A p-rwa method and device based on an auxiliary graph

Abstract

This invention addresses the high time complexity of existing routing and wavelength assignment (RWA) algorithms in multi-fiber networks equipped with blocking optical cross-connects (OXCs). It discloses a progressive first-hit routing and wavelength assignment method and apparatus based on an auxiliary graph. This method leverages the characteristic that the result of most requested RWA requests can be determined solely through link-state information. It initially attempts to execute RWA using almost exclusively link-state information. Only when optical path establishment fails due to internal OXC congestion will it simultaneously use link-state information and exchange OXC states to re-execute RWA. This invention, while ensuring no loss of network non-blocking performance, significantly reduces the algorithm's runtime by several orders of magnitude compared to existing algorithms. It provides strong technical support for the application of large-scale blocking OXCs in future multi-fiber networks, demonstrating excellent practicality and broad application prospects.

Description

Technical Field

[0001] This invention relates to the field of optical network communication technology, specifically to a routing and wavelength assignment (RWA) method applicable to multi-fiber optical networks equipped with blocking optical cross-connects (OXC), and particularly to a progressive first-fit RWA (p-RWA) method based on an auxiliary graph. Background Technology

[0002] With the rapid development of bandwidth-intensive services such as high-definition video streaming and online gaming, optical networks are forced to increase capacity by deploying multiple optical fibers on each link. This trend means that the number of ports on the core component of an optical node, the OXC, will inevitably exceed one hundred in the near future.

[0003] However, the design of large-scale non-blocking OXCs faces numerous challenges. The size of a standard OXC is entirely limited by the number of ports on commercial wavelength selective switches, currently capped at only 49. Existing large-scale non-blocking OXC schemes proposed in related research all suffer from high costs and excessive insertion loss. Against this backdrop, blocking OXCs have become a viable option.

[0004] While blocking OXCs offer a low-cost advantage, deploying them in optical networks significantly increases the complexity of the Redirect Wire Arrangement (RWA) algorithm. In optical networks with non-blocking OXCs, optical paths never experience congestion within nodes, allowing the RWA process to be completed solely based on link-state information. However, in optical networks with blocking OXCs, even if an available wavelength can be found on the path from the source node to the destination node for a request, congestion may still occur due to resource contention within the OXC. To reduce the probability of request congestion, the RWA process must also consider the switching states of each OXC, resulting in extremely high time complexity.

[0005] For optical networks with blocked OXCs, existing RWA algorithms can be divided into two categories: RWA algorithms based on auxiliary graphs and those based on... The Shortest Path RWA algorithm.

[0006] The first RWA algorithm based on auxiliary graphs, called Dynamic Wavelength Grouping and Fiber Selection Algorithm, was proposed for HIER structures. This algorithm defines an auxiliary graph for each wavelength, mapping the exchange states of each fiber and the input and output fibers within the OXC to virtual vertices and virtual edges, respectively. The algorithm searches for the shortest path across all auxiliary graphs and selects the path with the minimum cost.

[0007] Another RWA algorithm based on auxiliary graphs is called the Routing, Fiber, Band, and Spectrum Allocation Algorithm, which is proposed for FLEX structures. This algorithm maps each input / output port of the OXC to a virtual vertex, and each virtual edge in each auxiliary graph corresponds to a fiber or the switching state between input / output ports. The algorithm searches for the shortest path in all auxiliary graphs and selects the one with the lowest cost.

[0008] Another RWA algorithm based on auxiliary graphs is called the Dynamic Path Control (DPC) algorithm, designed for ring OXCs. A ring OXC is composed of multiple smaller OXCs interconnected by intra-node optical fibers. In the auxiliary graph oriented towards the ring OXC, each virtual vertex represents a smaller OXC, and each virtual edge corresponds to an inter-node link or intra-node link. The DPC algorithm first enumerates all shortest paths on all wavelength planes between all combinations of smaller OXCs from the source node to the destination node, and then selects the path that satisfies the preset hop count constraint and has the minimum hop count.

[0009] To simultaneously capture link-state information and the exchange state of each OXC in a multi-fiber network, the auxiliary graph-based RWA algorithm must construct an auxiliary graph containing a large number of virtual vertices on each wavelength plane. Therefore, although the auxiliary graph-based RWA algorithm can achieve a low blocking rate, its time complexity is extremely high and increases dramatically with the number of fibers on each link.

