Spectrum sensing hypergraph partitioning method for mfs massive signal processing

Abstract

The application discloses a spectrum sensing hypergraph partitioning method for MFS large-scale signal processing, which is used for partitioning a super large-scale integrated circuit which is comprehensively completed on an MFS platform, and comprises the following steps: hypergraph coarsening based on an LSH algorithm; performing an initialization method with spectrum sensing on the most coarsened hypergraph to obtain an initialization partition; running an FM algorithm with distance weighting on the obtained initialization partition to perform optimization, then desparsing, restoring the coarsened hypergraph to the hypergraph of the previous level, again using the FM algorithm to locally optimize, and alternately performing desparsing and the FM algorithm until the most original hypergraph, and completing the hypergraph partitioning. Compared with a traditional multi-polarized hypergraph partitioning method, the application can perform topology optimization for an MFS system, can process multi-dimensional weights, is helpful to improve the performance of the distributed circuit, and leaves more resource redundancy for subsequent wiring.

Description

Technical Field

[0001] This invention belongs to the field of high-performance parallel signal processing and reconfigurable computing, and specifically relates to a spectral sensing hypergraph partitioning method for large-scale MFS signal processing. Background Technology

[0002] With the exponential growth in complexity of modern signal processing algorithms (such as multi-channel real-time filtering, high-order FFT, deep learning inference, and radar beamforming), a single FPGA can no longer meet the real-time and throughput requirements of ultra-large-scale parallel signal processing tasks. Multi-FPGA systems (MFS) have become the industry's mainstream high-performance signal processing prototyping and acceleration platform by partitioning and mapping signal processing algorithm modules onto multiple FPGA chips for collaborative execution.

[0003] Traditional hypergraph partitioners (such as Metis and KaHyPar) primarily optimize the number of cut edges, neglecting the specific constraints of MFS in parallel signal processing—such as data flow dependencies, computation-to-communication imbalances, cross-FPGA latency sensitivity, pipeline synchronization requirements, and resource heterogeneity (e.g., DSP / BRAM distribution). This leads to poor performance of the partitioning results in practical deployments (e.g., decreased throughput, wasted clock cycles, and uneven load). In recent years, algorithm-semantic-aware hypergraph partitioning methods and signal processing topology-aware partitioners specifically designed for MFS have emerged, improving partitioning quality and hardware utilization to some extent.

[0004] Spectral clustering, as a partitioning method that can capture the global structure of a graph, performs well in ordinary graph partitioning. However, in large-scale hypergraph partitioning, direct partitioning results are still poor and lack topology awareness. While traditional hypergraph partitioning methods achieve acceptable results, they lack global awareness and have room for further improvement. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a spectral-aware hypergraph partitioning method for large-scale signal processing in MFS, aiming to collaboratively optimize edge cutting, maximum hop count, and multidimensional weight balancing, thereby generating a high-quality partitioning scheme that can be directly used for MFS prototype verification.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A spectral-aware hypergraph partitioning method for large-scale MFS signal processing includes:

[0008] Step S1: Use the MinHash method to estimate the similarity between every two nodes, merge similar nodes to generate a coarsened hypergraph, and after multiple coarsening processes, form a hierarchical series of coarsened hypergraphs from large to small.

[0009] Step S2: Perform a spectral-aware initialization method on the coarsest hypergraph to obtain the initial partition;

[0010] Step S3: On the obtained initial partition, run the distance-weighted FM algorithm for optimization, then desparse the hypergraph and restore the coarsened hypergraph to the previous level hypergraph. Use the FM algorithm for local optimization again. Desparse the algorithm and the FM algorithm are alternated until the original hypergraph is obtained, thus completing the hypergraph partitioning.

[0011] Further, step S1 specifically includes: constructing a neighborhood set for each node in the hypergraph, wherein the neighborhood set is the set of all hyperedges in which the node participates; generating a MinHash signature for the neighborhood set of each node using k independent hash functions; estimating the similarity between each pair of nodes by counting the number of collisions between node pairs through bucketing, and performing node matching using a greedy strategy to generate a set of matching node pairs; and shrinking the hypergraph according to the set of matching node pairs to generate a sparse coarsened hypergraph.

