CN100369432C - A Spanning Tree Topology Abstraction Method Applied to Asymmetric Networks - Google Patents
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Abstract
The present invention discloses a method which is applied to spanning tree topology abstract in an asymmetrical network, which carries out a triangular matrix method (TM) of the topology abstract for state parameters of an asymmetrical link. The method has the steps: by an original topology, a complete connected graph abstract topology M of one boundary node is established; undirected complete connected graph abstract topologies (Mu and Ml) are established based on the complete connected graph abstract topology M; minimum spanning tree topologies of Mu and Ml are calculated, which are respectively expressed as Tu and Tl; a directed tree abstract topology T<1>u is established based on the Tu, and each undirected logical link on the Tu is replaced as a pair of directed logical links; three tree abstract topologies (T<1>u, Tu and Tl) are obtained, and the three tree abstract topologies are published to other route domain nodes of the network. All of the asymmetrical information is contained in the tree abstract topologies, and the distortion can be effectively reduced after topology abstract.
Description
Technical Field
The present invention relates to a topology abstraction method applied in an asymmetric network, and more particularly, to a topology abstraction method applied in an asymmetric automatically switched optical network in the communication field.
Background
In order to realize the expandability and the safety of the network, a layered multi-domain network structure is adopted in both an IP network, an ATM network and an Automatic Switched Optical Network (ASON) which appears in recent years. In a hierarchical network, topology information for each routing domain is first abstracted by a particular topology abstraction algorithm to be published to other routing domains in the network. In this way, each routing domain only maintains the detailed topology information of itself and the abstract topology information of other domains, thereby greatly reducing the amount of information required to be stored and distributed in the network. However, since the abstract topology information is often not accurate enough, the "feasible" route selected according to the information cannot actually meet the Quality of Service (QoS) requirement of the traffic. A well-behaved topology abstraction algorithm attempts to find the best balance point between the two.
The topology abstraction process typically involves two steps. Step 1 is called as 'full connected graph construction', and a full connected graph abstract topology of boundary nodes is formed by constructing a logic link between each pair of boundary nodes. Each logical link is associated with one or more quality of service level parameters according to different quality of service level routing algorithms. The quality of service level parameter may be additive, such as latency; or may be restrictive such as bandwidth. These parameters are derived from the quality of service class parameters of the paths between the border nodes on the original topology. Step 2 is called "full connectivity graph compression", and the full connectivity graph abstract topology is further compressed into a more sparse topology, such as a tree or star topology. The abstracted topology and its corresponding quality of service class parameters are published to other routing domains. If a node in a routing domain receives a tree or star topology of another routing domain, it needs to first decode the topology into a full connectivity graph topology before it can route on the topology.
In recent years, most of the research on the topology abstraction problem takes a symmetric network as a research object. However, asymmetric networks are closer to the actual network model and the topology abstraction problem of asymmetric networks is much more complex than that of symmetric networks. There is a document that replaces two reverse links between each pair of edge nodes in an asymmetric network with a non-directional link, converts the asymmetric network into a symmetric network, and applies a topology abstraction method for the symmetric network thereto. This method, although simple, completely loses the asymmetric information in the original network.
An abstract model: a domain is represented by a three-dimensional vector (V, B, E), where V is a set of nodes within the domain, B V is a set of nodes at the boundary of the domain, and E is a set of bidirectional links connecting nodes in V. Full connectivity graph for this domain abstracts the topology with (B, L) m ) Is represented by the formula, wherein L m For the logical links between each pair of border nodes. There is a corresponding weight for each logical link. This weight is equal to the weight of the shortest path between logical link boundary nodes in the original topology.
In the case of using the minimum spanning tree abstraction method, the cells with O (| B $) 2 ) The full connectivity graph abstract topology of the logical links will be further abstractly compressed into a minimal spanning tree abstract topology with O (| B |) logical links. With (B, L) t ) Representing the compressed topology, where L t Is a set of logical links. Due to L t L m With L m-t Represents L m -L t The set of logical links in (1). Wherein the set L m The cardinality of (a) is | B | (| B | -1)/2, L t Radix of | B | -1,L m-t Has a cardinal number of 1/2|B 2 -3/2|B | +1. When the spanning tree topology is decoded at the receiving end to be a fully connected graph topology, the logical link (u, v) belongs to L t The weight value of can be directly expanded from the spanning treeDerived from the mapping table, and the logical link (u, v) belongs to L m-t The weight of the user cannot be directly obtained. The following theorem can be derived:
theorem 1: for any logical link (u, v) ∈ L m-t The weight w (u, v) of the link satisfies the following inequality:
wherein P is uv Is the only path on the minimum spanning tree for an end node of a logical link (u, v).