[0010] Other works have proposed based on Shortest path RWA algorithm. This type of algorithm first considers each wavelength... The algorithm calculates the routing cost of all possible fiber combinations on the candidate paths, then extends the calculation to all wavelength planes, and finally selects the combination with the minimum cost from all paths and wavelengths. However, this type of algorithm has two drawbacks: 1. High time complexity; 2. Compared with the auxiliary graph-based RWA algorithm, the KSP-based RWA algorithm has a higher blocking rate due to the limited number of candidate paths.

[0011] Existing RWA algorithms struggle to simultaneously meet the dual performance requirements of low blocking probability and low time complexity. Therefore, given the increasingly urgent need for large-scale deployment of blocking OXCs in multi-fiber networks, a novel RWA method is urgently needed to significantly shorten the algorithm's runtime while ensuring no loss of network blocking performance. Summary of the Invention

[0012] The purpose of this invention is to address the high time complexity of existing RWA algorithms in multi-fiber networks equipped with blocking OXCs. It proposes a progressive first-hit RWA method based on auxiliary graphs, which significantly reduces the algorithm's running time by several orders of magnitude while ensuring no blocking performance loss. This method features low time complexity and no blocking rate performance loss, providing technical support for the application of large-scale blocking OXCs in future multi-fiber networks.

[0013] The principle of this invention is as follows: Leveraging the characteristic that the RWA result for most service requests can be determined solely through link-state information, RWA is performed for a single request using both link-state information and OXC exchange state information only when necessary. The algorithm first attempts to establish an optical path based solely on link-state information; only when the initial path establishment attempt fails due to internal OXC congestion does the RWA process re-execute, combining link-state information with OXC exchange state.

[0014] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: A progressive RWA method based on auxiliary graphs includes the following steps: Step 1, Generating the auxiliary graph: For each wavelength supported by each optical fiber in the network Three different granularity auxiliary graphs were constructed for each: link-level auxiliary graph, direction-level auxiliary graph, and port-level auxiliary graph. This represents the total number of wavelengths on a single optical fiber.

[0015] Link-level auxiliary graph: This graph uses the entire optical node as a vertex and contains only link state information. Specifically, each optical node in a multi-fiber network is abstracted as a vertex in the graph; if any fiber between two adjacent nodes has an idle channel at the corresponding wavelength, an edge is established between the corresponding vertices of the two nodes.

[0016] Directional auxiliary graph: Using the physical directions of the OXC as vertices, it includes link state information and partial OXC switching state information. Specifically, each physical direction of each OXC node is abstracted as an independent vertex in the graph; inside the node, if there is an available internal switching channel between the input and output directions at the current wavelength, a directed edge is established between the corresponding vertex of the input direction and the corresponding vertex of the output direction; outside the node, if there is an idle channel in the corresponding wavelength for the input / output fiber corresponding to a certain direction, an edge is established between the corresponding directional vertices of adjacent nodes. The partial OXC switching state information refers to the information on whether there is an available internal switching channel between different physical directions.

[0017] Port-level auxiliary graph: Using the input / output physical ports of the OXC as vertices, it includes link state information and all OXC switching state information. Specifically, each input port and each output port of each OXC node is abstracted as an independent vertex in the graph. Inside a node, if an available internal switching channel exists between an input port and an output port at the current wavelength, a directed edge is established between the corresponding vertex of the input port and the corresponding vertex of the output port. Outside a node, if an optical fiber connected to a port has an idle channel at the corresponding wavelength, an edge is established between the corresponding port vertices of adjacent nodes. The "all OXC switching state information" refers to the information on whether an available internal switching channel exists between any specified input port and any specified output port.

[0018] Step 2, execute the link-level RWA algorithm: Upon receiving a service request, the system first searches for the shortest available path in the link-level auxiliary graphs corresponding to all wavelengths. Specifically, the search process involves executing the shortest path-first algorithm on the link-level auxiliary graphs for each wavelength plane, calculating the path cost from the source vertex to the destination vertex, and selecting the path with the minimum cost and where all edges represent available resources as the feasible shortest path across all wavelength planes. If a feasible shortest path is found, an optical path is established based on that path, and the entire RWA process is terminated immediately.

