A data processing method and system based on aging balanced tree

Abstract

The application relates to a time-effect balanced tree-based data processing method and system, and relates to a time-effect balanced tree-based data processing method and system which solves the problem that the node with the highest query frequency in a short period usually consumes a high cost on the balanced tree structure of a computer, the single query consumption is usually fixed as logarithmic level time, the balanced tree lacks sensitivity to the query frequency and the time-effectiveness of recent queries, and the query time is too long each time. The application constructs a time-effect balanced tree, stores data according to the structure of the time-effect balanced tree, and the empty tree, single node, left subtree and right subtree of the time-effect balanced tree are all time-effect balanced trees. Each node on the time-effect balanced tree comprises a retrieval key value pair, a time-effect weight and a record query round, and the time-effect weight is calculated by a decay method. The unbalance degree, balance state and rotation mode of the time-effect balanced tree are defined. The computer data processing is completed according to the definition, the time-effect balanced tree and the time-effect weight. The application belongs to the field of computer data processing.

Description

Technical Field

[0001] This invention relates to a data processing method and system, specifically to a data processing method and system based on a time-balanced tree, belonging to the field of computer data processing. Background Technology

[0002] A balanced tree is a data structure in computer science, an improved binary search tree. Compared to a regular binary search tree, a balanced tree averages the distance from the target data to the root, making the depth of all leaf nodes more balanced, or lowering the amortized complexity of all possible searches in the tree. Balanced trees generally support basic operations such as rotation, insertion, deletion, and modification. Commonly used balanced trees in computer science include AVL trees, Treaps, SplayTrees, and Red-Black Trees.

[0003] Existing balanced tree techniques in computing, such as AVL trees and red-black trees, generally emphasize the balance of the entire tree structure, which does not change with the frequency of data queries. This means that the worst-case complexity of a balanced tree structure is logarithmic time, and also implies that at least logarithmic time is required to execute a single data query. Even if some data queries are extremely frequent, these tree structures will still consume logarithmic time to complete the query operation, making the nodes most frequently queried in the short term excessively costly. Structures like splay trees, on the other hand, lack effective representation of timeliness, failing to recognize that recent frequent data queries require more timely optimization than past frequent queries. Therefore, balanced trees lack sensitivity to query frequency and the timeliness of recent queries, resulting in excessively long query times. A balanced tree method is needed to reduce the cost of recent frequent queries. Summary of the Invention

[0004] To address the problem that in computer balanced tree structures, the nodes most frequently queried in the short term typically consume excessive costs, and the time consumed by a single query is usually fixed at logarithmic levels, making the balanced tree lack sensitivity to query frequency and the timeliness of recent queries, resulting in excessively long query times, this invention proposes a data processing method and system based on time-balanced trees.

[0005] The technical solution adopted in this invention is:

[0006] It includes the following steps:

[0007] S1. Construct a time-balanced tree:

[0008] The time-balanced tree is a binary search tree. Each node in the time-balanced tree has at most one left subtree and at most one right subtree. Each node in the time-balanced tree is used to retrieve key-value pairs, calculate and record the time-balanced weight and the number of query rounds. The time-balanced weight is the cumulative number of times the node has been used.

[0009] S2. Define the imbalance of the time-balanced tree as the absolute value of the difference between the time-balanced weights of the left and right subtrees;

[0010] The time-balanced tree is in a balanced state when the imbalance of each subtree is minimized.

[0011] The rotation methods for each node in the time-balanced tree are defined as follows: unidirectional right rotation LL, unidirectional left rotation RR, left-to-right bidirectional rotation LR, and right-to-left bidirectional rotation RL.

[0012] S3. Store the data in the computer database according to the time-balanced tree structure;

[0013] S4. Obtain the computer data to be processed, input the computer data to be processed into the time-balanced tree of S1, find the node where the current data is located, record the time weight of the node, rotate the structure of the time-balanced tree from bottom to top based on S2 and the time weight of the node, update the time weight of all nodes in the time-balanced tree until the time-balanced tree is in a balanced state, and output the processing result.