[0012] Furthermore, the spectral-aware initialization method specifically includes:

[0013] Step 2-1: Apply a fusion and unfolding strategy to the coarsened hypergraph to transform it into a graph, resulting in a fused graph;

[0014] Step 2-2: Calculate the spectrum of the fusion graph and construct the spectral embedding matrix;

[0015] Steps 2-3: Select from the spectral embedding matrix Using the spectral embedding vector as the initial cluster center, all unassigned vertices are sorted according to their distance to each cluster center, and vertex assignment is performed. If the assignment is successful, the vertex partition is set to the corresponding FPGA. If the assignment is unsuccessful, the constraints are relaxed and the assignment is performed again until all nodes are successfully assigned.

[0016] Steps 2-4: Use the spectral characteristics of the current FPGA physical layout as a reference matrix. For the reference matrix Perform Procrustes alignment and use the aligned results as the cluster centers for the next round. Repeat steps 2-3.

[0017] Furthermore, step 2-1 employs a fusion expansion strategy: fusion is performed using a weighted average of the clique expansion and the directional star expansion. The weighted fusion strategy is specifically expressed as follows:

[0018]

[0019] in Let be the adjacency matrix of the clique unfolded graph. Adjacency matrix of an oriented star unfolded graph These are the weighting coefficients.

[0020] The spectrum of the fusion graph in step 2-2 is calculated as follows:

[0021]

[0022] in It is the Laplace matrix of the weighted fusion graph. It is the degree matrix of the graph. After obtaining its generalized eigenvectors, take the first... Each eigenvector is used as its spectral embedding.

[0023] Furthermore, the method for constructing the directional star-shaped unfolded graph is as follows: for each superedge, with its source node as the center, directed edges are established to all other nodes within the superedge, and then the directed graph is converted into an undirected graph.

[0024] Furthermore, the constraints include:

[0025] Multidimensional weight constraint: The weight of each node and FPGA has multiple dimensions. The multidimensional weight of a node is the total amount of various resources occupied by that node, and the multidimensional weight of the FPGA is the total amount of various resources it possesses. The constraint requires that the weight of each node assigned to each FPGA does not exceed the maximum total amount of resources possessed by that FPGA. This constraint is a hard constraint and cannot be violated.

[0026] Maximum hop constraint: For a partitioning scheme, the maximum number of hops is the maximum of the minimum number of FPGAs that need to be traversed from all hyperedge source nodes to their target nodes. This constraint is a soft constraint, and the goal is to minimize the maximum number of hops.

[0027] Furthermore, the constraint relaxation refers to gradually increasing the maximum jump constraint from 0 to the maximum number of jumps in the FPGA graph.

[0028] Furthermore, regarding the reference matrix The goal of Procrustes alignment is:

[0029] ;

[0030] in For uniform scaling factor, It is an orthogonal matrix used to represent rotation. It is a translation vector. Length is A column vector of all 1s. The target matrix is ​​denoted as .

[0031] Furthermore, the distance-weighted FM algorithm in step S3 specifically includes:

[0032] Step 3-1, Gain Calculation: For each hyperedge, based on the distribution of its source and target nodes, use matrix operations to calculate the gain of moving any vertex to any FPGA, and sort them in descending order of gain. If the maximum gain is greater than 0, the algorithm ends; otherwise, proceed to step 3-2.

[0033] Step 3-2: Without violating the multidimensional weight constraints, select the legal move pair with the highest gain for swapping;

[0034] Step 3-3: Update the gain values ​​of the vertices related to the affected superedge, and continue to execute step 3-2;

[0035] Steps 3-4: When all vertices have been moved, or when there are no positive gain moves for several consecutive rounds, terminate the iteration and output the final partitioning scheme.

[0036] Furthermore, in step 3-1, moving any vertex to the gain of any FPGA... The calculation formula is:

[0037] ;

[0038] ;

[0039] ;

[0040] in, Source node mobility gain; For the target node's movement gain, For a certain edge The gain result after any node assigned to FPGA a is moved to FPGA b. The distance weighting coefficients between FPGA a and FPGA b are used. For super-edge The source node is assigned to the FPGA, which will The movement gain of each target node is calculated and organized. , It is A matrix of all 1s It is the weight vector of the hyperedge. It is the source node indicator matrix of the hyperedge. It is the assignment matrix of the target nodes of the hyperedge. It is the indicator matrix of the source node. It is the indicator matrix of the target node. This is the final allocation matrix. It is the distance matrix of the graph in MFS.