[0019] If insufficient end-to-end link wavelength resources result in no connected path being found on any wavelength plane, the service request is directly deemed blocked and the entire RWA process is terminated immediately.

[0020] Step S3 is executed only if the shortest path found in the link-level auxiliary graph of at least one wavelength plane is infeasible due to switching congestion within the OXC node.

[0021] Step 3, execute the directional RWA algorithm: If step S2 fails due to internal switching congestion in the OXC, the shortest available path is searched in the directional auxiliary graphs corresponding to all wavelengths. The search process is similar to step S2, that is, the shortest path first algorithm is executed in the directional auxiliary graphs corresponding to all wavelength planes.

[0022] If a feasible shortest path is found, an optical path is established based on that path, and the entire RWA process is terminated immediately.

[0023] If insufficient end-to-end link wavelength resources result in no connected path being found on any wavelength plane, the service request is directly deemed blocked and the entire RWA process is terminated immediately.

[0024] Step S4 is executed only if the shortest path found in the directional-level auxiliary graph of at least one wavelength plane is infeasible due to internal switching blockage of the OXC.

[0025] Step 4, execute the port-level RWA algorithm: If step S3 still fails due to internal switching congestion in the OXC, the shortest available path is searched in the port-level auxiliary graphs corresponding to all wavelengths. The search process also involves performing the shortest path first algorithm in the port-level auxiliary graphs corresponding to all wavelength planes.

[0026] If a feasible shortest path is found, an optical path is established based on that path, and the RWA process is terminated.

[0027] If no feasible path can be found in the port-level auxiliary graphs of all wavelength planes, the service request is deemed blocked and the RWA process is terminated.

[0028] Furthermore, the progressive search order executed in the method has a strict priority hierarchy: the link-level RWA algorithm has a higher priority than the direction-level RWA algorithm, and the direction-level RWA algorithm has a higher priority than the port-level RWA algorithm. The next priority algorithm is only triggered when the path becomes infeasible due to internal switching congestion in the OXC; failure due to insufficient link resources does not trigger priority escalation.

[0029] Furthermore, both steps S2 and S3 include an early termination mechanism based on the identification of blocking causes. Specifically, during the execution of the link-level RWA algorithm or the direction-level RWA algorithm, two reasons for path search failure are distinguished in real time: the first type of failure is insufficient link wavelength resources on the end-to-end path. For this type of failure, the service request is directly determined to be blocked and all subsequent steps are terminated immediately; the second type of failure is internal switching blockage within the OXC node. Only for this type of failure is it allowed to proceed to the next priority RWA algorithm step.

[0030] Furthermore, the feasible shortest path finally established in the method includes the following resource allocation information: the working wavelength identifier assigned to the service request; the end-to-end physical fiber link sequence traversed by the working wavelength; and the switching configuration from the inbound to the outbound direction within each OXC node, or the binding relationship between the identifiers of the input ports and the identifiers of the output ports.

[0031] Furthermore, the method is applicable to various OXC structures. These OXCs include, but are not limited to, any one of HIER structure OXC, FLEX structure OXC, or ring interconnect structure OXC. The division of "physical direction" in the direction-level auxiliary diagram and the granularity and mapping relationship of "port" in the port-level auxiliary diagram can be adapted and adjusted according to the actual internal switching architecture of the deployed OXC.

[0032] Compared with the prior art, the beneficial effects of the present invention are: (1) Taking advantage of the fact that most service requests only require link state information to complete RWA, the link-level auxiliary graph with extremely low computational overhead is used as the default search space. Only in a few requests that fail due to internal blocking of OXC are the direction-level and port-level auxiliary graphs with higher computational overhead gradually enabled.

[0033] (2) Although decisions are made based on coarse-grained information in most cases, a complete "failure fallback" mechanism is designed. Once the optical path establishment faces the risk of blockage due to insufficient information granularity, the algorithm will automatically and seamlessly upgrade to a finer-grained auxiliary graph containing complete OXC exchange state information for accurate search. The final routing and wavelength allocation results of this invention are completely equivalent in decision-making capability to traditional algorithms that always perform global search on port-level auxiliary graphs, ensuring zero loss in network congestion probability performance.

