CN103763171A - Construction method for interconnection network of massively parallel computing system - Google Patents
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Abstract
The invention discloses a construction method for an interconnection network of a massively parallel computing system. The OCT interconnection network is formed by 8*2k*2m nodes. Firstly, every eight nodes are connected to form one Octagon interconnection network, 2k*2m Octagon interconnection networks are obtained in total, and the nodes in each Octagon interconnection network are encoded through four-digit Johnson codes; secondly, the 2k*2m nodes which are the same in node code in each Octagon interconnection network are connected to form one Torus interconnection network, wherein each line of each Torus interconnection network has 2m nodes, each column of each Torus interconnection network has 2k nodes, and eight Torus interconnection networks are obtained in total; the nodes in each Torus interconnection network are encoded through (k+m)-digit Johnson codes, and namely the OCT interconnection network can be recorded as the OCT (k, m) interconnection network, wherein k and m are natural numbers and are parameters of the number of the nodes of the interconnection network. According to the construction method, expansion of the interconnection network is performed under the condition that node degree is kept unchanged; the OCT (k, m) interconnection network is a symmetrical and regular interconnection network, the Johnson coding method is adopted for node coding, codes of any adjacent nodes only have a one-digit difference, and therefore the routing algorithm is simple and efficient.
Description
Technical field
The invention belongs to parallel computing field, relate in particular to a kind of massive parallel processing interference networks building method.
Background technology
Along with the development of hardware technology, the particularly development of very lagre scale integrated circuit (VLSIC) technique, makes the extensive multicomputer system that comprises thousands of processors become possibility.For example the Milky Way-1A has the super computer system of 7168 computing nodes, Fujitsu to surpass 80,000 computing nodes.At several years of future, new application and algorithm impelled the quantity of single-chip processor core to reach the extensive super computer system number of nodes of setting up the eighties in 20th century.We are moving towards E level and are calculating (Exascale Computing) epoch, estimate 2018, and super computer system will reach 1exaFLOPS (1018FLOPS), enter E level and calculate (Exascale Computing) epoch.
Enter E level and calculate the epoch, it is millions of to up to ten million processor cores that multicomputer system scale will reach, interference networks have important impact to the performance of so large-scale multicomputer system, will determine calculating and the memory property of following large-scale parallel application.In order to improve the communication efficiency of parallel computation, people always simple at research structure, node degree is little, network diameter is little, routing policy is simple and good extendible interference networks.
The topological structure of Torus interference networks have normality, symmetry, fault-tolerance, short diameter, can embeddability etc. special nature, therefore being deeply subject to researcher and practitioners' welcome, is a kind of the most important and the most attractive parallel computer interconnection network topological structure.Yet, millions of in the interference networks of up to ten million processor cores, the diameter of tradition Torus interference networks becomes very large, be not suitable for the interconnection of following parallel system, meanwhile, because many concurrent programs will be communicated by letter frequently (being local communication) in a group node, therefore, the multiple hierarchical interconnection network (HINs, Hierarchical Interconnection Networks) based on Torus has been proposed.In these hierarchical interconnection networks, by computing node, form lower level interference networks and carry out local communication, by bunch higher level interference networks that form, be used for telecommunication.The diameter of these hierarchical interconnection networks is all long-pending by every layer network diameter, and relative diameter is still larger.Octagon interference networks are by people such as F.Karim for on-chip interconnection network, and the topological structure of these interference networks has the character such as normality, symmetry, short diameter.
The 2 dimension Torus interference networks (referred to as T (k, m)) of 2k * 2m are a kind of interference networks with following character: 1) 2k * 2m node and 8k * m bar direct link, consist of; 2) use the abscissa of 2m Johnson's code identification node of m position, ordinate with 2k Johnson's code identification node of k position, using the ordinate of node as high-order abscissa as low level, be combined into a nodes encoding, like this, any one node can identify by the binary coding of k+m position; 3) rule of nodes encoding is: in and if only if T (k, m), the coding of two nodes has and only have one when different, and two nodes are adjacent, between these two nodes, have a direct link.
Fig. 1 has provided topological structure and the nodes encoding (k=2, m=3) of T (k, m) interference networks.T (k, m) interference networks have following good nature: 1. the nodes encoding of each row and column is all binary unit Distance Cyclic Codes; 2. any one node have and only have four adjacent nodes (when nodes encoding figure place is more than or equal to 5,2 dimension Gray codes does not meet this characteristic), self-assembling formation Torus structure; If 3. k or m increase by one, corresponding node number only increases 4m or 4k (nodes that 2 dimension Gray codes form are 2k * 2m, if k or m increase by one, corresponding node number increases to 2 times of original interstitial content); 4. the number of any two nodes encoding XOR gained " 1 " is to two internodal minimum ranges; 5. there is Hypercube routing mechanism simple in structure.