[0041] Compared with existing technologies, the beneficial effects of this invention are as follows: The hyperedge neighborhood of each node in this invention is treated as a set, and a signature is generated for it using MinHash technology. This enables the rapid and approximate merging of structurally similar node pairs. Compared with traditional matching algorithms, this method has higher computational efficiency and better preserves the higher-order connectivity characteristics of the hypergraph. This invention dynamically guides and aligns the initial centers of k-means clustering through Procrustes analysis. During node allocation, a candidate FPGA propagation algorithm is embedded. This algorithm dynamically updates the legitimate FPGA candidate set of neighboring nodes based on the allocated nodes and combines multi-dimensional weight constraints for feasibility judgment, ensuring that the partitioning result meets the resource and topology constraints of MFS. Compared with traditional multi-polar hypergraph partitioning methods, this invention can perform topology optimization for MFS systems and handle multi-dimensional weights, which helps improve the performance of the allocated circuits and leaves more resource redundancy for subsequent routing. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a flowchart of a spectrum-aware hypergraph partitioner for large-scale signal processing (MFS) provided in an embodiment of the present invention.

[0044] Figure 2 This is a flowchart of step S2 provided in an embodiment of the present invention.

[0045] Figure 3 This is a flowchart of step S3 provided in an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to its embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of protection of the invention.

[0047] Combination Figure 1 This invention provides a spectral sensing hypergraph partitioning method for large-scale signal processing in MFS (Multi-Field Programmable Gate Array) systems, used for partitioning synthesized VLSI circuits on an MFS platform, including:

[0048] Step S1: Use the MinHash method to estimate the similarity between every two nodes, merge similar nodes to generate a coarsened hypergraph, and after multiple coarsening processes, form a hierarchical series of coarsened hypergraphs from large to small.

[0049] (1) Input preparation: Convert the synthesized circuit netlist into a directed hypergraph. Each vertex For a given logical module (such as a LUT or register group), its weights are multi-dimensional weights. Each directed superedge This represents a driving relationship, where the tail is a unique source node (driver end) and the head consists of multiple target nodes (load ends).

[0050] (2) Neighborhood modeling: For each vertex Construct its neighborhood set That is, all the superedges that the vertex participates in.

[0051] (3) MinHash signature generation: 128 independent hash functions are selected. For each vertex and each hash function Calculate its MinHash value: This results in a 128-dimensional MinHash signature vector.

[0052] (4) Node matching: Each bit of the signature is bucketed, and the number of collisions between node pairs is counted. All node pairs are sorted in descending order of collision count, and a greedy strategy is used for matching to ensure that each node participates in the matching at most once. The final set of matched node pairs is obtained. .

[0053] (5) Hypergraph Compression: Shrinking the hypergraph based on the set. Each pair of matching nodes Merged into a new supernode Its multidimensional weights are All related to or All connected hyperedges are updated to be the same as those in the previous version. Connected. If a superedge contains both and Only one will be retained after the merger. Repeat this coarsening process until the number of vertices in the hypergraph drops to several thousand or about 10% of the original graph.

[0054] In step S1, the hyperedge neighborhood of each node is treated as a set, and a signature is generated for it using the MinHash technique. This method can quickly and approximately find pairs of nodes with similar structures for merging. Compared with traditional matching algorithms, this method is more computationally efficient and can better preserve the higher-order connectivity properties of the hypergraph.

[0055] Step S2: Perform a spectral-aware initialization method on the coarsened hypergraph to obtain the initialization partitions, and combine... Figure 2 Specifically, it includes:

[0056] (1) Hypergraph to graph transformation: For the coarsened hypergraph, a fusion unfolding strategy is adopted to construct a clique unfolded graph. Replace each hyperedge with a complete subgraph; construct a directional star unfolded graph. : Using the source node of each hyperedge as the center, construct directed edges to all target nodes, then convert them into an undirected graph; merge the two: ,in Group deployment diagram The adjacency matrix, For the orientation star-shaped unfolded diagram adjacency matrix The weighting coefficient is 0.5 in this embodiment. The directional star unfolded graph is constructed as follows: for each hyperedge, a directed edge is established from its source node to all other nodes within the hyperedge, and then the directed graph is converted into an undirected graph for subsequent spectral calculation.

