraints, and the interval data distribution information is updated after each insertion, thereby constructing the cumulative distribution function of all univariate equivalence probability constraints.

[0027] Step 4, Parameter Instantiation: Based on all the cumulative distribution functions obtained in Steps 2 and 3, the last updated interval data distribution information, and the column value range, the cardinality of the column value range is assigned to all intervals. Finally, all parameters are instantiated based on the cardinality assigned to the intervals.

[0028] Specifically,

[0029] Step 1: Obtain the univariate probability constraints: Given an attribute column R (R is a non-key value column that does not participate in the join) and k univariate cardinal constraints UCC1, ..., UCC associated with this column. k (unary cardinality constraint), calculate the unary probability constraint UPC1, ..., UPC corresponding to each unary cardinality constraint. k (unary probability constraint). For example, given the cardinality of the attribute column's value range is |A|, if a univariate cardinality constraint |AΘP| is given... k If |=n, then the univariate probability constraint corresponding to this univariate cardinal constraint is:

[0030] Step 2. Obtain the cumulative distribution function of unary non - equal - value probability constraints: Given all the unary non - equal - value probability constraints obtained in Step 1, convert them into the form of cumulative distribution functions \(F_x(P_1)\), ……, \(F_x(P k ), and then divide the entire probability space into several non - overlapping intervals \((P i ,P j , where \(0 < i\leq j - 1\) and \(j\leq k\). In addition, the invention maintains two lists \(pv list \) and \(pb list , where \(pv list \) records the relative position information of all parameters. That is, when \(i < j\), \(P i < P j . And \(pb list \) records the corresponding cumulative probability density of the parameter at the same position, that is, \(P(x\leq P k )\) in the cumulative distribution function. For example, the cumulative probability density corresponding to the \(i\) - th parameter \(P list \) in \(pv i \) is the \(i\) - th cumulative probability density \(Pb list \) in \(pb i . The rules for converting unary non - equal - value probability constraints to cumulative distribution functions are as follows: If the given unary non - equal - value probability constraint is then convert it to the cumulative distribution function \(F_x(P i ) = P(x\leq P i ); If the given unary non - equal - value probability constraint is then convert it to the cumulative distribution function \(F_x(P i ) = P(x\leq P i - 1); If the given unary non - equal - value probability constraint is then convert it to the cumulative distribution function \(F_x(P i ) = P(x\leq P i ) = 1 - P(x > P i ); If the given unary non - equal - value probability constraint is then convert it to the cumulative distribution function \(F_x(P i ) = P(x\leq P i - 1) = 1 - P(x\geq P i ).

[0031] Step 3. Obtain the cumulative distribution function of unary equal - value probability constraints: For all the unary equal - value probability constraints obtained in Step 1 and the several intervals into which the entire probability space has been divided, insert all the unary equal - value probability constraints into the smallest interval that satisfies the constraints in turn according to the greedy algorithm, and update \(pv list and \(pb listAnd interval data distribution information, thus constructing the cumulative distribution function of all unary equal - probability constraints and the final interval data distribution information. The insertion rules are as follows: First, sort all unary equal - probability constraints in ascending order of probability, and then perform insertion operations in sequence. If a given unary equal - probability constraint in a certain insertion operation is The interval data distribution information updated after the previous insertion is (P i1 , P j1 …(P in , P jn . Using the greedy algorithm, find the smallest interval (P ik , P jk in the updated interval that satisfies the constraint, and then insert the parameter P i into the position between P list and P ik in pv list and insert the probability density corresponding to the cumulative distribution function Fx(Pi) at the same position in pb list (between Pb ik and Pb jk ). The calculation rule of the probability density corresponding to the cumulative distribution function is The subsequent interval (P ik , P jk is updated to In addition, if the current inserted unary equal - probability constraint is the same as a previously inserted unary equal - probability constraint , assume that the parameters of these two unary equal - probability constraints are the same, that is, P i = P m . During insertion, it will be inserted into the same position in the same interval. This can ensure that all unary probability constraints can be inserted into the interval.