Octagon interference networks are a kind of interference networks with following character: 1) 8 nodes and 12 direct link, consist of; 2) with the coordinate of Johnson's code identification node of 4; 3) each that two nodes encodings have and only have a difference or two nodes encoding XOR results in interference networks is during for " 1 ", and two nodes are adjacent, between these two nodes, have a direct link.
Fig. 2 is topological structure and the nodes encoding of Octagon interference networks.As shown in Figure 2, Octagon interference networks have following good character: 1) in network, the connection degree of arbitrary node is 3, and the diameter of whole network is 2, and network has the good characteristics such as normality, symmetry, short diameter, low connection degree; 2) in network, between any two nodes, have 3 without the link of handing over, if two nodes are directly connected, the length of these 3 links is respectively Isosorbide-5-Nitrae, and 4, otherwise be 2,3,3, therefore, there is good fault-tolerance and concurrency; 3) when any two nodes encoding XOR results are 1 " 1 " or 4 " 1 ", two nodes are adjacent, and when any two nodes encoding XOR results are 2 " 1 " or 3 " 1 ", the distance of two nodes is 2.Its shortcoming is that network does not possess extensibility.
Summary of the invention
The present invention proposes a kind of massive parallel processing interference networks building method, the interference networks of structure, in conjunction with the advantage of Torus interference networks and Octagon interference networks, have short diameter, normality, symmetry and good autgmentability.In interference networks building method, adopt Johnson's coding method to encode to interconnect network nodes, make Design of Routing Algorithm simple, designed respectively clean culture, broadcast algorithm based on hybrid coding.
The embodiment of the present invention is achieved in that a kind of massive parallel processing interference networks building method, and the method comprises:
First, every 8 nodes are connected into Octagon interference networks, obtain altogether 2k * 2m Octagon interference networks, each Octagon network is called a slice;
Secondly, every a slice is adopted to identical nodes encoding method, every middle node all uses 4 johnoson codes to encode;
Again, then 2k * 2m that in each sheet, nodes encoding is identical node is connected into the Torus interference networks of every row 2m node and every row 2k node, can be designated as T (k, m) interference networks, obtain altogether 8 T (k, m) interference networks;
Then, each T (k, m) interference networks is adopted to identical nodes encoding method, in each T (k, m) interference networks, node is encoded with k+m position johnoson code;
The interference networks of structure are called OCT interference networks like this, can be designated as OCT (k, m) interference networks, k wherein, and m is that natural number is the parameter of interconnect network nodes quantity.
Further, OCT (k, m) interference networks adopt following nodes encoding method, and each nodes encoding is by two parts (A
t, A
o) composition, wherein A
o(4 johnoson codes) is each Octagon nodes coding, A
t(k+m position johnoson code) is the coding of each Octagon sheet, is also the nodes encoding in each T (k, m) network.
Further, OCT (k, m) the interconnect network nodes scale of structure can be by expansion T (k, m) interference networks and expanding, as long as the figure place of encoding increases by one, m or k increase 1, at T (k, m) in interference networks, just increase by two row or two row (corresponding node number just increases 4k or 4m is individual), on OCT (k, m) network foundation, increase by 8 * 4k or 8 * 4m node, form OCT (k, m+1) or OCT (k+1, m) interference networks; Originally in OCT (k, m) network, each Octagon interconnect network nodes annexation does not change, and the connection degree of node does not change.In T (k, m+1) or T (k+1, m) interference networks, except the node being connected with newly-increased node, other node and annexation are without any change.
The present invention by the short diameter combined structure of the extensibility of Torus interference networks and Octagon interference networks a kind of simple extendible OCT (k, m) interference networks.These interference networks are that a kind of node degree is 7 the extendible interference networks of regular symmetry, can keep the constant expansion of carrying out network size of node degree, and network node coding adopts Johnson's coding method, makes routing algorithm simply efficient.Analyze and experimental result shows, OCT (k, m) interference networks have good communication performance, fault-tolerant ability, extensibility, are a kind of interference networks of applicable large-scale parallel calculating.
Accompanying drawing explanation
Fig. 1 is T (k, m) interference networks and the nodes encoding (k=2, m=3) that the embodiment of the present invention provides;
Fig. 2 is Octagon interference networks and the nodes encoding that the embodiment of the present invention provides;
Fig. 3 is the massive parallel processing interference networks building method flow chart that the embodiment of the present invention provides;
Fig. 4 is OCT (k, the m) interference networks (k=2, m=2) that the embodiment of the present invention provides.
