CN111786911A - Hybrid wireless optical network-on-chip architecture and multicast routing algorithm thereof - Google Patents
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Abstract
The invention requests to protect a hybrid wireless on-chip network architecture and a multicast routing algorithm thereof, wherein the hybrid wireless on-chip network architecture comprises an optical transmission layer, an electric control layer and a wireless transmission layer, and adopts a waveguide structure and a Walsh coding technology which are suitable for Zenneck surface wave transmission; the corresponding multicast routing method comprises a flexible allocation mechanism of a wireless transmission layer and an optical transmission layer and a multicast routing mechanism distributed based on nodes in a partition. Compared with the traditional ONOC multicast routing method, the method has better performance in the aspects of average hop count (average time delay) and the like.
Description
Technical Field
The invention belongs to the mobile communication technology, and particularly relates to a hybrid wireless optical network-on-chip architecture and a multicast routing algorithm thereof.
Background
With the advent of the big data era, modern artificial intelligence and other technologies increasingly depend on high-performance multi-core chips. In the development stage of a high-performance multi-core Chip, an Optical Network on-Chip (ONoC) has the advantages of high bandwidth, low power consumption, low time delay and the like, and the defects that a System on Chip (SoC) is difficult to expand in the past development and electric interconnection reliability and energy consumption in the Network on Chip (NoC) are poor and the like are overcome. However, high performance computing applications tend to have a high degree of parallelization, which results in a large amount of interactive data among the nodes of the ONoC, where multicast messages are high in proportion. The multicast message is regarded as a plurality of repeated unicast messages to be transmitted, thereby undoubtedly increasing the energy consumption of the ONoC, causing the resource waste on the chip and worsening the resource competition, and further improving the risk of network congestion. In addition, the message source node repeatedly sends the same message, so that other messages in the node are always in a waiting state, and the average delay becomes large. Therefore, there is a need to improve the ONoC multicast message transmission performance from both the network architecture and the routing mechanism.
The traditional ONoC architecture consists of an electrical control layer and an optical transmission layer, wherein the electrical control layer is used for transmitting a control message (message header) hop by hop from a source node to a destination node to perform optical path reservation; and transmitting the message to the destination node along the reserved optical path on the optical transmission layer. Since the multicast message has multiple destinations, the long delay generated by the electrical control layer transmitting the control message hop-by-hop is one of the main factors limiting the performance of the multicast transmission. If a wireless transmission layer can be formed on the electric control layer, long-distance single-hop and multi-direction message transmission can be realized, the pressure of the optical transmission layer is shared, and the multicast transmission efficiency is improved. Under new network architectures, routing mechanisms will also change, which will involve efficient coordination of the wireless transport layer and the optical transport layer.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A hybrid wireless optical network-on-chip architecture and a routing algorithm thereof are provided. The technical scheme of the invention is as follows:
a hybrid wireless on-chip network architecture, comprising: optical transmission layer, electrical control layer and wireless transmission layer: the optical transmission layer is positioned at the bottommost layer, the electric control layer is arranged between the optical transmission layer and the wireless transmission layer, wherein the optical transmission layer is responsible for transmitting a load with larger data volume, after the optical path is reserved, the load can be transmitted to a destination node from a source node along the optical path on the optical transmission layer, and each node in the optical transmission layer consists of an electric control unit with a preset optical switch and a five-port optical router for converting the transmission direction of the load.
An electrical control layer: the system is used for transmitting control information with small data volume, when a load is transmitted in a network, a control message is sent from a source node first, then the control message is transmitted to a destination node hop by hop on an electric control layer, and each time the control message reaches one end point, a corresponding optical router is configured for light path reservation; the mesh topology is equally divided into a plurality of subareas, a wireless transceiver module is integrated on an electric control layer unit of a node positioned in the center of each subarea, the wireless transceiver module is connected with a popup port of a local optical router to form a wireless function node, and the wireless function node has optical transmission capability.
A wireless transmission layer: and the wireless transmission layer is formed by connecting wireless links of wireless function nodes attached to the surface waveguide together, and simultaneously allocates a unique Walsh sequence code for each wireless function node.