[0057] (2) Spectral embedding computation: adjacency matrix based on fusion graph Constructing the normalized Laplace matrix Calculate its preceding... The eigenvectors corresponding to the smallest non-zero eigenvalues ​​constitute spectral embedding matrix ( (This represents the number of vertices after coarsening).

[0058] The specific method for calculating the spectrum is as follows:

[0059]

[0060] in It is the Laplace matrix of the weighted fusion graph. Given the degree matrix of a graph, find its generalized eigenvectors and then take the first... Each eigenvector is used as its spectral embedding.

[0061] (3) Random selection Each spectral embedding vector is used as the initial cluster center. All unassigned vertices are sorted by their distance to each cluster center. Each vertex-cluster center pair is tried sequentially. For each attempt, a candidate set of its neighboring nodes is calculated after placement. in The FPGA to be allocated is selected; it is then determined whether the allocation exceeds resource constraints and whether there are still available FPGAs in its neighboring nodes. If so, the FPGA is allocated; otherwise, the next node is processed.

[0062] The clustering process is not performed in an unconstrained abstract space, but rather incorporates an FPGA topology legitimacy detection module (also known as the "candidate FPGA propagation module") to determine in real-time whether a node can be legally assigned to a specific FPGA block at each clustering allocation decision step. Specifically, for each movable node in the hypergraph... The system maintains a set of valid FPGA candidates. ,in Total number of FPGAs This indicates that, under the current allocation state and MFS physical topology constraints, nodes can be legally placed. A set of all FPGA IDs.

[0063] The candidate FPGA set is updated during the clustering process, whenever a node... Actual allocation to FPGA blocks The system immediately triggers local candidate propagation: for all unassigned neighbor nodes in the original hypergraph Update its candidate set to:

[0064]

[0065] This is a rough update that only updates adjacent nodes and not more nodes. It can accurately determine the validity of a node while reducing a lot of computation.

[0066] (4) If all vertices are successfully assigned, the assignment ends. Otherwise, the hop constraint is relaxed, and the remaining nodes are assigned.

[0067] The constraints include:

[0068] Multidimensional weight constraint: Each node's weight to the FPGA has multiple dimensions. The node's multidimensional weight represents the total amount of various resources it occupies, and the FPGA's multidimensional weight represents the total amount of various resources it possesses. The constraint requires that the sum of the node weights allocated to each FPGA does not exceed the maximum total amount of resources possessed by that FPGA. This constraint is a hard constraint and cannot be violated.

[0069] Maximum hop constraint: For a partitioning scheme, the maximum number of hops is the maximum of the minimum number of FPGAs that must be traversed from all hyperedge source nodes to their target nodes. This objective is a soft constraint, and the goal is to minimize the maximum number of hops.

[0070] Relaxing the hop constraint means gradually increasing the maximum hop constraint from 0 to the maximum number of hops in the FPGA graph.

[0071] The multidimensional weights include various physical resources of the FPGA chip, specifically the resource vectors of lookup tables (LUTs), flip-flops (FFs), block RAM (BRAM), and digital signal processing units (DSPs).

[0072] (5) Procrustes Alignment: Use the spectral features of the current FPGA physical layout as the reference matrix. The current cluster center is used as the target matrix. The optimal transformation (rotation + scaling) is calculated through Procrustes analysis. Align to The aligned results will be used as the cluster centers for the next round. Repeat step (3).

[0073] To achieve topology awareness, the MFS system is modeled using a graph and its spectrum is calculated. Procrustes analysis is used to correct the final cluster center update in the k-means algorithm. Specifically, after each round of complete node allocation, the system uses Procrustes analysis to optimally align the spectral features of the current FPGA physical layout graph with the already formed cluster centers. The aligned FPGA graph is then used as the new cluster centers for the next round of cluster allocation. The alignment goal is:

[0074]

[0075] in For uniform scaling factor, It is an orthogonal matrix (satisfying) ), used to indicate rotation, It is a translation vector. Length is A column vector of all 1s.

[0076] Step S3: Refine the hypergraph using a distance-weighted FM algorithm. Run the distance-weighted FM algorithm on the obtained initial partition for optimization, then desparse the hypergraph, restoring the coarsened hypergraph to the previous level. Perform local optimization again using the FM algorithm. Alternate between desparsening and the FM algorithm until the original hypergraph is obtained, completing the hypergraph partitioning. Figure 3 Specifically, it includes:

[0077] (1) Gain calculation: For each hyperedge, based on the distribution of its source and target nodes, matrix operations are used to efficiently calculate the gain of moving any vertex to any FPGA. They are sorted in descending order of gain. This gain incorporates the reduction in edge cut and the reduction in hop count (communication distance).

