CN113708963A - Optimized topology recursion method and system meeting alliance chain partition tolerance - Google Patents

Optimized topology recursion method and system meeting alliance chain partition tolerance Download PDF

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CN113708963A
CN113708963A CN202110963008.8A CN202110963008A CN113708963A CN 113708963 A CN113708963 A CN 113708963A CN 202110963008 A CN202110963008 A CN 202110963008A CN 113708963 A CN113708963 A CN 113708963A
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李挥
吕琦
王菡
王子贤
张明龙
张汉裕
褚晓理
刘绍瑜
蓝卡空
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Abstract

The invention is suitable for the field of block chain technology improvement, and provides an optimized topology recursion method meeting the requirement of alliance chain partition tolerancerThe new node number after recursion is added with one bit backwards on the basis of the original node number, and the corresponding nodes of each r-level domain are connected into a topological structure of r-1-level domains by using physical links to form interconnection among domains. An extensible physical topology with good partition tolerance is constructed, the physical topology is based on a multi-dimensional hypercube, and the structured P2P network can be relievedTopology mismatch of the network. The proposed hierarchical recursive topology method inherits the strong regularity characteristic of the hypercube, and meanwhile, the long-distance link in the general hypercube topology is replaced by the short-distance link, so that the method is more realizable.

Description

Optimized topology recursion method and system meeting alliance chain partition tolerance
Technical Field
The invention belongs to the field of technical improvement of a alliance chain, and particularly relates to an optimized topology recursion method and system meeting the partition tolerance of the alliance chain.
Background
Bitcoin, the first widely deployed, decentralized global cryptocurrency, initiated hundreds of different cryptocurrency systems with its core decentralized infrastructure, blockchain technology. Although many protocols have been proposed by the predecessors to improve the performance of blockchains, none of them has got rid of the CAP (Consistency Availability, Partition tolerance) dilemma in the distribution theory. In particular, in distributed systems, consistency, availability, and partition tolerance cannot be fully satisfied at the same time.
To balance the three properties in the CAP dilemma, some methods are optimized at the consensus layer. The original consensus protocol satisfied good partition tolerance, such as the longest backbone principle, by the bifurcation selection rule. However, forking in the backbone can shift strong consistency to weak consistency or final consistency over a period of time, resulting in long acknowledgement times and limited throughput. Furthermore, some performance-driven consensus protocols guarantee consistency and partition tolerance through a representational mechanism, but reduce the number of core nodes participating in consensus.
Still other approaches have focused on optimizing the topology of the structured P2P network to speed up the spread of transactions and tiles through the blockchain. And C, constructing a star subgraph by the Decker, and taking the star subgraph as a central communication hub to reduce the number of routing hops between nodes. Muntader proposes a block chain network Clustering protocol Based on Super nodes, which is called BCBSN (Bitcoin Clustering Based on Super node), and reduces the propagation delay of transactions and blocks in the same cluster through Clustering Based on node locality. Furthermore, an LBC (location Based Clustering) protocol and a BCBPT (Bitcoin Clustering Based on Ping time) protocol are provided, and nodes in the block chain network are clustered according to physical position indexes such as geographic positions, Ping time and the like so as to reduce propagation delay of adjacent nodes.
Although some methods consider the influence of the physical structure on the performance, the problem of mismatching between the logical topology and the physical topology cannot be completely solved, and the improvement performance is limited. Furthermore, unlike public chains, nodes in a federation chain are more controllable, and thus none of the above approaches are applicable to federation chains.
For a structured P2P network in a federation chain, we have designed a general physical topology between supernodes based on a multidimensional hypercube. Management can be realized by connecting the super nodes and the common nodes through tree topology. The topology is applicable to not only fully distributed P2P networks, but also semi-distributed P2P networks.
In a general hypercube topology with base b 2, each node has the same responsibilities. The diameter of the network, i.e. the shortest path between the nodes with the highest number of node hops, is equal to log2N (N is the number of nodes). Therefore, the hypercube-based network topology has good characteristics in terms of load balancing and good redundancy.