Furthermore, the five ports of the optical router are east, west, south, north and injection/ejection, the structure of the optical router mainly comprises a micro-ring resonator and an optical waveguide, a local IP core is respectively responsible for generating and receiving data through the injection/ejection ports, the south, east, west and north ports are used for receiving data from other endpoints and forwarding the data to other endpoints, the routing function on the optical transmission layer is realized mainly by judging whether the wavelength of an optical signal is equal to the resonant wavelength of the micro-ring resonator MR, if so, the optical signal is coupled into an opened MR, otherwise, the optical signal is output from a closed MR through port, and the opening and closing of the MR is responsible for the local electrical control unit, so that the message forwarding among different ports in the optical router is realized.
Further, by default, all the microring resonators MR are in the off state.
4 furthermore, the wireless transceiver module adopts SiO with the thickness of 0.25mm2A dielectric material, which is a surface waveguide structure formed on a 0.01mm thick Cu layer, and a Zenneck wave is used as a surface wave, and an electromagnetic wave carrying a message can be transmitted while being confined to the surface, so that the surface wave can support the transmissionThe omnidirectional communication of the multicast messages is realized by adopting an inverted quarter-wave dipole antenna to couple an electromagnetic wave signal into a surface waveguide on a surface wave conversion layer and connecting the surface wave conversion layer with an integrated transceiver circuit module by utilizing a flip chip technology and a through silicon via technology.
Furthermore, after the wireless transmission layer allocates a unique Walsh sequence code to each wireless function node, the Walsh sequence code of each function node and the message to be sent are subjected to exclusive OR operation to obtain a message code, each node sends the message code through a public wireless channel, and then the coded signals are arithmetically superposed on the public wireless channel and sent to a receiving end; judging code word by code word according to the sequence of Walsh codes at a receiving end, if the current position Walsh code word is 1, accumulating corresponding digit of received data to a negative accumulator, otherwise, accumulating to a positive accumulator, comparing the result of the positive accumulator and the result of the negative accumulator, if the negative accumulator is small, finally receiving the message of 1, otherwise, receiving the message of 0, and avoiding a plurality of messages from forming conflict in a public wireless channel by using the method.
Furthermore, 4 wireless functional nodes are connected together by wireless links attached to the surface waveguide to form a wireless transmission layer.
A multicast routing algorithm for any of the network architectures, comprising the steps of:
step 1, a transmission layer flexible allocation mechanism: when data is transmitted, two options are available, one is to use the optical transmission layer only, and the other is to use the wireless optical hybrid transmission, and the rule is as follows:
rule 1, for unicast messages, 0, 1 and 2 respectively indicate that the occupation situation of a wireless function node buffer area is in an idle state, a light use state and a heavy use state, and only when a congestion flag bit is 0 and the Manhattan distance from a source node to a destination node, namely the sum of the XY axis distances between two nodes is greater than a threshold value, wireless optical hybrid transmission is selected;
rule 2, for multicast messages of which the destination node and the source node are not in the same partition, when the congestion zone bit is less than 2, selecting wireless optical hybrid transmission;
rule 3, for the case that the rules 1 and 2 are not satisfied, selecting an optical transmission layer, wherein the multicast routing mechanism of the optical transmission layer adopts the multicast routing mechanism in the step 2;
rule 4, multicast message priority is higher than unicast message;
step 2, a multicast routing mechanism based on node distribution in the partition: based on rule 3, selecting XY or YX multicast tree dimension route according to the distribution condition of source nodes and destination nodes of multicast message, wherein XY multicast tree dimension route means that the message is transmitted from X axis of row where the source node is located, when reaching Y axis of column direction where one of the destination nodes is located, copying the message, transmitting the copied message to the destination node along the column, and transmitting the original message to all the destination nodes according to the method; the YX multicast tree dimension order routing is opposite to the YX multicast tree dimension order routing, namely the message is transmitted along the Y axis, when the line of the destination node is met, the message is copied and transmitted, and the selection of the XY or YX multicast tree dimension order routing is based on the following formulas (1) and (2);
among them, WeightxIs the lateral distance Weight, between all destination nodes and their source nodes of a multicast messageyThe longitudinal distance weight between all destination nodes and source nodes of the multicast message is taken as the weight; DEST is the set of all destination nodes, x, of the multicast messageiFor the X-axis coordinate of the destination node i, XsrcAs the X-axis coordinate of the source node, yiFor the Y-axis coordinate of the destination node i, YsrcIs the Y-axis coordinate of the source node when Weightx>WeightyAnd selecting YX multicast tree dimension order route, otherwise selecting XY multicast tree dimension order route.
