A method for constructing partially repeated codes based on graph factorization

Abstract

The present invention discloses a method for constructing a partially repeated code based on graph factorization, which mainly includes the following steps: Step 1: transform each vertex v i (1≤i≤n) is a data block d stored as a partial repetition code i (1≤i≤n), and then the n-order complete graph G is factored; Step 2, determine the repetitiveness ρ of the constructed FR code, and number the edges or triangles of the selected factors in sequence according to whether it can be factored into 1 or 2 factors, and then treat each edge or triangle as each storage node of the FR code; in the constructed FR code with repetitiveness ρ, each node stores the data block d on the adjacent vertices of each edge or each triangle i (1≤i≤n). The present invention can select the construction parameters and the repetition of the data blocks in a wide range, and the construction method has the characteristics of diversity.

Description

Technical Field

[0001] The invention belongs to the field of computers and relates to a construction algorithm of a partially repeated code based on graph factor decomposition. Background Art

[0002] In distributed storage systems, Rouayheb and Ramchandran proposed an exact repair Fractional Repetition (FR) code in 2010. FR codes can tolerate low-complexity codeless repair of multiple faulty nodes, reduce repair bandwidth overhead and disk I / O overhead, and significantly improve system fault repair performance. However, the problem is that the construction process of FR codes is complex, the method of constructing FR codes is single, and the construction parameters and the repetition of data blocks cannot be flexibly selected. Summary of the invention

[0003] The purpose of the present invention is to provide a method for constructing a partially repetitive code based on graph factorization, so as to solve the problems in the prior art that the FR code construction process is complicated, the construction method is single, and the construction parameters and the repetition degree of data blocks cannot be flexibly selected.

[0004] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0005] An algorithm for constructing partially repeated codes based on graph factorization includes the following steps:

[0006] Step 1: Use graph factorization to factorize the n-order complete graph K n Factorize the m-graph to get multiple factors, where n and m are both natural numbers, each factor contains multiple edges, and each edge contains vertices;

[0007] Step 2, randomly select ρ factors from the multiple factors obtained in step 1, use the edge of each factor as the storage node of the partial repetition code, and use the vertices contained in each edge as the data blocks stored in the partial repetition code to construct the partial repetition code.

[0008] As a more specific implementation scheme, the method comprises the following steps:

[0009] Step 1: Use graph factorization to factorize the n-order complete graph K n The factor decomposition can be performed to obtain multiple factors, namely F1, F2, ..., F n-1 , n is an even number, each factor contains multiple edges, and each edge contains vertices;

[0010] Step 2, from F1, F2, ..., F n-1Randomly select ρ factors from , use each edge of each factor as a storage node of the partial repetition code, use the vertices contained in each edge as data blocks stored in the partial repetition code to construct the partial repetition code, and obtain a partial repetition code with a capacity of 2 for each storage node and a total of nρ data blocks stored.

[0011] As another more specific implementation, the method comprises the following steps:

[0012] Step 1: Use graph factorization to factorize the n-order complete graph K n Perform 2-graph factorization to obtain multiple factors, namely F1, F2, ..., F (n-1) / 2 , n is an odd number and n=3t, t is a natural number, each factor contains multiple edges, and the vertices of every two edges are connected to form a triangle;

[0013] Step 2, from F1, F2, ..., F (n-1) / 2 Choose ρ arbitrarily · factors, and use the triangles in each factor as storage nodes of the partial repetition code. The three vertices of each triangle are used as data blocks for storing the partial repetition code to construct the partial repetition code, so that each storage node has a capacity of 3 and stores a total of nρ data blocks of partial repetition codes.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] The present invention uses graph factorization to construct FR codes. There are multiple construction methods: When the factorization can be 1, the construction method of the FR code with a repetition degree of ρ is When the FR code with repetition degree ρ can be decomposed into 2 factors, the construction method is kind.

[0016] At the same time, the method of the present invention can select the number of construction parameter factors and the repetition of data blocks within a wide range. Different FR codes can be constructed by adjusting different construction parameters and the repetition of partial repetition codes, and the construction method is flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic diagram of the factorization of K6;

[0018] Figure 2 It is a schematic diagram of FR code based on 1 factorization;

[0019] Figure 3 This is a schematic diagram of the 3K3 factorization of K9;

[0020] Figure 4 It is a schematic diagram of FR code based on 2-factor decomposition. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0022] The n-order complete graph K of the present invention n The definition of is that any two different vertices of the graph G are adjacent.