In a general blockchain network, we use multidimensional hypercubes or variants thereof to construct the physical topology. A perfect hypercube is a closed, compact and convex figure whose one-dimensional skeleton is made up of a set of equal-length segments aligned with each dimension of the space in which they lie, with the opposite segments parallel to each other and the segments intersecting at a point orthogonal to each other. FIGS. 1-3 show examples of topologies constructed based on a 3-5 dimensional hypercube, where the crosses indicate that the corresponding nodes and links are unallocated or invalid in the network. Blue and purple represent the low-dimensional hypercube before and after movement, respectively, and green is the movement path.
For each node, an ID is assigned to uniquely identify the node. At this time, the hypercube is supported at a distance of 2iThe link is established between the node pairs to improve the query efficiency, that is, the logical distance between the node pairs with the IDs differing by only 1 bit is 1. Thus, in a structured P2P network, the hypercube topology may well match the upper layer protocols.
Furthermore, the invalid link will be actively repaired for a limited time. If the P2P network is unfortunately partitioned, the isolated node will first request data synchronization from its neighboring nodes and then resume work.
Fig. 1-3 evolve from 3-dimensions to 5-dimensions examples of complete or incomplete hypercube topologies. FIG. 1 is a complete 3-dimensional cube containing 8 nodes and 12 links. FIG. 2 is an incomplete 4-dimensional hypercube containing 15 nodes and 29 links. FIG. 3 is an incomplete 5-dimensional hypercube containing 32 nodes and 75 links.
As the network scale increases, the link redundancy is excessive due to the use of the hypercube-based physical topology, and the complexity of upper-layer algorithms such as routing algorithms increases. Thus, recursion is a good extension method.
With a large number of nodes, we have constructed a hierarchical recursive topology consisting of multiple domains. The nodes close together form a domain, and the domains form a hierarchical recursive relationship. As shown in FIG. 4, each domain is used by (i)1 i2i3…ir) Indicating that the ith left bit indicates the recursive dependency at the ith level.
The nodes in the same domain can adopt a hypercube-based topology and can also adopt any topology. In addition, a dedicated node is established within a domain for maintaining connectivity and communication with neighboring domains.
On the basis, three recursive methods for constructing a physical topology are designed: fully symmetric, semi-symmetric, and asymmetric. In a fully symmetric approach, each recursion takes a hypercube of the same dimension. In the semi-symmetric approach, the same layer of the recursion uses hypercubes of the same dimension, and hypercubes of different dimensions are used from layer to layer. In the asymmetric approach, a hypercube of different dimensions is used for each recursion. Fig. 5 shows the lowest boundary of the hierarchical recursive physical topology. Fig. 6-8 give examples of the three methods described above.
Fig. 5-8 illustrate examples of hierarchical recursive topologies. Fig. 5 is the lowest bound case. Fig. 6 is a fully symmetrical case. Fig. 7 is a semi-symmetrical case. FIG. 8 is an asymmetric case with 4, 8, 4 secondary domains using 4-dimensional hypercube, 3-dimensional cube, and 7-point full-link topologies, respectively.
The traditional hierarchical recursion method arranges a special node in the domain to be responsible for the communication with the adjacent domain, so that the topology after recursion cannot keep the advantage of strong regularity of the hypercube. Therefore, we propose to design an optimized hierarchical recursive method.
Disclosure of Invention
The invention aims to provide an optimized topology recursion method meeting the partition tolerance of a alliance chain, and aims to solve the technical problem.
The invention is realized in such a way that the optimized topology recursion method meeting the partition tolerance of the alliance chain comprises recursion and interconnection, wherein each recursion enables an original node to become a domain, and the domain number of the defined r-th layer is irThe new node number after recursion is added with one bit backwards on the basis of the original node number, and the corresponding nodes of each r-level domain are connected into a topological structure of r-1-level domains by using physical links to form interconnection among domains.