The invention has the following advantages and beneficial effects:
the invention designs a hybrid wireless optical network-on-chip multicast routing method for improving multicast message transmission efficiency. Firstly, a new wireless-optical hybrid network-on-chip architecture is proposed, namely, a wireless transmission layer is added on a traditional optical network-on-chip adopting an optical-electrical hybrid scheme, the advantage of wireless single-hop transmission is utilized to reduce the communication distance on chip, and the characteristic of wireless omni-directional transmission (natural fan-out) is utilized to naturally support the forwarding of multicast messages. Secondly, an on-chip surface waveguide structure is designed aiming at high attenuation of on-chip wireless signals, and Zenneck surface waves which can be attached to the surface of the waveguide structure for transmission are adopted as more reliable wireless transmission media; and simultaneously, a Walsh coding mechanism is designed for message forwarding of a wireless transmission layer for solving the problem of wireless channel resource contention, the mechanism allocates a unique sequence code for each wireless function node, and a plurality of sub-channels which are distinguished based on the sequence codes and are mutually independent are established between each pair of wireless function nodes, so that multi-channel signal transmission on the same complete channel is realized. Finally, in order to ensure the efficient cooperation of information transmission between the optical transmission layer and the wireless transmission layer and relieve the pressure problem of single-layer transmission information, a corresponding multicast routing method is provided, wherein the multicast routing method comprises a flexible allocation mechanism of the wireless transmission layer and the optical transmission layer and a multicast routing mechanism based on node distribution in a partition. Compared with the traditional ONOC multicast routing method, the method has better performance in the aspects of average hop count (average time delay) and the like.
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FIG. 1 is an exemplary diagram of a hybrid wireless optical network-on-chip architecture according to the preferred embodiment of the present invention;
FIG. 2 is an exemplary diagram of a multicast routing algorithm;
fig. 3 is a flow chart of multicast routing according to an embodiment of the present invention;
fig. 4 is a comparison graph of average hop counts for embodiments of the present invention compared to conventional ONoC multicast message transmission methods.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
a hybrid wireless on-chip network architecture, comprising:
1-1: light transmission layer: each node in the optical transmission layer is composed of an electric control unit and a five-port optical router. The optical router comprises five ports, namely east, west, south and north, and injection/ejection, the structure of the optical router mainly comprises a micro-ring resonator and an optical waveguide, and a local IP core is respectively responsible for generating and receiving data through the injection/ejection ports. The routing function on the optical transmission layer is realized mainly by judging whether the wavelength of the optical signal is equal to the resonance wavelength of the micro-ring resonator (MR). If equal, the optical signal is coupled into the open MR and vice versa from the through port of the closed MR. The switching of the MRs (in default, all MRs are in a closed state) is controlled by the local electric control unit, so that the message forwarding among different ports in the optical router is realized, and the forwarding path is determined by the multicast routing algorithm.
1-2: an electrical control layer: the mesh topology is equally divided into a plurality of subareas, a wireless transceiver module is integrated on an electric control layer unit of a node positioned at the central position of each subarea, and the module is connected with a popup port of a local optical router to form a wireless function node (the node has optical transmission capability at the same time). The wireless transceiver module adopts SiO with the thickness of 0.25mm2As a dielectric material, a surface waveguide structure formed on a Cu layer having a thickness of 0.01mm was covered. The surface wave adopts Zenneck wave, and the electromagnetic wave carrying the message can be bound on the surface for transmission. In order to support the omnidirectional communication of the multicast messages, an inverted quarter-wave dipole antenna is adopted on the surface wave conversion layer to couple electromagnetic wave signals into the surface waveguide, and the surface wave conversion layer is connected with the integrated transceiver circuit module by utilizing a flip chip technology and a through silicon via technology. The flip chip technology and the through silicon via technology both belong to packaging technologies, wherein the through silicon via technology is to manufacture a through hole which can be filled with a conductive material on a silicon wafer so as to realize the conduction of the front and back sides of a silicon wafer; the flip chip technology is to directly interconnect the devices to the substrate and the carrier through bumps on the chip, and integrate the antenna into the system.