[0032] Step 4. Parameter instantiation: Given the pv list and pb list finally obtained in Step 3, the interval data distribution information, and the cardinality |A| of the value range of the column, allocate the cardinality of the value range of the column to all intervals. Finally, according to the cardinality assigned to the interval, instantiate the parameters from P i to P k .

[0033] The instantiation rules are as follows. For the parameters P list to P i in pv list k (as known from Step 3, when i < j, P i < P k ), let P (i-1) be the parameter P list in pv list and the parameter P iThe first parameter, if the interval (P) (i-1) ,P i If the interval is the same as one of the intervals obtained in step three, then the interval represents a univariate equivalence probability constraint; otherwise, the interval represents a univariate non-equivalence probability constraint.

[0034] The instantiation process is as follows: First, a cardinality is assigned to each interval from the cardinality |A| of the range. Then, the remaining cardinality is randomly assigned to the intervals representing univariate non-equivalence probability constraints. Finally, let the interval (P) (i-1) ,P i The cardinality of ] is |r i |, then it can be determined by the formula The instantiation of parameters is completed by assigning values ​​to all parameters and writing the assigned parameters back into the predicate conditions corresponding to the unary cardinality constraints.

[0035] Example

[0036] According to the definition of the parameter instantiation problem in this invention, the input of this method includes unary cardinality constraints UCC1, ..., UCC related to the non-key column A. k The cardinality |A| of the range of column A. The implementation process of this method includes four steps: obtaining the univariate probability constraints, obtaining the cumulative distribution function of the univariate non-equivalent probability constraints, obtaining the cumulative distribution function of the univariate equivalent probability constraints, and parameter instantiation. The output of this method is the predicate condition corresponding to the reassigned univariate cardinality constraints.

[0037] Obtain univariate probability constraints: Based on the given nonkey column A and the associated univariate cardinality constraints UCC1, ..., UCC k This yields the corresponding univariate probability constraints UPC1, ..., UPC. k For example, the cardinality of the range of a non-key column A is |A| = 20, and the unary cardinality constraint associated with A is...

[0038] UCC1: |A≤P1|=10UCC2: |A≥P2|=6UCC3: |A=P3|=8

[0039] UCC4:|A=P4|=5UCC5:|A=P5|=5

[0040] Convert them into univariate probability constraints

[0041] UPC1: UPC2:

[0042] UPC3: UPC4:

[0043] UPC5:

[0044] To obtain the cumulative distribution function of the univariate non-equivalence probability constraint: first initialize pv list and pb list Two lists are used, with the parameters pvs and pve, where pvs represents the minimum value in the range and pve represents the maximum value in the range. For the univariate non-equivalence probability constraints obtained in the previous step, i.e., UPC1 and UPC2, they are first transformed into cumulative distribution functions according to the transformation rules in step two:

[0045] Fx(P1)=P(x≤P1)=50% Fx(P2)=P(x≤P2-1)=70%

[0046] Then as attached Figure 1 As shown in step two, insert P1 and P2 into pv. list In the middle, insert 50% and 70% into pb list In China. And based on PV. list and pb list This yields three non-overlapping intervals (pvs, P1], (P1, P2], and (P2, pve], with sizes of 50%, 20%, and 30%, respectively.