The further technical scheme of the invention is as follows: the recursion also comprises the following steps:
s11, calculating the partition tolerance probability of the hierarchical recursive topology by utilizing the partition tolerance probability of the general topology structure;
and S12, calculating the average minimum repair time of the hierarchical recursive topology by using the average minimum repair time of the general topology.
The further technical scheme of the invention is as follows: the partition tolerance probability is not only related to the adopted topological structure, but also related to the recursive path, and the obtained integral partition tolerance probability is as follows:
Figure BDA0003222786610000051
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure BDA0003222786610000057
tolerating probabilities for the topological partitions of the domains of layer r.
The further technical scheme of the invention is as follows: in step S12, the overall average minimum repair time is obtained according to the topology average minimum repair time in the recursive process
Figure BDA0003222786610000052
Figure BDA0003222786610000053
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure BDA0003222786610000054
the mean minimum repair time is the topology of the domain of the r-th layer.
The further technical scheme of the invention is as follows: and obtaining the influence of the recursive path on the tolerance of the whole partition according to the tolerance probability of the whole partition and the whole average minimum repair time, wherein the influence is greater than the topological structure of the domain.
The further technical scheme of the invention is as follows: the fully symmetric topology in the recursion process takes the same dimension for each recursion, for any (i)1,i2,i3,…,ir)，
Figure BDA0003222786610000055
Are all a fixed value, denoted dim, r-1The number of nodes of the level recursion is Nsymm,r＝2dim×rAt the number of links is satisfied
Figure BDA0003222786610000056
When the number of links is Lsymm,r＝2r×dim-1×r×dim。
The further technical scheme of the invention is as follows: the same dimension hypercube is used for the domains of the same layer of semi-symmetrical topology in the recursive process, and for any ir，
Figure BDA0003222786610000061
Are all a fixed value, and the number of nodes of the r-1 recursion level is
Figure BDA0003222786610000062
Number of links satisfies
Figure BDA0003222786610000063
When the number of links is
Figure BDA0003222786610000064
Another object of the present invention is to provide an optimized topology recursive system satisfying the partition tolerance of the federation chain, which includes a recursive module and an interconnection module, wherein the recursive module is configured to make an original node become a domain at each recursion, and the domain number of the r-th layer is defined as irAfter recursion, the new node number is added with one bit backwards on the basis of the original node number; the interconnection module is used for connecting the corresponding nodes of each r-level domain into a topological structure of the r-1-level domain by using physical links to form interconnection among domains.
The further technical scheme of the invention is as follows: the recursive module also comprises
A tolerance probability unit for calculating a partition tolerance probability of the hierarchical recursive topology using the partition tolerance probability of the general topology;
and the repair time unit is used for calculating the average minimum repair time of the hierarchical recursive topology by utilizing the average minimum repair time of the general topology.
The further technical scheme of the invention is as follows: the partition tolerance probability is not only related to the adopted topological structure, but also related to the recursive path, and the obtained integral partition tolerance probability is as follows:
Figure BDA0003222786610000065
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure BDA0003222786610000066
a topology partition tolerance probability for a domain of layer r;
the overall average minimum repair time obtained in the repair time unit according to the topological average minimum repair time in the recursion process is
Figure BDA0003222786610000071
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure BDA0003222786610000078
a topological average minimum repair time for a domain of layer r;
obtaining the influence of the recursive path on the tolerance of the whole partition according to the tolerance probability of the whole partition and the whole average minimum repair time, wherein the influence is greater than the topological structure of the domain;
the fully symmetric topology in the recursion process takes the same dimension for each recursion, for any (i)1,i2,i3,…,ir)，
Figure BDA0003222786610000072
Are all fixed values, denoted dim, the number of nodes for the r-1 recursion level is Nsymm,r＝2dim×rAt the number of links is satisfied
Figure BDA0003222786610000073
When the number of links is Lsymm,r＝2r×dim-1×r×dim；
The same dimension hypercube is used for the domains of the same layer of semi-symmetrical topology in the recursive process, and for any ir，
Figure BDA0003222786610000074
Are all a fixed value, and the number of nodes of the r-1 recursion level is
Figure BDA0003222786610000075
Number of links satisfies
Figure BDA0003222786610000076
When the number of links is
Figure BDA0003222786610000077
The invention has the beneficial effects that: an extensible physical topology with good partition tolerance is constructed, the physical topology is based on a multi-dimensional hypercube, and the problem of topological mismatch of the structured P2P network can be relieved.