[0014] Furthermore, the time-balanced tree in S1 satisfies the following conditions:

[0015] Condition 1: Both empty trees and single-node trees are time-balanced trees;

[0016] Condition 2: Both the left and right subtrees of the time-balanced tree are time-balanced trees.

[0017] Furthermore, the time weight of each node in the time balance tree in S1 is calculated by the decay method.

[0018] Furthermore, the attenuation method is as follows:

[0019] c*η^(FH)

[0020] Where c represents the timeliness weight of a node, η represents the decay rate, F represents the current processing round of a node, and H represents the latest processing round of a node in history.

[0021] Furthermore, the unidirectional right-handed balancing process LL in S2 is as follows:

[0022] The root node of the left subtree of root node A is B, the right subtree of root node A is E, the left subtree of the left subtree root node B is C, and the right subtree of the left subtree root node B is D. When root node A performs a right rotation operation, the left subtree root node B becomes the new root node, the left subtree C becomes the left subtree of the new root node B, the root node A becomes the right subtree root node of the new root node B, the right subtree D is the left subtree of the right subtree root node A, and the right subtree E is the right subtree of the right subtree root node A.

[0023] The unidirectional left-handed balance treatment RR is:

[0024] The left subtree of root node A is B, the root node of the right subtree of root node A is C, the left subtree of the right subtree root node C is D, and the right subtree of the right subtree root node C is E. When root node A performs a left rotation operation, the right subtree root node C becomes the new root node, the right subtree E becomes the right subtree of the new root node C, the root node A becomes the left subtree root node of the new root node C, the left subtree D becomes the right subtree of the left subtree root node A, and the left subtree B becomes the left subtree of the left subtree root node A.

[0025] The left-to-right bidirectional rotational balancing process is as follows:

[0026] Perform a one-way left rotation RR on the left subtree of a node, and then perform a one-way right rotation LL on the entire current time-balanced tree.

[0027] The bidirectional rotational balancing process (RL) is as follows:

[0028] Perform a one-way right rotation LL on the right subtree of a given node, and then perform a one-way left rotation RR on the entire current time-balanced tree.

[0029] Furthermore, the processing in S4 includes data querying, data addition, data deletion, and data modification.

[0030] Furthermore, the specific process of S4 is as follows:

[0031] Input the computer data to be processed into the time-balanced tree of S1, obtain the node where the current data is located, record the time-balanced weight of the current node, obtain all nodes on the path from the current node to the root node of the time-balanced tree, and rotate the subtrees of all nodes in the time-balanced tree in order from bottom to top. Determine whether the imbalance of each subtree is reduced after rotation. When the imbalance is reduced, calculate the time-balanced weight of the current node using the decay method. If the time-balanced weight of the left subtree of the current node increases or the time-balanced weight of the right subtree decreases, perform unidirectional right rotation balancing process LL and bidirectional rotation balancing process LR (left then right) in sequence. If the time-balanced weight of the left subtree of the current node decreases or the time-balanced weight of the right subtree increases, perform unidirectional left rotation balancing process RR and bidirectional rotation balancing process RL (right then left) in sequence until the imbalance of the corresponding subtree is minimized, and the subtree processing is completed. Otherwise, maintain the original state of the subtree. When the imbalance of each subtree is minimized, the time-balanced tree is in a balanced state, and the processing result is output.

[0032] Furthermore, the specific process of calculating the time-sensitivity weight of the current node using the decay method is as follows:

[0033] For the current processing, set the decay rate η and the query window size M, 0≤η≤1, where M is a positive integer. Define the current processing as the Kth processing of the current node. Round down the quotient of K and M to get the current processing round F. That is, when M is 100, the 0th to 99th queries are the first round, the 100th to 199th queries are the second round, and so on. Based on the latest historical processing round H of the current node, update the timeliness weight c of the current node using the decay method, and assign F the value H.

