CN111030701B - Method for constructing partial repetition code based on Harary graph - Google Patents
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Abstract
The invention discloses a method for constructing a partial repetition code based on a Harary graph. By combining with the design in the graph theory, the partial repeated codes capable of being locally repaired are designed, the parameter selection range is large, the problem that the selection of the construction parameters of the partial repeated codes is limited at present is solved, the faults of a plurality of nodes can be accommodated, and each fault node has a plurality of repair schemes.
Description
Technical Field
The invention belongs to the field of computers, and particularly relates to a method for constructing a partial repetition code based on a Harary diagram.
Background
In recent years, with the rapid development of computer technology and the high-speed growth of network information, big data poses a serious challenge to storage systems. Meanwhile, the research on mass data storage technology and system design has also taken a new step. Distributed storage systems are increasingly becoming the mainstream storage systems in modern times due to their efficient storage performance, such as high availability, high scalability, etc. However, in a large-scale storage system, failures such as node offline and sudden power failure often occur, and how to provide reliable data storage services on unreliable storage nodes has become an important research topic in the field of distributed storage.
Currently, research on regenerated codes mainly focuses on minimum storage regeneration MSR (minimum storage regeneration) codes and minimum bandwidth regeneration MBR (minimum bandwidth regeneration) codes. However, the repair process for regenerated codes is computationally complex and typically involves a large number of finite field operations. In the node repairing process, the nodes which need to participate in repairing read out the stored data blocks and carry out specific linear operation, and then transmit the combined data blocks to the replacing nodes. Considering that the read-write bandwidth of a node in an actual system is smaller than the network bandwidth, the read-write bandwidth is easy to become a system performance bottleneck. In order to reduce the operation complexity of the repair process, el Rouayheb and ramchandar propose the concept of partial repetition codes on the basis of MBR codes, wherein the partial repetition codes combine the advantages of regeneration codes and copy strategies and can provide accurate and effective non-coding repair.
However, the current partial repetition codes still have the limitations of limited design parameter selection, single fault point repair scheme and the like.
Disclosure of Invention
In view of the defects or shortcomings in the prior art, the present invention provides a method for constructing a partially repeated code based on a Harary graph.
In order to realize the task, the invention adopts the following technical scheme:
a method for constructing a partial repetition code based on a Harary diagram is characterized by comprising the following steps:
step one, design parameters (k, p) of a Harary graph are given, wherein k is the number of nodes connected with each node, and p is the number of vertexes;
step two, constructing a Harary diagram according to three conditions that the given Harary diagram parameters (k, p) are respectively odd numbers or even numbers:
(1) k is an even number
Let k =2r, then H k,p The structure is as follows:
it has the peak 0,1,2, …, i, …, j, …, p-1, and only when | i-j | ≦ r, the two peaks i are connected with j;
(2) k is an odd number and p is an even number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex i with vertex
Is connected and->
(3) k is an odd number, p is an odd number
If k =2r +1, then H 2r+1,p The construction is as follows:
first, make H 2r,p Then add edges that tie vertex O to vertex
And &>
And connects vertex i to vertex->
And->
Filling data into the generated Harary graph according to a rule, wherein the requirement that two adjacent nodes share the same data block is met, a single node and all connected nodes thereof share one data block respectively, and the data blocks in one node are different;
1) Determining parameters n, theta, rho, alpha of the partially repeated code according to kp = n alpha = rho theta, n = k, alpha = p;
2) Filling the outermost edge of Harary graph with the first 2p data blocks
Numbering the outermost layer edges in the Harary graph, and numbering node 0 and node 1, node 2 and node 3, … and node
And node
Is formed to->
The sides are formed by 1,2, … ->
Numbered and node 1 and node 2, node 3 and node 4, …, node->
And node p constitute->
Used for side>
…, p number; starting the first round of data filling after numbering is finished; will be ahead->
The data blocks are filled in sequence from small to large to the number 1,2, … ->
In the edges of (1), two nodes connected with each edge share the data block filled in the edge; then fill in the remaining parts of the previous p data blocks in turn>
…, p; each node comprises two data blocks, and two adjacent nodes share one data block;
3) Filling the inner layer edge of the Harary graph with the residual np-2p data blocks
Numbering the inner layer edges in the Harary image; numbering the edges of the closed graph surrounded by all vertexes meeting the requirement of i-j = r by p +1, p +2, … and theta in a counterclockwise direction from the 0 th node until all the edges of the inner layer are numbered; sequentially filling data according to the serial number sequence until all the remaining data packets are filled, and after filling is completed, meeting the requirement that any node and all connected nodes thereof share one data block respectively;
and fourthly, reading the number of the edge formed by each vertex in the Harary graph, wherein the vertex of the Harary graph corresponds to a node in the storage system, and the number of each edge corresponds to a coding block in the storage system, so that the construction of a part of repeated codes with the repetition degree of rho is completed.