The proposed hierarchical recursive topology method inherits the strong regularity characteristic of the hypercube, and meanwhile, the long-distance link in the general hypercube topology is replaced by the short-distance link, so that the method is more realizable.
Experiments show that the proposed physical topology has no influence on the performance of the upper layer protocol. Therefore, on the basis that the physical topological structure ensures good partition tolerance, the system can reach the CAP limit by combining upper-layer protocols with good consistency and availability, such as a PPoV consensus protocol.
Drawings
Fig. 1 is a schematic three-dimensional cube.
FIG. 2 is a schematic view of an incomplete four-dimensional hypercube.
FIG. 3 is a schematic view of an incomplete five-dimensional hypercube.
Fig. 4 is a schematic diagram of domain numbering in a recursive topology.
FIG. 5 is a diagram of a hierarchical recursive topology lowest boundary case.
FIG. 6 is a schematic diagram of a fully symmetric case of a hierarchical recursive topology.
FIG. 7 is a schematic diagram of a semi-symmetric case of a hierarchical recursive topology.
FIG. 8 is a schematic diagram of an asymmetric case in which the hierarchical recursive topology has 4, 8, and 4 secondary domains respectively, and adopts a 4-dimensional hypercube, a 3-dimensional cube, and a 7-point full-connection topology.
FIG. 9 is a schematic diagram of a two-step configuration of a fully symmetric two-dimensional hypercube topology provided by an embodiment of the present invention.
Fig. 10 is a diagram illustrating throughput of an N-16 time consensus protocol according to an embodiment of the present invention.
Fig. 11 is a diagram illustrating average throughput of the consensus protocol in the entire network according to an embodiment of the present invention.
Detailed Description
Blockchains have shown promise as an infrastructure for secure transactions in untrusted scenarios. However, bitcoin-derived blockchains and their variants are limited by the CAP dilemma, which is difficult to solve by methods that merely optimize consensus protocols. On the other hand, the P2P network of blockchains has efficiency and reliability issues without matching the proper physical topology.
Aiming at the problems, the invention provides an optimized topology recursion method meeting the partition tolerance of a alliance chain, provides an optimized hierarchical recursion topology, uses more medium-short links to balance the reliability requirement and the cost of a physical network, and can well match an upper layer protocol. Thus, a block chain constructed with this topology can reach the CAP limit by a suitable consensus protocol.
Hierarchical recursive physical topology
The hierarchical recursive topology is generated by a general hypercube topology in two steps, including recursion and interconnection. Each recursion causes an original node to become a domain. Define the field number of the r-th layer as irEqual to the smallest node number n thereinmin. After recursion, the new node number is added with one bit backwards based on the original node number, so irThe first r-1 bit of (a) represents the attribution of the domain on a level 1 to r-1. Suppose a top level domain i1The hypercube topology node in 0 is numbered
Figure BDA0003222786610000091
Figure BDA0003222786610000092
Then the r-1 th (r ≧ 2) recursion post-field irNode in is numbered as
Figure BDA0003222786610000093
Wherein&A splice is indicated. The corresponding nodes of each r-level domain are connected into the topology structure required by the r-1 level domain by using physical links, so that the interconnection between the domains is completed.