Embodiment
In order to make object of the present invention, technological invention and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.
Fig. 3 has proposed a kind of massively parallel computer system interference networks building method that the invention process case provides, and the method comprises:
In step S101, first, every 8 nodes connect into Octagon interference networks according to above-mentioned Octagon interference networks describing mode, obtain altogether 2k * 2m Octagon interference networks, and each Octagon interference networks is called a slice;
In step S102,2k * 2m sheet connected into node in Torus network: 2k * 2m sheet as follows encodes with 4 johnoson codes, by the node that in each sheet, nodes encoding is identical according to above-mentioned T (k, m) mode that interference networks are described connects into T (k, m) interference networks;
In step S103, the nodes encoding of OCT (k, m) interference networks: OCT (k, m) adopts following coding method, each nodes encoding is by two parts (A
t, A
o) composition, wherein A
o(4 johnoson codes) is the nodes encoding in each Octagon interference networks, A
t(k+m position johnoson code) is the coding of each Octagon sheet, is also the nodes encoding in each T (k, m) network;
In step S104, connect into OCT (k, m) interconnection network topological structure.
Fig. 4 is the OCT (k that the embodiment of the present invention provides, m) interference networks (k=2, m=2), in figure, solid line represents Octagon interference networks link, dotted line represents T (k, m) interference networks link, small circle represents network node, has direct link to connect between the end points that label is identical up and down.OCT (k, m) can expanding by expansion T (k, m) network of interconnect network nodes scale, as long as the figure place of encoding increases by one, be that m or k increase 1, in T (k, m) network, just increase by two row or two row (corresponding node number just increases 4k or 4m is individual), at OCT (k, m) on network foundation, increase by a 8 * 4k or 8 * 4m node, form OCT (k, m+1) or OCT (k+1, m) interference networks.Originally in OCT (k, m) network, each Octagon sheet network annexation does not change, and the connection degree of node does not change.In T (k, m+1) or T (k+1, m) interference networks, except the node being connected with newly-increased node, other node and annexation are without any change.
The character of OCT (k, the m) interference networks of structure:
Character 1.OCT (k, m) interference networks are regular interference networks, and the connection degree of arbitrary node is 7.
Because each Octagon sheet is that regular interference networks and node connectivity are 3, according to OCT (k, m) construction process of network is easily known, Octagon sheet is regarded as to a node, this network be exactly T (k, m) interference networks and node connectivity be 4, so, OCT (k, m) network is regular network, and node connectivity is 3+4=7.
In character 2.OCT (k, m) interference networks any two internodal apart from maximum (network diameter), be k+m+2.
Due to T (k, m) diameter of interference networks is the diameter sum of diameter and 2k the node cycle of 2m node cycle, be m+k, according to OCT (k, m) construction process of network is easily known, T (k, m) interference networks are regarded as to a node, this network is exactly Octagon interference networks, and its diameter is 2.So OCT (k, m) network diameter is Torus diameter and Octagon diameter sum, i.e. m+k+2.
Character 3.OCT (k, m) interference networks are symmetrical networks.
According to the construction process of OCT (k, m) interference networks, easily know, in this network, any node identification is that initial point is all isomorphic to itself, and it is all the same from any node, observing network.Simplified the realization of routing algorithm, i.e. routing algorithm and location-unaware system.
The number of links of character 4.OCT (k, m) interference networks is 112 * k * m.
The number of links of OCT (k, m) interference networks is Torus number of links 2 * 2k * 2m sum of 2k * 2m Octagon number of links 12 and 8 2k * 2m, 2k * 2m * 12+8 * 2 * 2k * 2m=112 * k * m.
The partial width such as grade of character 5.OCT (k, m) interference networks is 24 * k * m.
The partial widths such as network are when network is divided into two equal networks, the minimal communications number of links that must leave out.OCT (k, m) interference networks decile is that the partial widths such as Octagon are 6 by 2k * 2m Octagon interference networks decile, so wait partial width, is 6 * 2k * 2m=24 * k * m.
In order to further illustrate OCT (k, m) good characteristic of interference networks, table 1 has provided OCT (k, m) interference networks, (2k, 2m, 3) contrast of-OMMH (also referred to as Torus Embedded Hypercube) interference networks and 2 dimension Torus interference networks, wherein N=8 * 2k * 2m=4k * 8m.