According to the present invention, the number of vertices of the Harary map parameter (k, p) in step 1 can be selected to be odd or even according to the design requirement.
Furthermore, a part of repeated codes constructed by the Harary graph can accommodate a plurality of node faults, each fault node has a plurality of repair schemes, and the number of data blocks stored in the node can be flexibly adjusted according to requirements.
Compared with the prior art, the method for constructing the partial repetition code based on the Harary diagram has the following technical effects:
1. compared with the existing construction mode, the FR code design based on the Harary graph is simpler and more visual. Moreover, the FR code with the structure can reach the system storage capacity in a random access mode, and the theoretical optimal is realized.
2. The repair mechanism is uncoded, i.e. a surviving node participates in the repair process by simply reading a packet from memory and sending it to the new node. The new node will store the received data packet directly without any further processing.
3. The parameter selection range of the partial repeated codes obtained by the Harary graph is also large, the problem that the selection of the construction parameters of the partial repeated codes is limited at present is solved, the faults of a plurality of nodes can be accommodated, and each fault node has a plurality of repair schemes.
Drawings
Fig. 1 is H (4,8) with ρ =2 and θ =16, completing the first round of data padding;
fig. 2 shows H (4,8) with all data filled when ρ =2 and θ = 16;
fig. 3 is H (4,8) with ρ =4 and θ =8, completing the first round of data padding;
fig. 4 shows H (4,8) in which all data is filled when ρ =4 and θ =8.
The present invention will be described in further detail with reference to the following drawings and examples.
Detailed Description
The design idea of the invention is that a Harary graph is constructed according to different conditions according to given parameters, then data blocks are filled in the obtained Harary graph according to a certain rule, and finally the Harary graph is converted into a corresponding partial repetition code. The parameter selection range of the partial repeated codes obtained by the Harary graph is also large, the problem that the selection of the construction parameters of the partial repeated codes is limited at present is solved, the faults of a plurality of nodes can be accommodated, and each fault node has a plurality of repair schemes.
It should be noted that, in the following embodiments, only the objects, technical solutions and advantages of the present invention will be made clear to those skilled in the art, and the present invention is not limited to these embodiments.
The embodiment provides a method for constructing a partial repetition code based on a Harary graph, and the method for storing an original file M into nodes in a distributed storage system comprises the following steps:
(1) k is an even number
Let k =2r, then H k,p The following can be constructed:
it has the peak 0,1,2, …, i, …, j, …, p-1, and only when | i-j | ≦ r, the two peaks i are connected with j;
(2) k is an odd number and p is an even number
If k =2r +1, then H 2r+1,p The construction is as follows:
first, make H 2r,p Then add edges that connect vertex i with vertex
Is connected with>
(3) k is an odd number, p is an odd number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex O to vertex
And &>
And connects vertex i to vertex->
And 3, filling data into the generated Harary graph, wherein the two adjacent nodes share the same data block, a single node and all connected nodes thereof share one data block respectively, and the data blocks in one node are different.
In this embodiment, only the case (1) is considered for the first time when k and p are both even numbers.
1) Parameters (n, θ, ρ, α) of the partial repetition code are determined according to kp = n α = ρ θ, n = k, α = p.