[0034] For nodes that are not currently being processed and have not been updated, their timeliness weight will be compared with η in the next update. a Multiply, where 'a' is the difference between any two query rounds.

[0035] Furthermore, the query window size M is set by the user based on the specific number of queries and the query time interval.

[0036] A data processing system based on a time-balanced tree includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any step of a data processing method based on a time-balanced tree.

[0037] Beneficial effects:

[0038] This invention constructs a time-balanced tree to store data from a computer database according to its structure. The time-balanced tree is essentially a binary search tree. Each node in the time-balanced tree has at most one left subtree and at most one right subtree. Empty trees and single-node trees are both time-balanced trees. The left and right subtrees of a time-balanced tree are also time-balanced trees. Each node in the time-balanced tree, in addition to being used for retrieving key-value pairs, also includes two attributes: a time-balanced weight and the number of query rounds recorded. The time-balanced weight is the cumulative number of times the node has been used. The time-balanced weight is calculated using the decay method proposed in this invention. When each node is processed, its cumulative query count increases by 1, but its time-balanced weight does not increase by 1; instead, it decays. This ensures that the time-balanced weight better represents recent frequent queries and tends to ignore older frequent queries, thus reasonably adjusting the time-balanced weight to maintain a continuous and effective balance. The imbalance of a time-balanced tree is defined as the absolute value of the difference between the time-balanced weights of the left and right subtrees. A time-balanced tree is considered balanced when the imbalance of each subtree is minimized. Rotation methods for each node in the time-balanced tree are defined as follows: unidirectional right rotation (LL), unidirectional left rotation (RR), left-to-right bidirectional rotation (LR), and right-to-left bidirectional rotation (RL). In application, the computer data to be processed is input into the time-balanced tree. The node containing the current data is located, and its time-balanced weight is recorded. Based on the above definitions and the node's time-balanced weight, the structure of the time-balanced tree is rotated from bottom to top, updating the time-balanced weights of all nodes in the tree until it is balanced. The processing result is then output.

[0039] This invention's time-sensitive balanced tree is based on the theory of weighted balanced trees. It influences the tree's balance structure and rotation method through time-sensitive weights, effectively reducing the time consumed by recently frequent queries by assigning weights related to query frequency and timeliness. This invention can be used for data querying, data addition, data deletion, and data modification. By using the balancing method of assigning time-sensitive weights to nodes, the rotation operation of the balanced tree is performed, allowing nodes with high query frequency and recent query times to be moved to more easily queried positions in the tree. In query environments where high-frequency nodes are frequently queried, the average query efficiency is effectively improved. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the structure of the present invention;

[0041] Figure 2 This is a schematic diagram of a unidirectional right-handed balance process;

[0042] Figure 3 This is a schematic diagram of a unidirectional left-handed balance process;

[0043] Figure 4 This is a schematic diagram of the initial state of the time-balanced tree in the embodiment;

[0044] Figure 5 This is a schematic diagram of the rotation state of the time-balanced tree in the embodiment;

[0045] Figure 6 This is a schematic diagram of the final state of the time-balanced tree in the embodiment; Detailed Implementation

[0046] Specific implementation method one: Combining Figures 1-3 This embodiment describes a data processing method based on a time-balanced tree, which includes the following steps:

[0047] S1. Construct a time-balanced tree to store data from the computer database according to the structure of the time-balanced tree.

[0048] A time-balanced tree is a binary search tree that satisfies the following conditions:

[0049] Condition 1: Both empty trees and single-node trees are time-balanced trees.

[0050] Condition 2: Both the left and right subtrees of the time-balanced tree are time-balanced trees.

[0051] Each node in the time-balanced tree has at most one left subtree and at most one right subtree. Besides being used for key-value retrieval, each node in the time-balanced tree also possesses two attributes: "time-balanced weight" and "query rounds." Both attributes are used in the rotation process of the time-balanced tree. The rotation of the time-balanced tree should be based on the time-balanced weights on both sides of the tree, where the time-balanced weight is the cumulative number of times the node has been used. The time-balanced weight designed in this invention has the characteristic of decaying over time. That is, the time-balanced weight is calculated according to the "decay method." When each node is queried, the cumulative query count increases by 1, but because the time-balanced decay rate is considered, the time-balanced weight does not increase by 1; instead, it decays.