[0047] Obtain the cumulative distribution function of the univariate equivalence probability constraints: For all univariate equivalence probability constraints obtained in step one and the entire probability space divided into several intervals, according to the greedy algorithm, all univariate equivalence probability constraints are sequentially inserted into the smallest interval that satisfies the distribution, and the pv is updated after each insertion. list and pb list Based on the distribution information of the interval data, the cumulative distribution function of all univariate equivalence probability constraints is constructed. For example, in this embodiment, the three univariate equivalence probability constraints UPC3, UPC4, and UPC5 are sorted in ascending order of probability: UPC4, UPC5, UPC3. First, insert UPC4. Since the interval sizes are 50%, 20%, and 30%, according to the greedy algorithm, the interval to be inserted is (P2, pve], with a size of 30%. Then, the cumulative distribution function is obtained as Fx(P4) = Fx(P2) + P(A = P4) = 70% + 25% = 95%. Then, P4 is inserted between P2 and pve, and 95% is inserted between 70% and 100%. The interval data distribution information is updated to (pvs, P1), (P1, P2), (P4, pve], with intervals of 50%, 20%, and 5%, respectively. According to the insertion rules, UPC5 and UPC3 are also inserted into the interval. Since UPC4 and UPC5 have the same probability, it is assumed that their parameters are the same and they are inserted in the same position, as shown in the appendix. Figure 1 As shown in step three, the final PV is obtained.list and pb list As shown in the figure, the interval is updated to (P3,P1], (P1,P2], (P4 / P5,pve], with corresponding sizes of 10%, 20%, and 5%, respectively.

[0048] Parameter instantiation: Given the final PV obtained in step three list and pb list The data distribution information of the intervals, and the cardinality |A| of the column's value range, are used to assign the cardinality of the column's value range to all intervals. Finally, based on the cardinality assigned to each interval, the data from P is processed. i To P k Instantiate the parameters. See attached... Figure 1 As shown in step four, the probability space is divided into five intervals: (pvs, P3], (P3, P1], (P1, P2], (P2, P4 / P5], and (P4 / P5, pve]. Let the cardinal numbers of these five intervals be |r1|, |r2|, |r3|, |r4|, and |r5|, respectively. First, a cardinal number is assigned to each interval from the cardinal number of the range, |A|.

[0049] |r1|=1, |r2|=1, |r3|=1, |r4|=1, |r5|=1

[0050] Then, for the range of non-equivalent univariate cardinality constraints, randomly assign the remaining 15 cardinalities (the cardinality of the range, 20, minus the already assigned cardinality, 5).

[0051] |r2|=1+4=5 |r3|=1+5=6 |r5|=1+6=7

[0052] At this point, the formula is used. It can perform parameter instantiation of univariate cardinality constraints.

[0053] pv3 = pv s +|r1|=0+1=1 pv1=pv3+|r2|=1+5=6

[0054] pv2=pv1+|r3|=6+6=12 pv4, pv5=pv2+|r4|=12+1=13

[0055] pv e =pv4 + |r5| = 13 + 7 = 20

[0056] Finally, we obtain the unary cardinal constraint after parameter instantiation.

[0057] UCC1: |A≤6|=10 UCC2: |A≥12|=6 UCC3: |A=1|=8

[0058] UCC4: |A = 13| = 5 UCC5: |A = 13| = 5

[0059] References

[0060] [1] Arasu A, Kaushik R, Li J. Data generation using declarative constraints, SIGMOD 2011.

[0061] [2] Binnig C, Kossmann D, Lo E, et al. QAGen: generating query-aware test databases, SIGMOD 2007.

[0062] [3] Gilad A, Patwa S, Machanavajjhala A. Synthesizing linked data under cardinality and integrity constraints, ICMD 2021.

[0063] [4] Li Y, Zhang R, Yang X, et al. Touchstone: Generating Enormous {Query-Aware} Test Databases, USENIX ATC 2018.

[0064] [5] Lo E, Cheng N, Hon W K. Generating databases for query workloads, VLDB 2010.

[0065] [6] Lo E, Cheng N, Lin W W K, et al. MyBenchmark: generating databases for query workloads, VLDB 2014.

[0066] [7] Sanghi A, Sood R, Haritsa J R, et al. Scalable and Dynamic Regeneration of Big Data Volumes, EDBT 2018.

[0067] The scope of protection of this invention is not limited to the above embodiments. Any variations and advantages that can be conceived by those skilled in the art without departing from the spirit and scope of this invention are included in this invention and are protected by the appended claims.

