US20020056023A1

US20020056023A1 - Mesh network with method and apparatus for interleaved binary exchange

Info

Publication number: US20020056023A1
Application number: US09/879,030
Authority: US
Inventors: Brent Baxter; Stuart Hawkinson; Satyanarayan Gupta
Original assignee: Individual
Current assignee: Individual
Priority date: 1994-05-11
Filing date: 2001-06-12
Publication date: 2002-05-09
Anticipated expiration: 2014-05-11
Also published as: US20030033500A1; US6356992B1; US6948048B2; US6173387B1; US6460128B1

Abstract

A method for transferring information within a mesh network that has an array of nodes defined by four quadrants. The method includes the initial step of transferring information from a set of nodes in one quadrant to a set of nodes located in an adjacent quadrant. The transfer of information simultaneously occurs in both a vertical and horizontal direction within the array. Information is then transferred between nodes within the same quadrant and subquadrants.

Description

BACKGROUND OF THE INVENTION

1. FIELD OF THE INVENTION

The present invention relates to a method of transmitting information within a network.

2. DESCRIPTION OF RELATED ART

To increase the size, speed and scalability of computer systems, computers may be linked together within a network to process information in parallel. Such systems are commonly referred to as parallel processing networks. Parallel processing networks typically have a plurality of microprocessor based components coupled together by busses and associated hardware. Each processor based component functions as a node which can transmit information to other nodes within the network.

The nodes can be arranged as a plurality of interconnected cubes, commonly referred to as a hypercube. Hypercubes require a large number of data links, which increase the size of the system.

The nodes can also be arranged in a two-dimensional array, commonly referred to as a network mesh. FIGS. 1 a-d show a method of transferring information within a mesh that is commonly referred to as the Direct Exchange Algorithm. In the Direct Exchange method, information is transferred from one node to another node within the same row of the mesh. The process is repeated until the information of one node is transferred to each of the nodes within the row. For example, as shown in FIG. 1a, in the first step, the information from node 1 is transferred to node 3, node 2 transfers information to node 1, node 3 transfers information to node 4 and the information of node 4 is transferred to node 2. The process of transferring information between nodes is repeated in accordance with the patterns shown in FIGS. 1b, 1 c and 1 d. The information can then be transferred between rows and the process is repeated. Although the Direct Exchange Algorithm has a relatively high transmission rate, the number of messages and the start-up time to send the messages from each node rapidly increases with the size of the mesh.

FIGS. 2 a-f and 3 a-d show other methods of transferring information within a mesh, commonly referred to as the Binary Exchange Algorithm and the Quadrant Exchange Algorithm, respectively. Both of theses methods utilize a store and forward approach, wherein each node can both receive and forward information transmitted by another node. As shown in FIG. 2a, in the first step of the Binary Exchange method, the nodes in one half of the mesh transmit information to nodes in the other half of the mesh in a horizontal direction. The process is repeated by sending the information from one half of the mesh to the other half of the mesh in a vertical direction, as shown in FIG. 2b. As shown in FIGS. 2c-f, the information is then transferred within quadrants and subquadrants of the mesh.

In the Quadrant Exchange method, information is transferred within rectangular groups of nodes as shown in FIGS. 3 a and 3 b. As shown in FIG. 3C, the information is then transferred within separate quadrants of the mesh. Although both the Binary and Quadrant Exchange methods can be used in large mesh networks, the start-up time and transmission rate are relatively slow. Additionally, the Quadrant method is susceptible to node contention. It would be desirable to provide an algorithm for a mesh network, that was not susceptible to node contention and had a relatively high complete information exchange rate.

SUMMARY OF THE INVENTION

The present invention is a method for transferring information within a mesh network that has an array of nodes defined by four quadrants. The method includes the initial steps of transferring information from a set of nodes in one quadrant to a set of nodes located in an adjacent quadrant. The transfer of information simultaneously occurs in both a vertical and horizontal direction within the array. Information is then transferred between nodes within the same quadrant and subquadrants.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and advantages of the present invention will become more readily apparent to those ordinarily skilled in the art after reviewing the following detailed description and accompanying drawings, wherein: [0010]
FIGS. 1[0011] a-d are schematics showing information being transferred between nodes arranged in a row in accordance with a method in the prior art;
FIGS. 2[0012] a-f are schematics showing information being transferred between nodes arranged in a two-dimensional array in accordance with a method in the prior art;
FIGS. 3[0013] a-c are schematics showing information being transferred between nodes arranged in a two-dimensional array in accordance with a method in the prior art;
FIG. 4 is a schematic of a mesh network having an array of nodes that can transfer information; [0014]
FIG. 5 is a schematic showing a node exchanging data with four neighboring nodes; [0015]
FIG. 6[0016] a is a schematic of a four by four array of nodes showing a first step of the present method;
FIG. 6[0017] b is a schematic similar to FIG. 3a showing a second step of the method;
FIG. 6[0018] c is a schematic similar to FIG. 3a showing a third step of the method;
FIG. 6[0019] d is a schematic similar to FIG. 3a showing a fourth step of the method;
FIGS. 7[0020] a-h are schematics showing the method in an eight by eight array of nodes.