[0052] The attenuation method is as follows:

[0053] c*η^(FH)

[0054] Where c represents the timeliness weight of a node, η represents the decay rate, F represents the current processing round of a node, and H represents the latest processing round of a node in history.

[0055] S2. Define the imbalance of the time-balanced tree as the absolute value of the difference between the time-balanced weights of the left and right subtrees.

[0056] A time-balanced tree is considered balanced when the imbalance of each subtree is minimized. A subtree is a tree structure consisting of each node (excluding the root node) and its corresponding left or right subtree, or both. If a node has no left or right subtree, or no left or right subtree, then that node is used as the root to form a subtree. Figure 5 As shown, all the subtrees of this tree are: the tree rooted at C: C; the tree rooted at D: D; the tree rooted at G: G; the tree rooted at E: EG; the tree rooted at F: FEG; and the tree rooted at B: BCD.

[0057] The rotation method for each node in the time-bound balance tree is defined as follows:

[0058] Unidirectional right-handed balance treatment LL: such as Figure 2 As shown, the root node of the left subtree of root node A is B, the root node of the right subtree of root node A is E, the left subtree of the left subtree root node B is C, and the right subtree of the left subtree root node B is D. If root node A undergoes a right rotation, making the left subtree root node B the new root node, then the left subtree C becomes the left subtree of the new root node B, root node A becomes the root node of the right subtree of the new root node B, the right subtree D is the left subtree of the right subtree root node A, and the right subtree E is the right subtree of the right subtree root node A.

[0059] Unidirectional left-handed balance treatment RR: such as Figure 3 As shown, the left subtree of root node A is B, the root node of the right subtree of root node A is C, the left subtree of the right subtree root node C is D, and the right subtree of the right subtree root node C is E. When root node A undergoes a left rotation, making the right subtree root node C the new root node, then the right subtree E becomes the right subtree of the new root node C, root node A becomes the left subtree root node of the new root node C, left subtree D becomes the right subtree of the left subtree root node A, and left subtree B becomes the left subtree of the left subtree root node A.

[0060] Left-to-right bidirectional rotation balancing process LR: First, perform a one-way left rotation balancing process RR on the left subtree of a certain node, and then perform a one-way right rotation balancing process LL on the current entire time-balanced tree.

[0061] Right-then-left bidirectional rotation balancing process RL: First, perform a one-way right rotation balancing process LL on the right subtree of a certain node, and then perform a one-way left rotation balancing process RR on the current entire time-balanced tree.

[0062] S3. When performing a query, add, delete, or modify operation on a piece of data to be processed in the computer database, the time-balanced tree in S1 is processed from top to bottom. The node containing the current data is located, and its time-balanced weight is recorded. Based on S2 and the node's time-balanced weight, the structure of the time-balanced tree is rotated level by level from bottom to top to update the time-balanced weights of all nodes in the tree until it is balanced. The query, add, delete, or modify result is then output. The specific process is as follows:

[0063] Input the computer data to be processed (queried, added, deleted, or modified) into the time-balanced tree of S1. Locate the node or subtree where the current data is located, record the time-balanced weight of the current node or subtree, find all nodes on the path from the current node or subtree to the root node of the time-balanced tree, and rotate the subtrees of all nodes in the time-balanced tree in a bottom-up order. By comparing the imbalance of each subtree before and after the rotation, determine whether the imbalance of each subtree has decreased. If the imbalance has decreased, calculate the time-balanced weight of the current node using the decay method. If the current node's left... When the time-weight of a subtree increases or the time-weight of the right subtree decreases, perform a one-way right rotation balancing process LL and a left-to-right bidirectional rotation balancing process LR in sequence. If the time-weight of the left subtree of the current node decreases or the time-weight of the right subtree increases, perform a one-way left rotation balancing process RR and a right-to-left bidirectional rotation balancing process RL in sequence until the imbalance of the corresponding subtree is minimized, thus completing the subtree processing. If the imbalance does not decrease, no operation is performed, and the original state of the subtree is maintained. The processing result is output when all subtrees have been processed and the time-balanced tree is in a balanced state.