The following takes as an example the 1-fold fully symmetric recursion of the simplest 2-dimensional square, as shown in fig. 9. The 4 nodes are respectively numbered as
Figure BDA0003222786610000094
At this time, each node recurses to be a 2-dimensional square domain, and the total number of the 2-dimensional square domain and the 16 nodes are respectively numbered as
Figure BDA0003222786610000095
Figure BDA0003222786610000096
Figure BDA0003222786610000101
Below we connect these 4 fields. And connecting the 4 nodes in the domain with the associated 2 nodes with the same second digit in the domain. Specifically, node 00 is connected to 10 and 30, node 01 is connected to 11 and 31, node 02 is connected to 12 and 32, node 03 is connected to 13 and 33, and so on.
Theoretical analysis
Partition tolerance
First, partition tolerance probability of a hierarchical recursive topology is calculated by using partition tolerance probability of a general topologyAnd (4) rate. By using
Figure BDA0003222786610000102
Representing the topology partition tolerance probability in the recursive process. Field irThe partition tolerance probability of (2) is not only related to the topology used, but also to the recursive path taken. Thus, the overall partition tolerance probability is
Figure BDA0003222786610000103
The average minimum repair time for the hierarchical recursive topology is then calculated using the average minimum repair time for the general topology. By using
Figure BDA0003222786610000104
Represents the topological average minimum repair time in the recursion process, and the overall average minimum repair time is
Figure BDA0003222786610000105
As can be seen from equations (1) and (2), the influence of the recursive path on the tolerance of the overall partition is greater than the topology of the domain itself. Therefore, it is proposed to use a topology with high partition tolerance probability and low average minimum repair time in the recursive process.
Link overhead
Considering that the number of nodes in the asymmetric recursion method is difficult to determine, this section only analyzes the fully symmetric and the semi-symmetric recursion methods.
In a fully symmetric topology, we define the dimensions of the hypercube of each domain as
Figure BDA0003222786610000111
Since each recursion takes the same dimension, for any (i)1,i2,i3,…,ir)，
Figure BDA0003222786610000112
Are all oneA fixed value, denoted dim. It is apparent that the number of nodes for the r-1 recursion level is Nsymm,r＝2dim×rThe number of links satisfies
Figure BDA0003222786610000113
Thus, the number of links is
Lsymm,r＝2r×dim-1X r x dim. formula (4)
Table 1 gives the number of nodes and the number of links for 0,1 and 2 fully symmetric recursions of a 2-to 5-dimensional hypercube, respectively.
TABLE 1 number of nodes and number of links in a fully symmetric recursive physical topology
Figure BDA0003222786610000114
Figure BDA0003222786610000121
In a semi-symmetric topology, since the same layer of domains uses hypercubes of the same dimension, for any ir，
Figure BDA0003222786610000122
Are all a fixed value. Obviously, the number of nodes for the r-1 recursion is
Figure BDA0003222786610000123
Figure BDA0003222786610000124
Number of links satisfies
Figure BDA0003222786610000125
Thus, the number of links is
Figure BDA0003222786610000126
Table 2 gives the number of nodes and the number of links for 0,1 and 2 semi-symmetric recursions, respectively, whose recursion paths are 4-dimensional, 3-dimensional and 2-dimensional hypercubes in that order.
TABLE 2 number of nodes and number of links in semi-symmetric recursion
Figure BDA0003222786610000127
Figure BDA0003222786610000131
Table 3 compares the link overhead and partition tolerance under different physical topology construction methods. Assume that the 0 th, 1 st, and 2 nd recursions use 5000km, 3000km, and 420km links, respectively.
Table 3 compares link overhead and partition tolerance under different physical topology construction methods
Figure BDA0003222786610000132
Figure BDA0003222786610000141
Although each recursion does not reduce the total number of links, it actually uses more medium-short links, greatly reducing the average minimum repair time. The higher the hypercube dimension on the recursive path, the less repair time is required. On the other hand, the hypercube-based topology has more links than the general tree topology, but the partition tolerance is much better, and the requirement of the actual alliance chain is met. The project can freely select the recursive method according to the reliability and cost requirements of the project.