[0023] The one-factor decomposition and two-factor decomposition described in the present invention are specifically: if for a given graph G, it can be decomposed into a number of spanning subgraphs F1, F2, ..., F2 with no common edges between them. n , and pre-requires F i (i=1,2,…,n) satisfies V(F i )=V(G), and E(F i )∩E(F j )=φ(i≠j), and require F i P i ,i=1,2,…,n,called F i (i=1,2,…,n) is the factor of G. Factor graph F is decomposed from graph G. i The process of factoring is called factorization of graph G. When a factor is an m-regular graph, then this factor is called an m-factor of graph G; if all the factors of graph G are m-regular graphs, then graph G is said to be m-factorizable.

[0024] At the same time, if the n-order complete graph G described in the present invention has a 2-factor decomposition, and any connected branch of each 2-factor is a triangle, then for a certain positive integer t, G is tK3-factor decomposable, so n=3t. Since the degree of any vertex v in G in each 2-factor of G is 2, the degree of v in G is an even number. Therefore, n-1 is an even number, so n=3t is an odd number, which means that t is an odd number. Therefore, there exists a certain non-negative integer k such that t=2k+1, n=6k+3. Therefore, G is (2k+1)K3-factor decomposable.

[0025] The specific steps of the present invention are as follows:

[0026] Step 1: Use graph factorization to factorize the n-order complete graph K n Perform 1-factor decomposition to obtain multiple factors, such as 1-factor decomposition and 2-factor decomposition. n Each vertex v i (1≤i≤n) is a data block d stored as a Fractional Repetition (FR) code i (1≤i≤n).

[0027] Step 2, factorize the graph into 1 or 2 factors:

[0028] Step 2.1. For the complete graph K n (n=2k,k∈N+) can be factorized to obtain F1, F2, …, F n-1 , determine the repetition degree ρ (1≤ρ≤n-1) of the constructed FR code, because each F i (1≤i≤n-1) contains all vertices of the complete graph, that is, all data blocks, so any F i (1≤i≤n-1) is a parallel class, so the construction method of FR code with repetition degree ρ is kind.

[0029] When the repetition degree ρ (1≤ρ≤n-1) of the FR code is determined, n-1 Select any ρ factors from the list to construct. Then number the edges of the selected ρ factors as e q (1≤q≤nρ / 2), each edge e in the ρ factors q (1≤q≤nρ / 2) is regarded as each storage node N of the FR code q (1≤q≤nρ / 2).

[0030] In the constructed FR code with repetition degree ρ (1≤ρ≤n-1), each node N q (1≤q≤nρ / 2) store each edge e q (1≤q≤nρ / 2) data blocks d on adjacent vertices i (1≤i≤n). The capacity of each storage node of the FR code constructed using the 1-factor decomposition of the complete graph is 2.

[0031] Step 2.2, for the complete graph K n (n=6k+3,k∈N+) can be factorized into 2 factors, and we get F1, F2, …, F (n-1) / 2 ;

[0032] Determine the repetition degree ρ′ (1≤ρ′≤(n-1) / 2) of the constructed FR code. j (1≤j≤(n-1) / 2) contains all vertices of the complete graph, that is, all data blocks, so any F j (1≤j≤(n-1) / 2) is a parallel class, so the construction method of constructing FR code with repetition degree ρ′(1≤ρ′≤(n-1) / 2) is kind.

[0033] When the repetition degree ρ′ (1≤ρ′≤(n-1) / 2) of the FR code is determined, jSelect any ρ′(1≤ρ′≤(n-1) / 2) factors from (1≤j≤(n-1) / 2) to construct. Then number the triangles of these ρ′ factors as Δ q (1≤q≤ρ′(2k+1)), each triangle Δ in the ρ′ factor q (1≤q≤ρ′(2k+1)) is regarded as each storage node N of the FR code q (1≤q≤ρ′(2k+1)).

[0034] In the constructed FR code with repetition degree ρ′ (1≤ρ′≤(n-1) / 2), each node N q (1≤q≤ρ′(2k+1)) stores each triangle Δ q (1≤q≤ρ′(2k+1)) Data block d on adjacent vertices i (1≤i≤n). The capacity of each storage node of the FR code constructed using the 2-factor decomposition of the complete graph is 3.

[0035] The following are specific embodiments:

[0036] Example 1

[0037] This embodiment provides a method for constructing a partially repeated code based on graph factorization, comprising the following steps:

[0038] Step 1: Use graph factorization method to decompose the 6th-order complete graph K6 into 5 factors F1, F2, …, F5. Each factor contains 3 edges, and each edge has 2 vertices.