DETAILED DESCRIPTION OF THE INVENTION

Referring to the drawings more particularly by reference numbers, FIG. 4 shows a mesh network which has a plurality of nodes labeled [0021] 1-16. Each node is capable of transmitting and receiving information from another node. As shown in FIG. 5, in the preferred embodiment, each node is a functional computer on a card 20 that can be plugged into the network. The card 20 contains a microprocessor, memory and other associated hardware required to process information. The computer cards 20 contain an interface 22 that couples the components of the card to a number of busses 24. The busses are connected to other cards (nodes) and provide a medium to transfer information between the cards. The cards typically process information in parallel, wherein the mesh is a parallel processing network.
Each card generates an address for the destination node, along with the information that is to be transmitted to the other node. The address and information are then sent to a node in accordance with the algorithm of the present invention. The transmitting node may also receive information from the destination node. The receiving node stores both the address and the information sent by the transmitting node. If the receiving node has a matching address (destination node) then the node processes the information. If the address of the receiving card does not match the destination address, then the card forwards the address and information to the next node, again in accordance with the algorithm of the present invention. In the preferred embodiment, each node transfers information to a receiving node through a dedicated bus, to avoid bus contention within the system. [0022]
The network has a [0023] controller 26 which controls the transfer of information between the nodes. The controller 26 controls which node will receive the information. For example, in accordance with the algorithm of the present invention, the card 20 at node 1 may initially exchange information with node 3, then exchange information with node 9 and finally exchange information with nodes 2 and 5. In the first step, the controller 26 enables the interface of the cards at nodes 1 and 3 to exchange information. The controller 26 may initially allow information generated by node 1 to be transmitted to node 3, and the information generated by node 3 to be subsequently transmitted to node 1. The controller can control the bus and corresponding node that is to receive the information by providing a command to the card or driving active one or more control signals that enable each bus.
If the information sent by [0024] node 3 is to be processed by node 1, the card at node 1 processes the information. If the information transmitted by node 3 is not to be processed by node 1, node 1 retransmits the information generated by node 3 to node 9 in accordance with the second step of the algorithm. Node 1 also receives information from node 9, and the process is repeated with nodes 2 and 5.
FIGS. 6[0025] a-d show the steps of transferring information in accordance with an algorithm of the present claimed invention. The method allows the nodes located along a diagonal line of the array to transfer information from one half of the mesh to another half of the mesh. The information is transferred in both a horizontal and vertical direction within the array. The process of vertically and horizontally transferring information from nodes along a diagonal line may be repeated a predetermined number of times. The information is then transferred between nodes within the same quadrant and subquadrants of the nodal array.
FIGS. 6[0026] a-d show the steps of transferring information within a 4 by 4 array of nodes in accordance with an algorithm of the present invention. The lines indicate the path of information transferred between the corresponding nodes. The first step is shown in FIG. 6a, wherein nodes 1, 6, 9 and 14 transfer information with nodes 3, 8, 11 and 16, respectively, in a horizontal direction of the array, and nodes 2, 4, 5 and 7 transfer information with nodes 10, 12, 13 and 15, in a vertical direction of the array. The transfer of information is interleaved between the nodes, so that none of the nodes both receive and transmit information from more than one node. The interleaving pattern prevents node contention.
The second step of the algorithm is shown in FIG. 6[0027] b, wherein the nodes that transferred information horizontally in the first step, transfer information vertically, and the nodes that transferred information vertically transfer horizontally. Accordingly, in the second step, nodes 1, 3, 6 and 8 transfer information with nodes 9, 11, 14, and 16, respectively in the vertical direction, and nodes 2, 5, 10 and 13 transfer information with nodes 4, 7, 12 and 15, respectively in the horizontal direction.
FIGS. 6[0028] c and 6 d, show steps three and four of the present algorithm, respectively, wherein the nodes transfer information within the same quadrant of the mesh. In step three (FIG. 6c) the nodes all transfer information horizontally with an adjacent node in the same quadrant. In step four (FIG. 6d) the nodes all transfer information vertically with an adjacent node in the same quadrant. The steps shown in FIGS. 6a-d are then repeated.
FIGS. 7[0029] a-h show the algorithm of the present invention being performed within an 8 by 8 array of nodes. Like the process of transferring information in the 4 by 4 array, the nodes in one quadrant of the mesh transfer information to nodes in an adjacent quadrant of the array in both the vertical and horizontal directions. The process of transferring information between quadrants of nodes is repeated three more times as shown in FIGS. 7b-d. The nodes then transfer information with nodes of the same quadrant and subquadrant as shown in FIGS, 7 e-h. Although 4 by 4 and 8 by 8 nodal arrays are shown and described, it is to be understood that the algorithm of the present claimed invention can be used in other two-dimensional nodal arrays.
The complete time to exchange information between nodes can be defined by the following three parameters. [0030]
Latency (α): the latency is defined as the start up time required to transfer a message and includes fixed overheads associated with each message. α typically has the units of seconds. [0031]
Bandwidth (B): the bandwidth is the rate at which information can be transmitted along the communication links between the nodes. B typically has the units of bytes/sec. [0032]
Rearrangement rate (δ): the rearrangement rate is the rate at which information can be rearranged at the node for further transmission. δ typically has the units of bytes/sec. [0033]
The complete exchange of information using the algorithm of the present invention is defined by the following equation. [0034] $2^{K} α + 2^{(K - 1)} \frac{mn}{B} + K \frac{mn}{δ}$
wherein; [0035]
m=the bytes of data transferred. [0036]
n=the number of nodes in the network. [0037]
K=log[0038] ₂{square root}{square root over (n)} {or k such that n=2^k·2^k}.