Claims

1. A method for parameter instantiation for unary basis constraints, the method comprising: receiving a parameter instantiation request for a parameter instantiation; determining a parameter instantiation constraint; determining a parameter instantiation constraint type; and instantiating the parameter instantiation based on the parameter instantiation constraint type. The method comprises the following steps: Step one, obtaining a unary probability constraint: for a given value domain of a non-key value column not participating in connection and a unary cardinality constraint related to the column, calculating a unary probability constraint corresponding to each unary cardinality constraint; In step one, the unary cardinality constraint is a database filter predicate consisting of a single column, a single relational symbol and a single parameter, and the row set of the column filtered via this predicate; the form of the unary cardinality constraint is |AΘP k |=k, where A refers to the column name, P k refers to the symbolic parameter, Θ refers to the symbol, including =, ≠, <, >, ≤, ≥, (NOT)IN, (NOT)LIKE, |A| is the cardinality of the value domain of the column, and k is the number of tuples satisfying the predicate condition AΘP k . Step two, obtaining a cumulative distribution function of a unary non-equality probability constraint: for all unary non-equality probability constraints obtained in step one, converting them into the form of a cumulative distribution function, and dividing the entire probability space into several disjoint intervals based on all cumulative distribution functions; Step three, obtaining a cumulative distribution function of a unary equality probability constraint: for all unary equality probability constraints obtained in step one and interval data distribution information in the probability space obtained in step two, sequentially inserting all unary equality probability constraints into the smallest interval satisfying the constraint according to a greedy algorithm, and updating the interval data distribution information after each insertion, thereby constructing a cumulative distribution function of all unary equality probability constraints; Step four, parameter instantiation: according to all cumulative distribution functions obtained in steps two and three, the last updated interval data distribution information, and the value domain of the column, distributing the cardinality of the value domain of the column to all intervals, and finally instantiating all parameters according to the cardinality distributed to the intervals.

2. The method for parameter instantiation against unary base constraint as claimed in claim 1, wherein, A unary probability constraint is composed of a unary cardinality constraint predicate and a filter-by on a relevant column, and has the form P(A Θ P k ) = pb, where A Θ P k is the unary cardinality constraint, and pb is the percentage of the total number of tuples in the table that satisfy this cardinality constraint.

3. The method for parameter instantiation against unary base constraint as claimed in claim 1, wherein, The unary non-equality probability constraint is a unary probability constraint calculated from a unary non-equality cardinality constraint, and has a form of P(AΘP k ) = pb, wherein a corresponding symbol Θ is a non-equality symbol, i.e., ≠, <, >, ≤, ≥. The unary equivalence probability constraint refers to a unary probability constraint calculated by a unary equivalence cardinality constraint, which is in the form of P(AΘP k ) = pb, and the corresponding symbol Θ is an equivalence symbol, i.e., =, IN, LIKE, NOT IN, NOT LIKE.

4. The method for parameter instantiation against unary base constraint of claim 1, wherein, In step two, the cumulative distribution function of the form Fx(P k ) = P(x≤P k ) is converted from the one-dimensional non-equivalent probability constraint, where Pk is the parameter corresponding to the one-dimensional base constraint, and Fx(P k ) is the probability that the column value is less than or equal to this parameter. The entire probability space is divided into several disjoint intervals based on all cumulative distribution functions, denoted as (p i ,p j ] where 0 < o ≤ j - 1, j ≤ k. The several intervals obtained by the division are mutually disjoint and the union is equal to the entire probability space.

5. The method for parameter instantiation against unary base constraint of claim 1, wherein, In step three, in order to ensure that all unary equality probability constraints can be smoothly inserted into the intervals, if the probabilities of two unary equality probability constraints are the same, the corresponding parameters are also considered to be the same, and the same position in the same interval is inserted when inserted, so as to ensure that all unary probability constraints can find a position for insertion.

6. The method for parameter instantiation against unary base constraint of claim 1, wherein, In step four, for the interval represented by all unary equality constraints, only one cardinality of the value domain is allocated to it, and for the remaining intervals, i.e., the intervals representing non-equality constraints remaining after the insertion of the equality probability constraints, the remaining cardinality of the value domain is randomly allocated.

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