1-3: a wireless transmission layer: wireless links attached to surface waveguides and located on an electric control layer and defined by wireless function nodes of claims 1-2 are connected together, and each wireless function node is assigned with a unique Walsh sequence code and is subjected to xor operation with a transmission message by using the unique Walsh sequence code, so that after coding, superposition of coded signals is completed on a common wireless channel, and code-by-code judgment is performed at a receiving end according to the sequence of Walsh codes. And if the current bit Walsh code word is 1, accumulating the corresponding bit number of the received data to a negative accumulator, and otherwise, accumulating to a positive accumulator. By comparing the positive accumulator result with the negative accumulator result, if the negative accumulator is small, the finally received message is 1, otherwise, the finally received message is 0, and the method is used for avoiding the plurality of messages from forming collision in the public wireless channel.
2. Aiming at the designed hybrid wireless optical network-on-chip topology, a multicast routing algorithm is designed, which comprises the following steps:
2-1: transport layer flexible allocation mechanism: when data is transmitted, two options exist, namely, only using an optical transmission layer and using wireless optical hybrid transmission, and the rule is as follows.
Rule 1: for unicast messages, wireless optical hybrid transmission is selected only when congestion flag bits are 0(0, 1, 2 respectively indicate that the wireless function node buffer area occupation condition is in an idle state, a light use state and a heavy use state), and the Manhattan distance from a source node to a destination node (the sum of the XY axis distances between two nodes) is greater than a threshold value;
rule 2: for the multicast message of which the destination node and the source node are not in the same partition, when the congestion zone bit is less than 2, selecting wireless optical hybrid transmission;
rule 3: for the case where rules 1 and 2 are not satisfied, selecting an optical transport layer whose multicast routing mechanism employs the multicast routing mechanism of claims 2-2;
rule 4: multicast messages are prioritized over unicast messages.
2-2: a multicast routing mechanism based on node distribution within a partition. Based on said rule 3, XY (or YX) multicast tree dimension routing will be selected according to the distribution of the source and destination nodes of the multicast message. The XY multicast tree dimension routing refers to that a message is transmitted from a row (X axis) where a source node is located, when the message reaches a column direction (Y axis) where one of destination nodes is located, the message is copied, the copied message is transmitted to the destination node along the column, an original message is continuously transmitted along the row, and according to the method, the multicast message is transmitted to all the destination nodes. The YX multicast tree dimension order routing is opposite to the YX multicast tree dimension order routing, namely that the message is transmitted along the Y axis, and when the line where the destination node is located is met, the message is copied and transmitted. The selection of XY or YX multicast tree dimension-ordered routing is based on the following equations (1) and (2).
Where DEST is the set of all destination nodes for a multicast message, xiFor the X-axis coordinate of the destination node i, XsrcAs the X-axis coordinate of the source node, yiFor the Y-axis coordinate of the destination node i, YsrcIs the Y-axis coordinate of the source node. When Weightx>WeightyAnd selecting YX multicast tree dimension order route, otherwise selecting XY multicast tree dimension order route.
As shown in fig. 1, a 10 × 10 mesh topology network is divided into 4 5 × 5 topology areas, and a wireless transceiver module is integrated into a node at the central position of each partition to form a wireless functional node. And integrating a wireless transceiver module on an electric control layer unit of the wireless function node, and connecting the module with a popup port of an optical router on a local optical transmission layer. The wireless transceiver module adopts a surface waveguide structure. In order to support the omnidirectional communication of the multicast messages, an inverted quarter-wave dipole antenna is adopted on the surface wave conversion layer to couple electromagnetic wave signals into the surface waveguide, and the surface wave conversion layer is connected with the integrated transceiver circuit module by utilizing a flip chip technology and a silicon through-silicon technology. And 4 wireless functional nodes are connected together by wireless links attached to the surface waveguide to form a wireless transmission layer.
In order to simulate the transmission of the multicast message, as shown in fig. 2, the node 1 is used as a source node of the multicast message transmission in the topology, and other gray nodes are used as destination nodes of the message transmission. At a source node of a multicast message, firstly, executing the transmission layer flexible distribution mechanism, discovering that some destination nodes (gray nodes except for 2, 3, 4 and 5 nodes in the figure) of the message are not in the same area with the source node, therefore, determining that the message needs to use a wireless transmission layer, setting a message header WI field value to be 1, and then executing the multicast tree dimension order routing strategy (if YX multicast tree dimension order routing is used, setting a message RS field to be 1) for determining that the message is used in each area according to weight comparison.