The performance characteristic of three kinds of static networks of table 1
In interference networks, adopt Johnson's coding method, make OCT (k, m) interference networks there is following character: to any two node A (Am+k+3 in OCT (k, m) interference networks ... Am+k, Am+k-1 ... AmAm-1 ... A1A0), B (Bm+k+3 ... Bm+k, Bm+k-1 ... BmBm-1 ... B1B0), Ai, Bi, Aj, Bj ∈ { 0,1}, i ∈ 4 ..., m+k+3}, j ∈ { 0,1,2,3}, any two node A, the distance between B is
Due to each nodes encoding in Octagon sheet and T (k, m) in, each nodes encoding is that Johnson encodes, by OCT (k, m) interference networks construction process is known, distance between any two nodes is that the distance of two nodes in T (k, m) and two nodes are in Octagon middle distance sum.Range coding in Octagon sheet between two nodes have and only have a difference or two nodes encoding XOR results each be adjacent node during for " 1 ", the distance between any two nodes is that the number of coordination or the number of two nodes encoding identical bits do not add 1 to two nodes encodings; Interior two nodes encodings of T (k, m) have and only have one to be adjacent nodes when different, and the distance between any two nodes is the not numbers of coordination of two nodes encodings.This character has facilitated the design of routing algorithm.
Unicast Routing Algorithm and the performance evaluation of OCT (k, m) interference networks:
1) Unicast Routing Algorithm
Suppose A (A
m+k+3... A
m+k, A
m+k-1... A
ma
m-1... A
1a
0) node is to B (B
m+k+3... B
m+k, B
m+k-1... B
mb
m-1... B
1b
0) node transmission data, the Hamming distance of A node and B node (D)
wherein "
" representing that A and B carry out step-by-step XOR, " Hamming " function represents the number sum operation of " 1 " after A and B XOR.Known by the coding method of Octagon and T (k, m) node and the construction process of OCT (k, m) interference networks, the shortest path routing procedure of OCT (k, m) is as follows: routing procedure is as follows:
If 1. A and B are in same Octagon sheet, so from 2.2 joints, the T (k, m) of A node and B node coding is identical,
As long as carry out A
o=A
3... A
0, B
o=B
3... B
0octagon sheet in route, the distance of source node A and destination node B is 1 or 2.If
or 4, node 4 directly sends data to Node B so; Otherwise, calculate A
othree adjacent nodes be A
o1, A
o2, A
o3with B
odistance, by node A
odata to send to destination node distance be 1 adjacent node, and then send to destination node B from adjacent node.
If 2. A and B are in same T (k, m), so from 2.2 joints, the nodes encoding of the Octagon of A node and B node is identical,
as long as carry out A
t=A
m+k+3... A
ma
m-1... A
5a
4node is to B
t=B
m+k+3... B
mb
m-1... B
5b
4the route of T (k, m) network.T (k, m) network left and right adjacent node coding only has abscissa to differ one, and neighbouring node only has ordinate to differ one, node A
tleft adjacent node be encoded to
right adjacent node is encoded to
Upper adjacent node is encoded to
Lower adjacent node is encoded to
A so
tadjacent node and B
tdistance be
。H
min=min{H
l, H
r, H
u, H
d, bag is sent to H
mincorresponding adjacent node and by A
tbe revised as the coding of this adjacent node, then calculate
value, if H ≡ 0, so A
tthe node of sign is destination node, otherwise repeats process above.
If 3. A and B are neither in same Octagon network, also not in same T (k, m) network, be two nodes arbitrarily, so first by mode 1., packet is routed in same Octagon network to node A ' (A
m+k-1... A
ma
m-1... B
3b
2b
1b
0), A ' is with B in same T (k, m), and the mode of then pressing is 2. routed to packet destination node B in T (k, m).
2) algorithm performance analysis
OCT (k, m) routing algorithm major advantage is T (k, m) network using Johnson coding method, make T (k, m) in network, the number of any two nodes encoding XOR gained " 1 " is two internodal minimum ranges, and this coding has implied overall routing iinformation and the relation between adjacent node.While making target node data, as long as the route data that the coding of storage present node and destination node just can be correct.Octagon network also adopts Johnson's coding method, when any two nodes encoding XOR results are 1 " 1 " or 4 " 1 ", two nodes are adjacent, when any two nodes encoding XOR results are 2 " 1 " or 3 " 1 ", the distance of two nodes is 2, and network routing variable is obtained simply.
According to OCT (k, m) Unicast Routing Algorithm, data are propagated under worst case in Octagon needs 2 to take turns traffic operation, at same T (k, m) in, propagate under worst case and need k+m wheel traffic operation, therefore, under worst case, altogether need k+m+2 wheel traffic operation.Algorithm can send to destination node by data from source node along shorter path, and the communication efficiency of algorithm is just higher.The forwarding data each time of above Unicast Routing Algorithm is undertaken by shortest path, so under worst case, the path of route can not surpass the diameter k+m+2 of network, the communication efficiency of algorithm is 1/ (k+m+2).