2) Filling the outermost edge of Harary graph with the first 2p data block data
Numbering the outermost layer edges in the Harary graph, and numbering node 0 and node 1, node 2 and node 3, … and node
And node
Is formed to->
The sides are formed by 1,2, … ->
Numbered and node 1 and node 2, node 3 and node 4, …, node->
And node p>
Used for side>
…, p numbered.
After numbering is finished, the first round of data filling is started, and the first round of data filling is started
The data blocks are filled in turn from small to large to the data blocks numbered 1,2, …, and combined in a manner that can be selected by the user>
In the edges of (1), two nodes connected with each edge share the data block filled in the edge; then the remaining portions of the previous p data blocks are filled in edge->
…, p. Each node contains two data blocks, and two adjacent nodes share one data block.
3) Filling the inner layer edge of the Harary graph with the residual np-2p data blocks
The edges of the inner layer in the Harary diagram are numbered: all the edges of the closed graph surrounded by the vertexes meeting i-j = r are numbered with p +1, p +2, …, theta in the counterclockwise direction from the 0 th node until all the inner layer edges are numbered. And sequentially filling data according to the numbering sequence until the rest data packets are completely filled. After filling, any node and all connected nodes thereof respectively share one data block.
And 4, reading the number of the edge formed by each vertex in the Harary graph, wherein the vertex of the Harary graph corresponds to a node in the storage system, and the number of each edge corresponds to a coding block in the storage system, so that the construction of a part of repeated codes with the repetition degree of rho is completed.
The following inventors give two specific examples with accompanying specific implementation steps.
Example 1:
In the present embodiment, the Harary graph is constructed using parameters of k =8, p = 4.
(1) k is an even number
Let k =2r, then H k,p The following can be constructed:
it has the peak 0,1,2, …, i, …, j, …, p-1, and only when | i-j | ≦ r, the two peaks i are connected with j;
(2) k is an odd number and p is an even number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex i with vertex
Is connected with>
(3) k is an odd number and p is an odd number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex O to vertex
And &>
And connects vertex i to vertex->
Making a (d) with n vertices according to the condition that the parity of a given parameter is satisfied 1 ,d 2 ,d 3 .....d m ) Harary diagram, in which (d) 1 ,d 2 ,d 3 .....d m ) Indicates the number of packets respectively stored by each node, and (d) 1 ,d 2 ,d 3 .....d m ) Is a positive divisor of n.
In the present embodiment, k =4 is an even number, and p =8 is an even number, which corresponds to the case (1) described above. Then, H with the parameter k =4, p =8 is made first 4,8 . The Harary graph has eight vertexes, and each vertex is connected with four different nodes, so that:
d 1 ＝d 2 ＝d 3 ＝d 4 ＝d 5 ＝d 6 ＝d 7 ＝d 8 ＝4。
1) Parameters (n, θ, ρ, α) of the partially repeated code are determined. In this embodiment, first, H 4,8 Where k =4, p =8.
To satisfy kp = n α = ρ θ, n = k, α = p, let ρ =2, θ =16.
2) The first round fills the Harary graph's outermost edges with the first 16 blocks of data, then numbers the outermost edges in the Harary graph, with node 0 and node 1, node 2 and node 3, …, and 4 edges formed by node 6 and node 7 numbered 1,2,3,4, and with node 1 and node 2, node 3 and node 4, …, and 4 edges formed by node 7 and node 8 numbered 5,6,7,8. And starting the first round of data filling after numbering is finished. Sequentially filling the first 4 data blocks (1,2,3,4) from small to large into edges numbered 1,2 and …, wherein two nodes connected with each edge share the data blocks filled in the edges; the remaining portions of the first 16 data blocks are then sequentially filled into edge 5,6,7,8. Each node contains two data blocks, and two adjacent nodes share one data block. As shown in fig. 1.
3) The second round fills the inner layer edge of the Harary graph with the remaining 16 data blocks
The inner layer edges of the Harary diagram are numbered. Starting from the 0 th node, numbering all edges of a closed graph surrounded by vertexes satisfying that i-j is less than or equal to 2 by 9, 10, … and 16 in a counterclockwise direction until all the edges of the inner layer are numbered. And sequentially filling data according to the numbering sequence until the rest data packets are completely filled. After filling, any node and all connected nodes thereof respectively share one data block. As shown in fig. 2.