The first term of the equation relates to the latency of the system, the second term corresponds to the system bandwidth, and the last term defines the rearrangement rate. Table I shows the different terms of the equation for the method of the present invention (entitled Interleaved Binary Exchange) with similar terms for information exchange equations relating to the Direct Exchange algorithm, Binary Exchange algorithm and the Quadrant Exchange algorithm.

TABLE I


Start-Up Time	Transmission Time	Rearrangement Time


Binary Exchange	Absolute	2(2^k− 1)α	$(2^{k} - 1) \frac{nm}{β}$	$k \frac{nm}{δ}$

	Relative	˜2	˜2	1

Direct Exchange	Absolute		2^(3k−2)α	$\frac{2^{k}}{4} \cdot \frac{nm}{β}$	None

	Relative
	2^2k/4	1/2	0

Quadrant Exchange	Absolute	3(2^k− 1)α	$\frac{3}{4} (2^{k} - 1) \frac{nm}{β}$	$k \frac{mn}{δ}$

	Relative	˜3	˜3/2	1

Interleaved Binary	Absolute		2^k α	$\frac{1}{2} (2^{k}) \frac{mn}{β}$	$k \frac{mn}{δ}$

Exchange	Relative		1	1	1

As shown in Table I, the algorithm of the present invention provides improved performance over both the Binary Exchange and Quadrant Exchange algorithms by reducing the start-up and transmission times. The Direct Exchange algorithm provides better performance for both the transmission time and the rearrangement time, but the start-up time and number of messages increases drastically for larger mesh networks. The present invention thus provides an algorithm that improves the performance of scalable parallel processing networks over algorithms in the prior art. [0040]
While certain exemplary embodiments have been described and shown in the accompanying drawings, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention, and that this invention not be limited to the specific constructions and arrangements shown and described, since various other modifications may occur to those ordinarily skilled in the art. [0041]

Claims

What is claimed is:

1. A method for transmitting information within a network that has an array of nodes arranged in four quadrants, comprising the steps of:

a) transferring information from nodes in each quadrant to nodes in an adjacent quadrant in both a horizontal direction and a vertical direction within the array; and,

b) transferring information between nodes within a same quadrant.

2. The method as recited in claim 1, wherein said step (a) is repeated a predetermined number of times before step (b).

3. The method as recited in claim 1, wherein step (b) is repeated a predetermined number of times.

4. The method as recited in claim 1, wherein in step (a) each node transfers information to another node having a same location within the adjacent quadrant.

5. A method for transmitting information within a network that has an array of nodes arranged in four quadrants, comprising the steps of:

a) transferring information from nodes in each quadrant to nodes having a same location in an adjacent quadrant in both a horizontal direction and a vertical direction within the array;

b) repeating step (a) a predetermined number of times;

c) transferring information between nodes within a same quadrant; and,

d) repeating step (b) a predetermined number of times.

6. A method for transmitting information within a network that has nodes one through sixteen arranged in a four by four array wherein nodes one through four are in a first row, nodes five through eight are in a second row, nodes nine through twelve are in a third row and nodes thirteen through sixteen are in a fourth row, comprising the steps of:

a) transferring information between node one and node three, between node nine and node eleven, between node six and node eight, between node fourteen and node sixteen, between node two and node ten, between node four and node twelve, between node five and node thirteen, between node seven and node fifteen;

b) transferring information between node one and node nine, between node three and node eleven, between node six and node fourteen, between node eight and node sixteen, between node two and node four, between node five and node seven, between node ten and node twelve, between node thirteen and node fifteen;

c) transferring information between node one and node two, between node three and node four, between node five and node six, between node seven and node eight, between node nine and node ten, between node eleven and node twelve, between node thirteen and node fourteen, between node fifteen and node sixteen; and,

d) transferring information between node one and node five, between node two and node six, between node three and node seven, between node four and node eight, between node nine and node thirteen, between node ten and node fourteen, between node eleven and node fifteen, between node twelve and node sixteen.

7. An information network, comprising:

an array of nodes arranged in four quadrants, said nodes transfer information from nodes in each quadrant to nodes in an adjacent quadrant in both a horizontal direction and a vertical direction within said array, and then further transfer information between nodes within a same quadrant.

8. The network as recited in claim 7, wherein each node transfers information to another node having a same location within the adjacent quadrant.