After determining the two fields, according to the flow shown in FIG. 3, at each along-route node: (1) selecting an appropriate multicast tree dimension routing strategy according to the RS field value, and calculating the output port of the message (copy) at the local optical router; (2) judging whether a wireless transmission layer is needed or not according to the WI field value, and if the WI field value is 0, executing (1); if the WI field value is 1, using the multicast tree dimension order routing strategy corresponding to the RS field, adding the wireless function node in the local partition as a destination node, calculating the output port of the message (copy) in the local optical router, and obtaining the corresponding forwarding path. Setting the WI field to 0 after the wireless function node receives the message to prevent the message from using the wireless link again to cause cycle deadlock, then executing the weight comparison of the claim 2-2 to determine that the wireless function node is used as the source node and the multicast tree maintenance routing strategy in the partition where the wireless function node is located, updating the RS field value, and executing the step (1).
Taking the example of the multicast message being transmitted from node 1 to the destination node in area 4, it is first determined that the destination node and the source node are not in the same area, and therefore a wireless transmission network is used, and the WI field of the message is set to 1. Secondly, the wireless function node 23 is used as one of destination nodes in the area 1, a multicast tree dimension routing strategy is determined according to the RS field value, the message is transmitted to the node 23, and the message is transmitted to the node 78 by applying a wireless transmission layer. After receiving the message, the node 78 sets the WI field of the message to 0, and then determines the multicast order-preserving routing policy in the partition where the node 78 is located, taking the node 78 as the source node according to the weight comparison as described in claims 2-2, and transmits the message to other destination nodes in the area according to the policy. To this end, the transmission of the multicast message in area 4 is completed.
This embodiment is a simulation platform written based on Java language, and fig. 4 compares the average hop count of the multicast message forwarding path in the embodiment of the present invention with that in the conventional ONoC. Under the same scale and multicast message ratio, the average hop count of the forwarding path obtained by the conventional ONoC by using the XY multicast tree dimension routing method is 12.3, while the average hop count of the forwarding path is only 6.1 in the embodiment, and the improvement rate exceeds 50%.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.
Claims (7)
1. A hybrid wireless on-chip network architecture, comprising: optical transmission layer, electrical control layer and wireless transmission layer: the optical transmission layer is positioned at the bottommost layer, and the electric control layer is arranged between the optical transmission layer and the wireless transmission layer, wherein the optical transmission layer is responsible for transmitting a load with a large data volume; each node in the optical transmission layer consists of an electric control unit with a preset optical switch and a five-port optical router for converting the transmission direction of the load;
an electrical control layer: the system is used for transmitting control information with small data volume, when a load is transmitted in a network, a control message is sent from a source node first, then the control message is transmitted to a destination node hop by hop on an electric control layer, and each time the control message reaches one end point, a corresponding optical router is configured for light path reservation; the method comprises the steps that a mesh topology is equally divided into a plurality of partitions, a wireless transceiver module is integrated on an electric control layer unit of a node located in the center of each partition, and the wireless transceiver module is connected with a popup port of a local optical router to form a wireless function node which simultaneously has optical transmission capacity;
a wireless transmission layer: and the wireless transmission layer is arranged above the electric control layer and used for replacing long-distance multi-hop transmission of the optical transmission layer and preferentially selecting the transmission layer in multicast message transmission, and is formed by connecting wireless links of wireless function nodes attached to the surface waveguide together, and simultaneously allocating a unique Walsh sequence code for each wireless function node.
2. The hybrid wireless optical on-chip network architecture of claim 1, wherein five ports of the optical router are east, west, south, north, and inject/pop-up, a structure of the hybrid wireless optical on-chip network architecture mainly comprises micro-ring resonators and optical waveguides, a local IP core is responsible for generation and reception of data through the inject/pop-up ports, the south-east and north-west ports are used for receiving data from other endpoints and forwarding the data to other endpoints, a routing function on an optical transmission layer is mainly implemented by judging whether an optical signal wavelength is equal to a resonance wavelength of the micro-ring resonators MR, if so, the optical signal is coupled into an open MR, otherwise, the optical signal is output from a closed MR through port, and the MR is switched on and off by a local electric control unit, so that message forwarding between different ports inside the optical router is implemented.