[0034] (3) An early termination mechanism based on blocking cause identification is introduced. By accurately distinguishing between "insufficient link resources" and "internal blocking within OXC" at the link-level and direction-level RWA stages, requests destined to fail due to insufficient link resources can be blocked in real time, preventing further invalid searches at higher granularities. This mechanism further eliminates unnecessary computational overhead and significantly improves the overall utilization efficiency of system resources.

[0035] (4) Without sacrificing network congestion probability performance, the algorithm's running time is significantly reduced by several orders of magnitude, and the larger the network size, the more significant the reduction in running time. The algorithm has strong versatility and can be adapted to deploy multi-fiber networks with different congestion OXCs. Attached Figure Description

[0036] Figure 1 The number of optical fibers in the link of this invention is The number of wavelengths is A schematic diagram of a multi-fiber optical network structure; Figure 2 The number of optical fibers is The number of wavelengths is The diagrams show three types of auxiliary diagrams, where: (a) is a link-level auxiliary diagram, (b) is a direction-level auxiliary diagram, and (c) is a port-level auxiliary diagram. Figure 3 The number of optical fibers is The number of wavelengths is The diagram shows the three sub-algorithms: (a) is the link-level RWA algorithm, (b) is the direction-level RWA algorithm, and (c) is the port-level RWA algorithm. Figure 4This is a schematic diagram of a multi-fiber network in this invention with 2 optical fibers and 2 wavelengths. Figure 5 yes Figure 4 The diagrams show three auxiliary diagrams when the number of optical fibers and wavelengths in the mid-link is 2, where: (a) is the link-level auxiliary diagram, (b) is the direction-level auxiliary diagram, and (c) is the port-level auxiliary diagram. Figure 6 yes Figure 4 The diagram shows the three sub-algorithms when the number of optical fibers and wavelengths in the mid-link is 2, where: (a) is the link-level RWA algorithm, (b) is the direction-level RWA algorithm, and (c) is the port-level RWA algorithm. Detailed Implementation

[0037] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0038] For example Figure 1 The number of optical fibers in the link shown is Wavelength number For a multi-fiber network, executing the p-RWA algorithm for a single request includes the following steps: Step 1, Generating the auxiliary plot. For each wavelength... Three different granularities of auxiliary graphs were constructed: link-level auxiliary graph, direction-level auxiliary graph, and port-level auxiliary graph. The link-level, direction-level, and port-level auxiliary graphs were obtained by mapping each node, each direction of the OXC, and each port of the OXC to a vertex in the graph, respectively. For example... Figure 2 As shown, a total of [number] were generated. A link-level auxiliary graph, Auxiliary diagrams at the directional level and Port-level auxiliary diagram.

[0039] Step 2, execute the link-level RWA algorithm. Perform the shortest path algorithm to search for a shortest path on all link-level auxiliary graphs, such as... Figure 3 As shown in (a), the path in wavelength layer 1 is the shortest path in all link-level auxiliary graphs. If the shortest path is feasible, the optical path is established and the RWA process is terminated. If the request is blocked due to insufficient link resources, the request is blocked and the RWA process is terminated. Step 3 is only performed if the request cannot be established due to internal OXC blocking.

[0040] Step 3, execute the directional RWA algorithm. The directional RWA algorithm searches for a shortest path on all directional auxiliary graphs, such as... Figure 3 As shown in (b), wavelength layer The path in the path is the shortest path in all direction-level auxiliary graphs. If the shortest path is feasible, the optical path is established and the RWA process is terminated. If the request is blocked due to insufficient link resources, the request is blocked and the RWA process is terminated. Step 4 is only performed if the request cannot be established due to internal OXC blocking.

[0041] Step 4: Execute the port-level RWA algorithm. The port-level RWA algorithm searches for a shortest path on all port-level auxiliary graphs, such as... Figure 3 As shown in (c), wavelength layer The path in the diagram is the shortest path in all port-level auxiliary graphs. If the shortest path is found, the optical path is established and the RWA process is terminated; otherwise, the request is blocked and the RWA process is terminated.