The lower bound of w (u, v) can be derived from the properties of the minimum spanning tree, while the upper bound of w (u, v) is derived from the fact that the weight of the logical link in the fully-connected graph abstract topology is equal to the shortest path weight in the original topology. Therefore, each edge in the abstract topology also called a full connected graph satisfies the rule of triangle inequality, that is, in the abstract topology of the full connected graph, there is a triangle-like graph composed of three undirected links, where the sum of the weights of any two undirected links is greater than the weight of the third undirected link.
Another document proposes that when the minimum spanning tree topology is decoded as a fully-connected graph abstract topology, the logical links (u, v) E L can be derived from the theorem m-t The upper or lower bound of the weight is used as the estimated weight of these logical links. However, this method introduces a large weight distortion.
Some documents propose a single-point approximation algorithm (SP) which can reduce distortion to a large extent. By w lb (u, v) represents the lower bound of the link (u, v) weight, w ub (u, v) represents the upper limit, w * (u, v) represents the decoded estimate, then the SP algorithm steps are:
(1) Calculating a floating point value dp according to equation (2) * ：
(2) This floating point value is published to other domains along with the abstract topology, and when the spanning tree topology is decoded to the fully connected graph topology, the estimated weight of the link is calculated using equation (3).
w * (u，v)＝w lb (u，v)+dp * ×(w ub (u，v)-w lb (u，v))(3)
Let w (v, u) and w (u, v) be the weights of two links (v, u) and (u, v) in opposite directions between a pair of nodes. Then ρ uv = w (u, v)/w (v, u) asymmetry factor for node pairs u and v. ρ = max (u，v)∈E (ρ uv ) Is an asymmetric constant for domain G (V, B, E). Document [1]]The AS method uses a non-directional link between each pair of edge nodes to replace the original two reverse links, and the weight of the non-directional linkHowever, this method has two problems. First, the asymmetry information of the link is completely lost. Secondly, because the weight in the full-connected graph abstract topology is obtained by calculating the shortest path weight from the original topology, each edge of the full-connected graph abstract topology meets the triangle inequality. The minimum spanning tree topology obtained from the fully connected graph topology can obtain the upper limit of the link weight according to the property. However, some links of the symmetric graph obtained by the AS algorithm may lose the triangle inequality property, so that the SP algorithm cannot be applied because the upper limit of the weight cannot be obtained.
Disclosure of Invention
The invention aims to solve the topology abstraction problem in the automatic switching optical network with the layered multi-domain structure and the distortion problem generated by asymmetric link state parameters in the network; the tree topology abstraction method of the triangular matrix type is provided, the space complexity after the topology abstraction is still O (| B |), and the information accuracy is guaranteed to the maximum extent.
The technical scheme adopted by the invention to realize the technical purpose is as follows.
A spanning tree topology abstract method applied to an asymmetric network forms a fully connected graph abstraction topology of a boundary node by constructing a logical link (u, v) between each pair of boundary nodes in an original topology
It is characterized in that: the step of generating the topological abstract of the tree is,
step 2, constructing an undirected fully-connected graph abstract topology M u And undirected fully-connected graph abstract topology M l Respectively, denoted as a minimum spanning tree topology T u And a minimum spanning tree topology T l For logical links not on the two minimum spanning tree topologies, a lower bound on their weights can be obtained;
The invention is in the abstract topology of the full connectivity graph
In the logical link, the direction is pointed from small to large according to the node number and is constructed in the undirected fully-connected graph abstract topology M u In the method, the direction is pointed from large to small according to the node number and is constructed in the undirected full-connectivity graph abstract topology M l In (1).