And reading the number of the edge formed by each vertex in the Harary graph, wherein the vertex of the Harary graph corresponds to a node in the storage system, and the number of each edge corresponds to a coding block in the storage system, so that the construction of the partial repetition code with the repetition degree of 2 is completed. Parameter is H after filling data 4,8 The Harary graph of (8, 16,2,4) is obtained as the FR code.
An FR code formed by nodes (1, 2,. 8, i.e. n = 8) in a distributed storage system, wherein the storage capacity of each node is α =4, i.e. each node stores four different data packets; {1,2,3,4.. 16} represents a group of code blocks (i.e., θ = 16), and the repetition rate ρ =2 of each code block, i.e., each packet is replicated twice, so that ρ -1=1 node failures can be tolerated by the available distributed storage system.
The specific blocks and storage conditions were as follows:
B 1 ＝{1,8,9,12},B 5 ＝{3,6,10,11},
B 2 ＝{1,5,13,16},B 6 ＝{3,7,14,15},
B 3 ＝{2,5,9,10},B 7 ＝{4,7,11,12},
B 4 ＝{2,6,13,14},B 8 ＝{4,8,15,16}.
when a single node fails, the failed node needs to be connected with 4 different nodes, and the restoration can be completed by respectively downloading a data block; for example:
when B1 fails, B2, B3, B7 and B8 are connected and are downloaded 1,9 and 12,8 respectively, and then the failed node can be repaired.
Example 2:
in this example, step 1 and step 2 are the same as in example 1, and step 3 also uses H 4,8 Replacement parameters ρ =4 and θ =8.
1) The first round fills the outermost edge of the Harary graph with the first 16 blocks of data. The outermost edges in the Harary graph are then numbered, with node 0 and node 1, node 2 and node 3, …, and the 4 edges formed by node 6 and node 7 being numbered 1,2,3,4, and with node 1 and node 2, node 3 and node 4, …, and node 7 and node 8 being numbered 5,6,7,8. And starting the first round of data filling after numbering is finished. Sequentially filling the first 4 data blocks (1,2,1,2) into edges which are numbered 1,2,3,4, wherein two nodes connected with each edge share the data blocks filled in the edges; then (3,4,3,4) are sequentially filled into the side 5,6,7,8. Each node contains two data blocks, and two adjacent nodes share one data block. As shown in fig. 3.
2) The second round fills the Harary graph inner edge with the remaining 16 data chunks. The inner layer edges in the Harary diagram are numbered. Starting from the 0 th node, numbering the edges of the closed graph surrounded by all vertexes meeting the condition that i-j is less than or equal to 2 by 9, 10, …,16 in the anticlockwise direction until all the edges of the inner layer are numbered. And sequentially filling data according to the numbering sequence until the rest data packets are completely filled. After filling, any node and all connected nodes thereof respectively share one data block. As shown in fig. 4.
And reading the number of an edge formed by each vertex in the Harary graph, wherein the vertex of the Harary graph corresponds to a node in the storage system, and the number of each edge corresponds to a coding block in the storage system, so that the construction of a part of repetition codes with the repetition degree of 4 is completed. Parameter is H after filling data 4,8 The Harary diagram of (5) to obtain the FR with the corresponding parameter of (8,8,4,4)And (4) code.
An FR code formed by nodes (1, 2,. 8, i.e. n = 8) in a distributed storage system, wherein the storage capacity of each node is α =4, i.e. each node stores four different data packets; {1,2,3,4.., 8} represents a group of code blocks (i.e., θ = 8), and the degree of repetition of each code block, ρ =4, i.e., each data packet is replicated four times, so that ρ -1=3 node failures can be tolerated by the available distributed storage system.
The specific blocks and storage conditions were as follows:
B 1 ＝{1,4,5,8},B 5 ＝{1,4,6,7},
B 2 ＝{1,3,5,8},B 6 ＝{1,3,6,7},
B 3 ＝{2,3,5,6},B 7 ＝{2,3,7,8},
B 4 ＝{2,4,5,6},B 8 ＝{2,4,7,8}.
when a single node fails, the failed node is connected with two different nodes, and then the repair can be completed.