3. The hybrid wireless optical network-on-chip architecture of claim 2, wherein all the micro-ring resonators MR are in an off state by default.
4. The hybrid wireless optical network-on-chip architecture of claim 1, wherein the wireless transceiver module is made of 0.25mm thick SiO2Covering a surface waveguide structure formed on a Cu layer with the thickness of 0.01mm as a dielectric material, wherein the surface wave adopts Zenneck wave, the electromagnetic wave carrying the message can be bound on the surface for transmission, in order to support the omnidirectional communication of the multicast message, an inverted quarter-wavelength dipole antenna is adopted on a surface wave conversion layer to couple the electromagnetic wave signal into the surface waveguide, and the flip chip technology and the through silicon via technology are utilized to couple the surface waveguideThe surface wave conversion layer is connected with the integrated transceiving circuit module.
5. The hybrid wireless optical on-chip network architecture of claim 1, wherein the wireless transport layer assigns a unique Walsh sequence code to each wireless function node, and performs xor operation on the Walsh sequence code of each function node and a message to be sent to obtain a message code, and each node sends the message code through a common wireless channel, and then arithmetically superimposes the coded signals on the common wireless channel and sends the result to a receiving end; judging code word by code word according to the sequence of Walsh codes at a receiving end, if the current position Walsh code word is 1, accumulating corresponding digit of the received superposed message to a negative accumulator, otherwise, accumulating to a positive accumulator, comparing the result of the positive accumulator and the result of the negative accumulator, if the negative accumulator is small, finally, the received message is 1, otherwise, the received message is 0, and the method is used for avoiding a plurality of messages from forming collision in a public wireless channel.
6. The hybrid wireless optical on-chip network architecture of any one of claims 1-5, wherein 4 wireless functional nodes are connected together by wireless links attached to surface waveguides to form a wireless transmission layer.
7. A multicast routing algorithm based on the network architecture of any of claims 1-5, characterized by the steps of:
step 1, a transmission layer flexible allocation mechanism: when data is transmitted, two options are available, one is to use the optical transmission layer only, and the other is to use the wireless optical hybrid transmission, and the rule is as follows:
rule 1, for unicast messages, 0, 1 and 2 respectively indicate that the occupation situation of a wireless function node buffer area is in an idle state, a light use state and a heavy use state, and only when a congestion flag bit is 0 and the Manhattan distance from a source node to a destination node, namely the sum of the XY axis distances between two nodes is greater than a threshold value, wireless optical hybrid transmission is selected;
rule 2, for multicast messages of which the destination node and the source node are not in the same partition, when the congestion zone bit is less than 2, selecting wireless optical hybrid transmission;
rule 3, for the case that the rules 1 and 2 are not satisfied, selecting an optical transmission layer, wherein the multicast routing mechanism of the optical transmission layer adopts the multicast routing mechanism in the step 2;
rule 4, multicast message priority is higher than unicast message;
step 2, a multicast routing mechanism based on node distribution in the partition: based on rule 3, selecting XY or YX multicast tree dimension route according to the distribution condition of source nodes and destination nodes of multicast message, wherein XY multicast tree dimension route means that the message is transmitted from X axis of row where the source node is located, when reaching Y axis of column direction where one of the destination nodes is located, copying the message, transmitting the copied message to the destination node along the column, and transmitting the original message to all the destination nodes according to the method; the YX multicast tree dimension order routing is opposite to the YX multicast tree dimension order routing, namely the message is transmitted along the Y axis, when the line of the destination node is met, the message is copied and transmitted, and the selection of the XY or YX multicast tree dimension order routing is based on the following formulas (1) and (2);
among them, WeightxIs the lateral distance Weight, between all destination nodes and their source nodes of a multicast messageyThe longitudinal distance weight between all destination nodes and source nodes of the multicast message is taken as the weight; DEST is the set of all destination nodes, x, of a multicast messageiFor the X-axis coordinate of the destination node i, XsrcAs the X-axis coordinate of the source node, yiFor the Y-axis coordinate of the destination node i, YsrcIs the Y-axis coordinate of the source node when Weightx>WeightyAnd selecting YX multicast tree dimension order route, otherwise selecting XY multicast tree dimension order route.
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