[0042] Example: For example Figure 4 Number of fiber optic links shown =2, Wavelength number For a multi-fiber network with a fiber optic ratio of 2, executing the p-RWA algorithm for a single request includes the following steps: Step 1, Generation of auxiliary diagrams: These represent wavelengths... and Define three types of auxiliary graphs. For example... Figure 5 As shown, a total of 2 link-level auxiliary graphs, 2 direction-level auxiliary graphs, and 2 port-level auxiliary graphs were generated.

[0043] Step 2: Execute the link-level RWA algorithm. Execute the shortest path algorithm to find the shortest path in all link-level auxiliary graphs, such as... Figure 6 As shown in (a), the path in wavelength layer 1 is the shortest path in all link-level auxiliary graphs. If the shortest path exists and is feasible, we establish an optical path for the request and terminate the RWA process. If the shortest path does not exist, the request is blocked and the RWA process is terminated. If the shortest path exists but is not feasible, the direction-level RWA algorithm continues to be executed.

[0044] Step 3: Execute the directional level RWA algorithm. Execute the shortest path algorithm to find the shortest path in all directional level auxiliary graphs, such as... Figure 6 As shown in (b), the path in wavelength layer 2 is the shortest path in all direction-level auxiliary graphs. If the shortest path exists and is feasible, we establish an optical path for the request and terminate the RWA process. If the shortest path does not exist, the request is blocked and the RWA process is terminated. If the shortest path exists but is not feasible, the port-level RWA algorithm continues to be executed.

[0045] Step 4: Execute the port-level RWA algorithm. Execute the shortest path algorithm to find the shortest path in all port-level auxiliary graphs, such as... Figure 6As shown in (c), the path in wavelength layer 2 is the shortest path in all port-level auxiliary graphs. If the shortest path exists, we establish an optical path for the request and terminate the RWA process. If the shortest path does not exist, we block the request and terminate the RWA process.

Claims

1. A p-RWA method based on auxiliary graphs, characterized in that, The method includes the following steps: Step 1, Generating the auxiliary graph: For each wavelength supported by each optical fiber in the network Three auxiliary graphs with different information granularities were constructed for each: a link-level auxiliary graph, a direction-level auxiliary graph, and a port-level auxiliary graph. The total number of wavelengths on a single optical fiber; The link-level auxiliary graph uses the entire optical node as the vertex and contains only link status information; The directional auxiliary graph uses the physical direction of the OXC as its vertex and includes link state information and some OXC switching state information. The port-level auxiliary graph uses the input / output physical ports of the OXC as vertices and includes link status information and all OXC switching status information. Step 2, execute the link-level RWA algorithm: Search for the shortest available path in the link-level auxiliary graph corresponding to all wavelengths; If a feasible shortest path is found, an optical path is established based on that path and the RWA process is terminated immediately. If insufficient end-to-end link resources result in no connected path being found on any wavelength plane, the service request is directly deemed blocked and the entire RWA process is terminated immediately. Step S3 is executed only if the shortest path found in the link-level auxiliary graph of at least one wavelength plane is infeasible due to switching congestion within the OXC node. Step 3, execute the directional RWA algorithm: Search for the shortest available path in the directional auxiliary graphs corresponding to all wavelengths; If a feasible shortest path is found, an optical path is established based on that path and the entire RWA process is terminated immediately. If the lack of end-to-end link wavelength resources results in no connected path being found on any wavelength plane, the service request will be directly determined to be blocked and the entire RWA process will be terminated immediately. Step S4 is executed only if the shortest path found in the directional-level auxiliary graph of at least one wavelength plane is not feasible due to internal switching blockage of the OXC; Step 4, execute the port-level RWA algorithm: Search for the shortest available path in the port-level auxiliary graphs corresponding to all wavelengths; If a feasible shortest path is found, an optical path is established based on that path and the RWA process is terminated. If no feasible path can be found in the port-level auxiliary graphs of all wavelength planes, the service request is deemed blocked and the RWA process is terminated.