For example:
when B1 fails, the nodes B2 and B5 are connected, and the nodes B2 and B5 are downloaded (1,5,8) and (4) respectively, so that the failed node can be repaired (or the nodes B2 and B4 can be connected to finish repairing).
When two nodes fail, the failed node needs to be connected with 3 different nodes at most for repair.
For example:
when the nodes B1 and B2 fail, the connecting nodes B3, B5, and B7 download (3,5), (1,4), and (8), respectively, so that the two failed nodes can be repaired (or the connecting nodes B4, B5, and B7 can also complete the repair).
When the three nodes have faults, the fault nodes can be repaired by connecting at most three nodes. For example:
when the nodes B1, B3, and B5 fail, the nodes B2, B4, and B6 are connected and download (1,3,5,8), (2,4,6), and (7), respectively, so that the three failed nodes can be repaired (or the nodes B2, B5, and B8 can complete the repair).
Claims (3)
1. A method for constructing a partial repetition code based on a Harary diagram is characterized by comprising the following steps:
step one, design parameters (k, p) of a Harary graph are given, wherein k is the number of nodes connected with each node, and p is the number of vertexes;
step two, constructing a Harary diagram according to three conditions that the given Harary diagram parameters (k, p) are respectively odd numbers or even numbers:
(1) k is an even number
Let k =2r, then H k,p The structure is as follows:
it has the peak 0,1,2, …, i, …, j, …, p-1, and only when | i-j | ≦ r, the two peaks i are connected with j;
(2) k is an odd number and p is an even number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex i with vertex
Are connected to each other and
(3) k is an odd number, p is an odd number
If k =2r +1, then H 2r+1,p The structure is as follows:
first, make H 2r,p Then add edges that connect vertex O to vertex
And
and connecting vertex i to vertex
And is provided with
Filling data into the generated Harary graph according to a rule, wherein the requirement that two adjacent nodes share the same data block is met, a single node and all connected nodes thereof share one data block respectively, and the data blocks in one node are different;
1) Determining parameters n, theta, rho, alpha of the partially repeated code according to kp = n alpha = rho theta, n = k, alpha = p;
2) Filling the outermost edge of Harary graph with the first 2p data block data
Numbering the outermost layer edges in the Harary graph, and numbering node 0 and node 1, node 2 and node 3, … and node
And node
Is composed of
For use on edges
Numbering, and connecting node 1 with node 2, node 3 with node 4, …, node
Formed with node p
For use on edges
Numbering; starting the first round of data filling after numbering is finished; will be ahead of
The data blocks are sequentially filled from small to large to the serial number
In the edges of (1), two nodes connected with each edge share the data block filled in the edge; then filling the remaining parts of the previous p data blocks into the edges in sequence
Performing the following steps; each node comprises two data blocks, and two adjacent nodes share one data block;
3) Filling the inner layer edge of Harary graph with the residual np-2p data blocks
Numbering the inner layer edges in the Harary image; numbering the edges of the closed graph surrounded by all vertexes meeting the requirement of i-j = r by p +1, p +2, … and theta in a counterclockwise direction from the 0 th node until all the edges of the inner layer are numbered; sequentially filling data according to the serial number sequence until the rest data packets are completely filled, and after filling, meeting the requirement that any node and all connected nodes thereof share one data block respectively;
and fourthly, reading the number of the edge formed by each vertex in the Harary graph, wherein the vertex of the Harary graph corresponds to a node in the storage system, and the number of each edge corresponds to a coding block in the storage system, so that the construction of a part of repeated codes with the repetition degree of rho is completed.
2. The method of claim 1, wherein the number of vertices of the Harary map parameter (k, p) in step 1 is selected to be odd or even according to design requirements.
3. The method of claim 1, wherein the partial repetition code constructed from the Harary graph is capable of accommodating multiple node failures, and wherein there are multiple repair schemes for each failed node, and wherein there is flexibility to adjust the number of data blocks stored by a node as needed.
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