[0039] Step 2: Determine the repetition degree ρ (1≤ρ≤5) of the constructed FR code. For example, ρ=3, so there are A method for constructing FR codes with repetition degree ρ = 3. Select any three factors from F1, F2, ..., F5 and transform each vertex v of the 6th-order complete graph K6 into i (1≤i≤6) is a data block v stored as FR code i (1≤i≤6), such as Figure 1 As shown, select factors F2, F4, and F5, and then number the edges of F2, F4, and F5 in sequence as e q (1≤q≤9), such as Figure 1 Then, each side e of the three factors q (1≤q≤9) is regarded as each storage node N of the FR code q (1≤q≤9), each node N q (1≤q≤9) store each edge e q (1≤q≤9) data blocks d on adjacent vertices i(1≤i≤6). The capacity of each storage node of the FR code constructed by factoring the complete graph is 2, and the partial repetition code obtained is as follows Figure 2 shown.

[0040] Embodiment 2:

[0041] This embodiment provides a method for constructing a partially repeated code based on graph factorization, comprising the following steps:

[0042] Step 1: Use the graph factorization method to decompose the 9th-order complete graph K9 into 2-factors and obtain 4 factors F1, F2, …, F4, each of which contains 3 triangles.

[0043] Step 2: Determine the repetition degree ρ′ (1≤ρ′≤4) of the constructed FR code, and take ρ′=3, so there are A construction method of FR code with repetition degree ρ′=3. Select any 3 factors from F1, F2, …, F4 for construction. For example, select factors F1, F3, F4, and then number the triangles of F1, F3, F4 in sequence as Δ q (1≤q≤9), such as Figure 3 As shown. Put each triangle Δ in the 3 factors q (1≤q≤9) is regarded as each storage node N of the FR code q (1≤q≤9), each node N q (1≤q≤9) stores each triangle Δ q (1≤q≤9) data blocks d on adjacent vertices i (1≤i≤9). The capacity of each storage node of the FR code constructed by using the 2-factor decomposition of the complete graph is 3, and the partial repetition code obtained is as follows Figure 4 shown.

Claims

1. A method for constructing a partially repetitive code based on graph factorization, wherein the repetition degree of the partially repetitive code is ρ, It is characterized in that The steps include: Step 1: Use graph factorization to factorize the n-order complete graph K n Decompose to get multiple factors, and transform the n-order complete graph K n Each vertex v i Data block d stored as partial repetition code i , 1≤i≤n; Step 2: When n=2k, k∈N+, for the complete graph K n Factorize it to get F 1 ,F 2 ,…,F n-1 ; Determine the repetition degree ρ of the constructed FR code, because each F i Contains all vertices of the complete graph, that is, all data blocks, so any F i is a parallel class, so the construction method of FR code with repetition degree ρ is species, 1≤ρ≤n-1, 1≤i≤n-1; When the repetition rate ρ of the FR code is determined, 1 ,F 2 ,…,F n-1 Select any ρ factors from the list to construct; then number the edges of the selected ρ factors in sequence as e q , each edge e in the ρ factors q Each storage node N of the FR code q , 1≤q≤nρ / 2; In the constructed FR code with repetition degree ρ, each storage node N q Store each edge e q Data blocks d on adjacent vertices i ; The capacity of each storage node of the FR code constructed using the 1-factor decomposition of the complete graph is 2; Step 3, when n=6k+3,k∈N+, for the complete graph K n Factorize it into 2, and you get F 1 ,F 2 ,…,F (n-1) / 2 ; Determine the repetition degree ρ′ of the constructed FR code; because each F j Contains all vertices of the complete graph, that is, all data blocks, so any F j is a parallel class, so the construction method of constructing FR code with repetition degree ρ′ is species, 1≤ρ′≤(n-1) / 2, 1≤j≤(n-1) / 2; When the repetition degree ρ′ of the FR code is determined, j Select any ρ′ factors from the list to construct; then number the triangles of these ρ′ factors Δ q , each triangle Δ in the ρ′ factors q Each storage node N of the FR code q , 1≤q≤ρ′(2k+1); In the constructed FR code with repetition degree ρ′, each node N q Store each triangle Δ q Data blocks d on adjacent vertices i , 1≤i≤n; the capacity of each storage node of the FR code constructed using the 2-factor decomposition of the complete graph is 3.

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