[0078] Traditional FM algorithms only focus on edge cut gain. This invention explicitly introduces the communication distance (hop count) between FPGAs into its gain function as a penalty or reward term. When moving a vertex helps reduce long-distance communication (i.e., reduces hop count), it may be accepted even if the edge cut gain is negative. This allows the algorithm to optimize multiple objectives simultaneously in the local search, further improving the final partitioning quality. The specific function for evaluating the quality of a partition is defined as:

[0079]

[0080] in It is the weight vector of each edge. It is the source node indicator matrix of the hyperedge. It is the assignment matrix of the target nodes of the hyperedge. It is the indicator matrix of the source node. It is the indicator matrix of the target node. This is the final allocation matrix. It is the distance matrix of the graph in MFS, which can be modified by weighting, and the default is to use exponential weighting. It is a binary function, defined as: .

[0081] The function for calculating the gain of movement for each node is:

[0082]

[0083] in For nodes As the gain of the source node, For nodes As the gain of the target node.

[0084] The calculation result of the mobility gain of the node as the source node is as follows:

[0085]

[0086] in It is A matrix of all 1s. It is the weight vector of the hyperedge.

[0087] The calculated mobility gain of the node as the target node is as follows:

[0088]

[0089] in This represents the distance between the two FPGAs. For the edge The FPGA where the source node is located, It is the FPGA where it was located before the move. It refers to the FPGA where the device is located after the move. ,

[0090] Sorting out after calculation and get and , For nodes Let be the set of hyperedges of the source node. For the target node to contain nodes The set of hyperedges. Then the final gain is:

[0091]

[0092] For gain updates, after a move, it is only necessary to identify the affected hyperedges and update the move gain of the other nodes associated with those hyperedges. Specifically:

[0093] for The source node of the hyperedge has changed, so the movement gain of all nodes associated with the hyperedge (including other target nodes) needs to be recalculated.

[0094] for In this architecture, hyperedges only need to be updated when movement causes a change in the occupancy class of their target node on a given FPGA. These occupancy classes are divided into three categories: 0, 1, and greater than 1 occupancy on a given FPGA. This significantly reduces the number of nodes requiring updates, thus accelerating computation.

[0095] (2) Without violating the multidimensional weight balance constraint, select the legal move pair with the highest gain for exchange.

[0096] (3) Update the gain values ​​of the vertices related to the affected superedge (the superedge containing the vertex). Then continue with step (2).

[0097] (4) Terminate the iteration when all vertices have been moved, or when there are no positive gain moves for several consecutive rounds. Output the final partitioning scheme.

[0098] Step S3 refines the high-quality initial plan using a greedy algorithm. This algorithm calculates the movement gain for each node and selects the movement scheme with the highest gain. It then updates the movement gains of all movement schemes and re-selects a movement scheme. This greedy iteration continues until no feasible movement scheme is found or the movement gains of all movement schemes are less than 0.

[0099] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A spectral-aware hypergraph partitioning method for large-scale signal processing of massive spectral sensing graphs (MFS), characterized in that, include: Step S1: Use the MinHash method to estimate the similarity between every two nodes, merge similar nodes to generate a coarsened hypergraph, and after multiple coarsening processes, form a hierarchical series of coarsened hypergraphs from large to small. Step S2: Perform a spectral-aware initialization method on the coarsest hypergraph to obtain the initial partition; Step S3: On the obtained initial partition, run the distance-weighted FM algorithm for optimization, then desparse the hypergraph and restore the coarsened hypergraph to the previous level hypergraph. Use the FM algorithm for local optimization again. Desparse the algorithm and the FM algorithm are alternated until the original hypergraph is obtained, thus completing the hypergraph partitioning.

2. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 1, characterized in that, Step S1 specifically includes: constructing a neighborhood set for each node in the hypergraph, wherein the neighborhood set is the set of all hyperedges in which the node participates; generating a MinHash signature for the neighborhood set of each node using k independent hash functions; estimating the similarity between each pair of nodes by counting the number of collisions between node pairs through bucketing, and performing node matching using a greedy strategy to generate a set of matching node pairs; and shrinking the hypergraph based on the set of matching node pairs to generate a sparse coarsened hypergraph.

3. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 1, characterized in that, Spectrum-aware initialization methods specifically include: Step 2-1: Apply a fusion and unfolding strategy to the coarsened hypergraph to transform it into a graph, resulting in a fused graph; Step 2-2: Calculate the spectrum of the fusion graph and construct the spectral embedding matrix; Steps 2-3: Select from the spectral embedding matrix Using the spectral embedding vector as the initial cluster center, all unassigned vertices are sorted according to their distance to each cluster center, and vertex assignment is performed. If the assignment is successful, the vertex partition is set to the corresponding FPGA. If the assignment is unsuccessful, the constraints are relaxed and the assignment is performed again until all nodes are successfully assigned. Steps 2-4: Use the spectral characteristics of the current FPGA physical layout as a reference matrix. For the reference matrix Perform Procrustes alignment and use the aligned results as the cluster centers for the next round. Repeat steps 2-3.

4. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 3, characterized in that, In step S2-1: the fusion unfolding strategy for the coarsened hypergraph is to use a weighted fusion of the clique unfolding graph and the directional star unfolding graph.

5. The spectral sensing hypergraph partitioning method for large-scale signal processing of MFS according to claim 4, characterized in that, The method for constructing the directed star unfolded graph is as follows: for each superedge, with its source node as the center, a directed edge is established to all other nodes within the superedge, and then the directed graph is converted into an undirected graph.

6. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 3, characterized in that: The constraints include: Multidimensional weight constraint: The weight of each node and FPGA has multiple dimensions. The multidimensional weight of a node is the total amount of various resources occupied by that node, and the multidimensional weight of the FPGA is the total amount of various resources it possesses. The constraint requires that the weight of each node assigned to each FPGA does not exceed the maximum total amount of resources possessed by that FPGA. This constraint is a hard constraint and cannot be violated. Maximum hop constraint: For a partitioning scheme, the maximum number of hops is the maximum of the minimum number of FPGAs that need to be traversed from all hyperedge source nodes to their target nodes. This constraint is a soft constraint, and the goal is to minimize the maximum number of hops.

7. The spectral sensing hypergraph partitioning method for large-scale signal processing of MFS as described in claim 3, characterized in that, The constraint relaxation refers to gradually increasing the maximum jump constraint from 0 to the maximum number of jumps in the FPGA graph.

8. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 3, characterized in that, For the reference matrix The goal of Procrustes alignment is: ； in The scaling factor is uniform. It is an orthogonal matrix used to represent rotation. It is a translation vector. Length is A column vector of all 1s The target matrix is ​​denoted as .

9. The spectral sensing hypergraph partitioning method for large-scale MFS signal processing according to claim 6, characterized in that, The distance-weighted FM algorithm in step S3 specifically includes: Step 3-1, Gain Calculation: For each hyperedge, based on the distribution of its source and target nodes, use matrix operations to calculate the gain of moving any vertex to any FPGA, and sort them in descending order of gain. If the maximum gain is greater than 0, the algorithm ends; otherwise, proceed to step 3-2. Step 3-2: Without violating the multidimensional weight constraints, select the legal move pair with the highest gain for swapping; Step 3-3: Update the gain values ​​of the vertices related to the affected superedge, and continue to execute step 3-2; Steps 3-4: When all vertices have been moved, or when there are no positive gain moves for several consecutive rounds, terminate the iteration and output the final partitioning scheme.

10. The spectral-aware hypergraph partitioning method for large-scale MFS signal processing according to claim 9, characterized in that, In step 3-1, moving any vertex to the gain of any FPGA The calculation formula is: ； ； ； in, Source node mobility gain; For the target node's movement gain, For a certain edge The gain result after any node assigned to FPGA a is moved to FPGA b. The distance weighting coefficients between FPGA a and FPGA b are used. For super-edge The source node is assigned to the FPGA, which will The movement gain of each target node is calculated and organized. , It is A matrix of all 1s It is the weight vector of the hyperedge. It is the source node indicator matrix of the hyperedge. It is the assignment matrix of the target nodes of the hyperedge. It is the indicator matrix of the source node. It is the indicator matrix of the target node. This is the final allocation matrix. It is the distance matrix of the graph in MFS.

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