2. The auxiliary graph based p-RWA method of claim 1, wherein, The specific construction methods for the three auxiliary graphs in step S1 are as follows: The link-level auxiliary graph abstracts each optical node in the multi-fiber network as a vertex in the graph. If there is an idle channel on the corresponding wavelength in any optical fiber between two adjacent nodes, an edge is established between the corresponding vertices of the two nodes. The directional auxiliary graph abstracts each physical direction of each OXC node as an independent vertex in the graph. Inside the node, if there is an available internal switching channel between the input and output directions at the current wavelength, a directed edge is established between the corresponding vertex of the input direction and the corresponding vertex of the output direction. Outside the node, if there is an idle channel in the output / input fiber corresponding to a certain direction at the corresponding wavelength, an edge is established between the corresponding directional vertices of adjacent nodes. The port-level auxiliary graph abstracts each input port and each output port of each OXC node as an independent vertex in the graph. Inside the node, if there is an available internal switching channel between an input port and an output port at the current wavelength, a directed edge is established between the vertex corresponding to the input port and the vertex corresponding to the output port. Outside the node, if there is an idle channel in the optical fiber connected to a port at the corresponding wavelength, an edge is established between the corresponding port vertices of adjacent nodes.

3. The auxiliary graph based p-RWA method of claim 1, wherein, The progressive search method is as follows: The link-level RWA algorithm has a higher priority than the direction-level RWA algorithm, and the direction-level RWA algorithm has a higher priority than the port-level RWA algorithm. The next-level RWA algorithm is only started when the previous-level algorithm fails to establish an optical path due to internal OXC blocking.

4. The auxiliary graph based p-RWA method of claim 1, wherein, Steps S2 and S3 also include an early termination mechanism, specifically manifested as follows: When the link-level or directional RWA algorithm finds a feasible shortest path, it establishes an optical path and immediately terminates the entire RWA process; when the link-level or directional RWA algorithm detects that a request is blocked due to insufficient link resources, it blocks the request and immediately terminates the entire RWA process.

5. The auxiliary graph based p-RWA method according to claim 1 or 4, c h a r a c t e r i z e d by, Both steps S2 and S3 include an early termination mechanism based on the identification of the cause of the blockage, specifically manifested as follows: During the execution of link-level RWA or direction-level RWA algorithms, the two reasons that cause path search failure are distinguished in real time: The first type of failure is due to insufficient link wavelength resources on the end-to-end path. For this type of failure, the service request is directly blocked and all subsequent steps are terminated immediately. The second type of failure is due to internal switching blockage within the OXC node. Only for this type of failure is it allowed to proceed to the next priority RWA algorithm step.

6. The auxiliary graph based p-RWA method of claim 1, wherein, The partial OXC switching status information refers to information on whether there is an available internal switching channel between different physical directions; the complete OXC switching status information refers to information on whether there is an available internal switching channel between any specified input port and any specified output port.

7. The auxiliary graph based p-RWA method of claim 1, wherein, The OXC includes any one of the HIER structure OXC, FLEX structure OXC, or ring interconnect structure OXC; the division method of "physical direction" in the direction-level auxiliary diagram and the granularity and mapping relationship of "port" in the port-level auxiliary diagram are adapted and adjusted according to the actual deployed OXC internal switching architecture.

8. A progressive first-hit routing and wavelength allocation device based on an auxiliary graph, characterized in that, include: The auxiliary graph generation module is used to generate auxiliary graphs with three different information granularities for each wavelength plane: link-level auxiliary graph, direction-level auxiliary graph, and port-level auxiliary graph. The link-level RWA processing module is used to perform shortest path search in the link-level auxiliary graph, and decide whether to establish an optical path, directly block the request, or trigger the direction-level RWA processing module based on the search results and the cause of the blockage. The directional-level RWA processing module is used to perform shortest path search in the directional-level auxiliary graph, and decide whether to establish an optical path, directly block the request, or trigger the port-level RWA processing module based on the search results and the cause of the blockage. The port-level RWA processing module is used to perform shortest path search in the port-level auxiliary graph and decide whether to establish an optical path or block the request based on the search results. Both the link-level RWA processing module and the directional RWA processing module include a blocking cause identification unit, used to distinguish between blocking caused by insufficient link resources and infeasibility caused by internal OXC switching blocking.

9. A computer-readable storage medium having stored thereon computer program instructions, wherein, When the computer program instructions are executed by the processor, they implement the steps of the method as described in any one of claims 1 to 7.

10. An optical network control system comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

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