Analysis of experiments
We have deployed the proposed physical topology on 8 servers, each with two 8-core CPUs and 10Gbps network bandwidth. Next, we execute the PPoV protocol on a different topology. The PPoV protocol is a federation chain consensus protocol with strong consistency and high availability. As a non-branching BFT consensus protocol in the federation chain, any attempt by an attacker to change the PPoV consensus consistency will result in longer consensus times, even timeouts, so we use throughput as an indicator. Our experiments generated 60000 transactions per second on average, each transaction being 24 bytes in size. A block can store up to 10000 transactions and the block size is up to 235 MB.
Due to resource limitations, we do not run any ordinary nodes. Since we only evaluate the impact of the physical topology on the consensus protocol, we shut down the signature verification and transaction execution process to ensure that the super node has sufficient computational resources.
Fig. 10 shows a consensus protocol efficiency comparison of the hierarchical recursive topology and the star topology when the network size N is 16. The result shows that the one-time recursion topology of the two-dimensional hypercube can optimally support the upper-layer consensus protocol.
Through experimental observation, under the parameters, no matter how the number of the nodes changes, each super node can realize the 100% utilization rate of a single CPU. At this time, the throughput is only affected by the network transmission rate. Fig. 11 shows the average throughput for different sized networks. It can be seen that the performance of the consensus protocol based on the hypercube topology is more stable as the number of nodes increases compared to the star topology. This means that the proposed physical topology does not only not affect the performance of the upper layer protocol, but also has good scalability.
The technical scheme constructs an extensible physical topology with good partition tolerance, and the physical topology is based on the multidimensional hypercube and can relieve the problem of topology mismatching of the structured P2P network.
The proposed hierarchical recursive topology method inherits the strong regularity characteristic of the hypercube, and meanwhile, the long-distance link in the general hypercube topology is replaced by the short-distance link, so that the method is more realizable.
Experiments show that the proposed physical topology has no influence on the performance of the upper layer protocol. Therefore, on the basis that the physical topological structure ensures good partition tolerance, the system can reach the CAP limit by combining upper-layer protocols with good consistency and availability, such as a PPoV consensus protocol.
The invention constructs a novel physical topology recursion method, inherits the strong regularity advantage of the multidimensional hypercube, replaces a long-distance link with a short-distance link in use, and is better suitable for an application scene of a alliance link system.
The analysis method is provided, and by analyzing two indexes of the partition tolerance probability and the average minimum repair time of the hierarchical recursive topology, the provided topology is proved to need less repair time on the basis of ensuring high partition tolerance probability. The developer can use the topology of high partition tolerance probability and low average minimum repair time in the upper recursive path, thereby realizing the tuning of the whole system on the two partition tolerance indexes.
The PPoV consensus protocol is implemented on a hypercube-based physical topology. Experiments show that the proposed physical topology can optimally support the PPoV consensus protocol while satisfying partition tolerance. That is, by employing a transport protocol and a consensus protocol that satisfy strong consistency and high availability, the block chain constructed based on the proposed topology can reach the CAP limit without modifying the upper layer protocols.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. The optimized topology recursion method meeting the partition tolerance of the alliance chain is characterized by comprising recursion and interconnection, wherein each recursion enables an original node to become a domain, and the domain number of the r-th layer is defined asirThe new node number after recursion is added with one bit backwards on the basis of the original node number, and the corresponding nodes of each r-level domain are connected into a topological structure of r-1-level domains by using physical links to form interconnection among domains.
2. The optimized topology recursion method for meeting federation chain partition tolerance of claim 1, wherein the recursion further comprises the steps of:
s11, calculating the partition tolerance probability of the hierarchical recursive topology by utilizing the partition tolerance probability of the general topology structure;
and S12, calculating the average minimum repair time of the hierarchical recursive topology by using the average minimum repair time of the general topology.
3. The optimized topology recursion method for meeting federation chain partition tolerance of claim 2, wherein the partition tolerance probability is not only related to the adopted topology but also related to the recursion path, and the obtained overall partition tolerance probability is:
Figure FDA0003222786600000011
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure FDA0003222786600000014
tolerating probabilities for the topological partitions of the domains of layer r.