Broadcast algorithm and the performance evaluation of OCT (k, m) interference networks:
1) broadcast algorithm
Suppose to send data to other all nodes by node A.First, the data of node A are broadcast in the Octagon at place sheet to all nodes of place sheet, the node of then receiving data message spreads data acquisition to all nodes within the T (k, m) at place separately with recurrence method for doubling.
2) algorithm performance analysis
Carry out by this way broadcast, node A needs 2 to take turns traffic operation to all nodes in the Octagon sheet of place data broadcast, and then data are broadcasted within T (k, m) needs m+k wheel traffic operation.So whole broadcast needs k+m+2 wheel traffic operation, the communication efficiency of algorithm is 1/ (k+m+2).
The present invention combines the extensibility of the short diameter of Octagon interference networks and Torus interference networks, structure OCT (k, m) interference networks: first, every 8 nodes connect into an Octagon network according to the mode of definition 6, obtain altogether 2k * 2m Octagon network, each Octagon network is called a slice; 2k * 2m sheet connected into Torus network: 2k * 2m sheet as follows and with 4 johnoson codes, encode, the node that in each sheet, nodes encoding is identical is connected into T (k, m) interference networks according to the mode of definition 5; The coding of OCT (k, m): OCT (k, m) adopts following coding method, and each nodes encoding is by two parts (A
t, A
o) composition, wherein A
o(4 johnoson codes) is the nodes encoding of each Octagon network, A
t(k+m position johnoson code) is the coding of each Octagon sheet, is also the nodes encoding in each T (k, m) network.Clean culture, broadcast algorithm based on OCT (k, m) interconnection network architecture have been designed again
The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.
Claims (5)
1. a massive parallel processing interference networks building method, is characterized in that, the interference networks of structure are called Octagon and connect interference networks, and OCT interference networks are comprised of 8 * 2k * 2m node, and this building method comprises:
First, every 8 nodes are connected into Octagon interference networks, obtain altogether 2k * 2m Octagon interference networks, in each Octagon interference networks, node is encoded with 4 johnoson codes;
Secondly, identical 2k * 2m node of again each Octagon interconnect network nodes being encoded connects into the Torus interference networks of every row 2m node and every row 2k node, can be designated as T (k, m) interference networks, obtain altogether 8 T (k, m) interference networks, in each T (k, m) interference networks, node is encoded with k+m position johnoson code, these OCT interference networks can be designated as OCT (k, m) interference networks, k wherein, m is that natural number is the parameter of interconnect network nodes quantity.
2. massive parallel processing interference networks building method as claimed in claim 1, it is characterized in that: every 8 nodes connect into an Octagon network, obtain altogether 2k * 2m Octagon interference networks, each Octagon interconnect network nodes coding adopts identical Johnson's coding.
3. massive parallel processing interference networks building method as claimed in claim 1, it is characterized in that: the identical node of nodes encoding in 2k * 2m Octagon interference networks is connected into T (k, m) interference networks, obtain altogether 8 T (k, m) interference networks, each T (k, m) interconnect network nodes coding adopts identical Johnson's coding.
4. massive parallel processing interference networks building method as claimed in claim 1, is characterized in that: each nodes encoding of OCT (k, m) interference networks is by two parts (A
t, A
o) composition, wherein A
o(4 johnoson codes) is each Octagon interference networks interior nodes coding, A
t(k+m position johnoson code) is the coding of each Octagon interference networks, is also each T (k, m) interference networks interior nodes coding.
5. massive parallel processing interference networks building method as claimed in claim 1, it is characterized in that: connect into OCT (k, m) interconnection network topological structure, OCT (k, m) interconnect network nodes scale can be by expansion T (k, m) network and expanding, as long as the figure place of encoding increases by one, m or k increase 1, at T (k, m) in network, just increase by two row or two row, corresponding node number just increases 4k or 4m is individual, at OCT (k, m) on network foundation, increase by a 8 * 4k or 8 * 4m node, form OCT (k, m+1) or OCT (k+1, m) interference networks; At OCT (k, m+1) or OCT (k+1, m) in interference networks, original each Octagon interconnect network nodes annexation does not change, each T (k, m+1) or T (k+1, m), in interference networks, except the node being connected with newly-increased node, the annexation of other node is without any change.
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| CN112039786A (en) * | 2019-06-04 | 2020-12-04 | 清华大学 | Torus network-based broadcasting method |
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