[0064] The above calculation of the time-sensitivity weight of the current node using the decay method is as follows:

[0065] For the current processing, set the decay rate η and the query window size M, where 0 ≤ η ≤ 1, and M is a positive integer. M is set by the user based on the specific number of queries and the query time interval. Define the current processing as the Kth processing operation of the current node. Round down the quotient of K and M to get the current processing round F. For example, when M is 100, queries 0-99 are the first round, queries 100-199 are the second round, and so on. Based on the latest historical processing round H of the current node (assuming the current processing round F is the 5th, then the latest historical processing round H is the 4th), update the timeliness weight c of the current node using the decay method, and update H with F, assigning F to H, i.e., F := H. This process has the following guarantees:

[0066] For nodes that are not currently being processed and have not been updated, their timeliness weight will be compared with η in the next update. a Multiplying, where 'a' is the difference between the rounds to which any two queries belong, the resulting time-balanced tree structure still satisfies the balance state.

[0067] Specific Implementation Method Two: Combining Figures 1-3 This embodiment describes a data processing system based on a time-balanced tree, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any step of a data processing method based on a time-balanced tree.

[0068] Example

[0069] like Figures 4-6 As shown, this invention considers the impact of multiple query operations on the time-sensitive balanced tree structure. To demonstrate the balancing method of the time-sensitive balanced tree, all query operations are performed in the same round, without considering time-sensitive decay. The initial state is as follows: Figure 4 As shown, there are 7 nodes to be queried, and the inorder traversal result is CBDAFEG. The rotation operation will ensure that the inorder traversal result remains unchanged. After querying node B 4 times and node F 4 times, the following will occur: Figure 5 The changes are as follows: Node F is rotated to the root of the right subtree, while node B remains in its original position. After querying node F 15 more times, it becomes clear that only when node F is the root node will the imbalance between the left and right subtrees be minimized. A left rotation is then performed to move node F to the root. The final tree shape is as follows. Figure 6 As shown, the most frequently queried node F is located at the root of the tree and is the easiest to access. The previous root node A, having received no queries, had a very low weight and was rotated to a deeper position in the tree.

Claims

1. A data processing method based on a time-balanced tree, characterized in that: It includes the following steps: S1. Construct a time-balanced tree: The time-balanced tree is a binary search tree. Each node in the time-balanced tree has at most one left subtree and at most one right subtree. Each node in the time-balanced tree is used to retrieve key-value pairs, calculate and record the time-balanced weight and the number of query rounds. The time-balanced weight is the cumulative number of times the node has been used. The time-related weight of each node in the time-related balanced tree is calculated using the decay method, which is as follows: c*η ^ (FH) Where c represents the timeliness weight of a node, η represents the decay rate, F represents the current processing round of a node, and H represents the latest processing round of a node in history. S2. Define the imbalance of the time-balanced tree as the absolute value of the difference between the time-balanced weights of the left and right subtrees; The time-balanced tree is considered balanced when the imbalance of each subtree is minimized. The rotation methods for each node in the time-balanced tree are defined as follows: unidirectional right rotation LL, unidirectional left rotation RR, left-to-right bidirectional rotation LR, and right-to-left bidirectional rotation RL. S3. Store the data in the computer database according to the time-balanced tree structure; S4. When performing a query, addition, deletion, or modification operation on a certain data to be processed in the computer database, obtain the computer data to be processed, input the computer data to be processed into the time-balanced tree of S1, find the node where the current data is located, record the time-balanced weight of the node, rotate the structure of the time-balanced tree from bottom to top based on S2 and the time-balanced weight of the node, update the time-balanced weight of all nodes in the time-balanced tree until the time-balanced tree is in a balanced state, and output the processing result.