4. The method of claim 3, wherein the overall average minimum repair time obtained in step S12 is the minimum repair time obtained from the topology average minimum repair time in the recursion process
Figure FDA0003222786600000012
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure FDA0003222786600000013
the mean minimum repair time is the topology of the domain of the r-th layer.
5. The optimized topology recursion method for meeting federation chain partition tolerance of claim 4, wherein the influence of the recursion path on the whole partition tolerance obtained according to the whole partition tolerance probability and the whole average minimum repair time is larger than the topology structure of the domain itself.
6. The optimized topology recursion method for meeting federation chain partition tolerance of claim 5, wherein the fully symmetric topology in the recursion process each recurses with the same dimension for any (i)1,i2,i3,…,ir)，
Figure FDA0003222786600000021
Are all fixed values, denoted dim, the number of nodes for the r-1 recursion level is Nsymm,r＝2dim×rAt the number of links is satisfied
Figure FDA0003222786600000022
When the number of links is Lsymm,r＝2r×dim-1×r×dim。
7. The optimized topology recursion method for meeting federation chain partition tolerance of claim 5, wherein the same dimension hypercube is used for domains at the same layer of semi-symmetric topology in the recursion process, for any ir，
Figure FDA0003222786600000023
Are all a fixed value, and the number of nodes of the r-1 recursion level is
Figure FDA0003222786600000024
Number of links satisfies
Figure FDA0003222786600000025
When the number of links is
Figure FDA0003222786600000026
8. The optimized topology recursion system meeting the partition tolerance of the alliance chain is characterized by comprising a recursion module and an interconnection module, wherein the recursion module is used for enabling an original node to become a domain in each recursion, and the domain number of the r-th layer is defined as irAfter recursion, the new node number is added with one bit backwards on the basis of the original node number; the interconnection module is used for connecting the corresponding nodes of each r-level domain into a topological structure of the r-1-level domain by using physical links to form interconnection among domains.
9. The optimized topology recursion system for meeting federation chain partition tolerance of claim 8, further comprising in the recursion module
A tolerance probability unit for calculating a partition tolerance probability of the hierarchical recursive topology using the partition tolerance probability of the general topology;
and the repair time unit is used for calculating the average minimum repair time of the hierarchical recursive topology by utilizing the average minimum repair time of the general topology.
10. The optimized topological recursive system for meeting federation chain partition tolerance of claim 9, wherein the partition tolerance probability is not only related to the adopted topology but also related to the recursive path, and the overall partition tolerance probability is obtained as follows:
Figure FDA0003222786600000031
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure FDA0003222786600000035
a topology partition tolerance probability for a domain of layer r;
the overall average minimum repair time obtained in the repair time unit according to the topological average minimum repair time in the recursion process is
Figure FDA0003222786600000032
r is the total layer number of the recursive topology, irIs the domain number of the r-th layer,
Figure FDA0003222786600000033
a topological average minimum repair time for a domain of layer r;
obtaining the influence of the recursive path on the tolerance of the whole partition according to the tolerance probability of the whole partition and the whole average minimum repair time, wherein the influence is greater than the topological structure of the domain;
the fully symmetric topology in the recursion process takes the same dimension for each recursion, for any (i)1,i2,i3,…,ir)，
Figure FDA0003222786600000034
Are all fixed values, denoted dim, the number of nodes for the r-1 recursion level is Nsymm,r＝2dim×rAt the number of links is satisfied
Figure FDA0003222786600000041
When the number of links is Lsymm,r＝2r×dim-1×r×dim；
The same dimension hypercube is used for the domains of the same layer of semi-symmetrical topology in the recursive process, and for any ir，
Figure FDA0003222786600000042
Are all a fixed value, and the number of nodes of the r-1 recursion level is
Figure FDA0003222786600000043
Number of links satisfies
Figure FDA0003222786600000044
When the number of links is
Figure FDA0003222786600000045
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