2. The data processing method based on a time-balanced tree as described in claim 1, characterized in that: The time-balanced tree in S1 satisfies the following conditions: Condition 1: Both empty trees and single-node trees are time-balanced trees; Condition 2: Both the left and right subtrees of the time-balanced tree are time-balanced trees.

3. The data processing method based on a time-balanced tree as described in claim 2, characterized in that: The unidirectional right-handed balance treatment LL in S2 is as follows: The root node of the left subtree of root node A is B, the right subtree of root node A is E, the left subtree of the left subtree root node B is C, and the right subtree of the left subtree root node B is D. When root node A performs a right rotation operation, the left subtree root node B becomes the new root node, the left subtree C becomes the left subtree of the new root node B, the root node A becomes the right subtree root node of the new root node B, the right subtree D is the left subtree of the right subtree root node A, and the right subtree E is the right subtree of the right subtree root node A. The unidirectional left-handed balance treatment RR is: The left subtree of root node A is B, the root node of the right subtree of root node A is C, the left subtree of the right subtree root node C is D, and the right subtree of the right subtree root node C is E. When root node A performs a left rotation operation, the right subtree root node C becomes the new root node, the right subtree E becomes the right subtree of the new root node C, the root node A becomes the left subtree root node of the new root node C, the left subtree D becomes the right subtree of the left subtree root node A, and the left subtree B becomes the left subtree of the left subtree root node A. The left-to-right bidirectional rotational balancing process is as follows: Perform a one-way left rotation RR on the left subtree of a node, and then perform a one-way right rotation LL on the entire current time-balanced tree. The bidirectional rotational balancing process (RL) is as follows: Perform a one-way right rotation LL on the right subtree of a given node, and then perform a one-way left rotation RR on the entire current time-balanced tree.

4. The data processing method based on a time-balanced tree according to claim 3, characterized in that: The specific process of S4 is as follows: Input the computer data to be processed into the time-balanced tree of S1, obtain the node where the current data is located, record the time-balanced weight of the current node, obtain all nodes on the path from the current node to the root node of the time-balanced tree, and rotate the subtrees of all nodes in the time-balanced tree in order from bottom to top. Determine whether the imbalance of each subtree is reduced after rotation. When the imbalance is reduced, calculate the time-balanced weight of the current node using the decay method. If the time-balanced weight of the left subtree of the current node increases or the time-balanced weight of the right subtree decreases, perform unidirectional right rotation balancing process LL and bidirectional rotation balancing process LR (left then right) in sequence. If the time-balanced weight of the left subtree of the current node decreases or the time-balanced weight of the right subtree increases, perform unidirectional left rotation balancing process RR and bidirectional rotation balancing process RL (right then left) in sequence until the imbalance of the corresponding subtree is minimized, and the subtree processing is completed. Otherwise, maintain the original state of the subtree. When the imbalance of each subtree is minimized, the time-balanced tree is in a balanced state, and the processing result is output.

5. The data processing method based on a time-balanced tree according to claim 4, characterized in that: The specific process of calculating the time-sensitivity weight of the current node using the decay method is as follows: For the current processing, set the decay rate η and the query window size M, 0≤η≤1, where M is a positive integer. Define the current processing as the Kth processing of the current node. Round down the quotient of K and M to get the current processing round F. That is, when M is 100, the 0th to 99th queries are the first round, the 100th to 199th queries are the second round, and so on. Based on the latest historical processing round H of the current node, update the timeliness weight c of the current node using the decay method, and assign F the value H. For nodes that are not currently being processed and have not been updated, their timeliness weight will be compared with η in the next update. a Multiply, where 'a' is the difference between any two query rounds.

6. The data processing method based on a time-balanced tree according to claim 5, characterized in that: The size M of the query window is set by the user based on the specific number of queries and the query time interval.

7. A data processing system based on a time-balanced tree, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

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