The invention discloses a full connectivity graph abstract topology
The weight value of each logic link in the network is respectively connected with the undirected full connectivity graph abstract topology M u Undirected fully connected graph abstract topology M l Corresponding respective logic inThe weights of the edit links are equal in value.
The minimum spanning tree topology T of the invention u Minimum spanning tree topology T l The weight value of each logical link is respectively connected with the undirected full connectivity graph abstract topology M u Undirected fully connected graph abstract topology M l Middle pairThe weights of the corresponding logical links are equal in value.
The invention relates to a directed tree abstract topology
The weight value of each logic link in the network is respectively connected with the abstract topology of the full connectivity graph
The weights of the corresponding logical links in the group are equal.
The invention provides the abstract topology of the full connectivity graph
Wherein a logical link is not included in said directed tree abstract topologyMinimum spanning tree topology T u And a minimum spanning tree topology T l In any of the above, the upper and lower bounds of the logical link weight may then be obtained by,
step 2, if the number of the node u is less than the number of the node v, the lower bound of the weight can be obtained by generating a tree topology T according to the minimum u Obtaining a logic link weight value with the maximum weight value on the unique path between the upper node u and the node v;
When the only path between two end nodes of the logical link (u, v) on the spanning tree abstract topology has only one middle node, the invention sets the third node except the node u and the node v as the node r, and can obtain the upper bound and the lower bound of the weight of the logical link (u, v) and the logical link (v, u) according to the following steps, wherein the serial number of the node r is less than the serial numbers of the node u and the node v,
step 2, when the number of the node u is smaller than the number of the node v, comparing the weight value of the logical link (r, u) with the weight value of the logical link (r, v), wherein the large weight value is the lower bound of the weight value of the logical link (u, v);
and 3, when the number of the node u is larger than the number of the node v, comparing the weight value of the logical link (r, u) with the weight value of the logical link (r, v), wherein the large weight value is the lower bound of the weight value of the logical link (v, u).
Once the upper and lower bounds of the logic link weight lost in the process of generating the tree topology abstraction are obtained, the single-point approximation algorithm can be applied to decode.
Assuming that the number of node u is less than node v, i.e., u < v, then the topology M is abstracted for undirected fully-connected graphs u And M l Respectively have the following components in percentage by weight,
wherein w Mu (u, v) and w Ml (u, v) is allocated to M u And M l Of each of the undirected links (u, v). Let M u The decoded link weight is denoted as w Mu * (u, v), and M l The decoded link weight value is denoted as w Ml * (u, v). Due to full connectivity graph abstract topologyThe direction of each link has been implied at M u And M l Thus can obtain
The decoded weight of each link in the system is as follows:
due to M u And M l The above partial logical links do not satisfy the triangle rule, but the SP algorithm cannot be applied to M u And M l The above.
Directed fully-connected graph abstract topology
The weight value of each directed logical link (u, v) in (b) is represented as w (u, v).
Based on T u Constructed directed tree abstract topology
Will T u Each undirected logical link in the above is replaced by a pair of directed logical links, and the weight of each directed logical link is as follows:
this method of dealing with asymmetric networks is called a Triangular Matrix (TM) method because it requires the acquisition of the upper and lower triangular matrices of a directed graph.
Due to the adoption of the measures, the invention has the following advantages and effects: the invention can carry out topology abstraction on the state parameters of the asymmetric links, so that all asymmetric information can be contained in the abstract topology; the accuracy of the information is guaranteed to the maximum extent; limiting the spatial complexity to O (| B |); the simulation result shows that the performance of the method is greatly superior to that of the traditional asymmetric network topology abstract method (AS).
Drawings
FIG. 1 is a schematic diagram of a fully connected graph abstract topology of a symmetric network;
FIG. 2 is a schematic diagram of a fully connected graph abstract topology of an asymmetric network;
FIG. 3 is a non-directional fully-connected graph M of an embodiment of the invention u A schematic diagram of (a);
FIG. 4 is a non-directional fully connected graph M of an embodiment of the present invention l A schematic diagram of (a);
FIG. 5 is a minimum spanning tree topology T of an embodiment of the present invention u A schematic diagram of (a);
FIG. 6 is a minimum spanning tree topology T of an embodiment of the present invention l A schematic diagram of (a);
FIG. 7 is a directed tree abstraction topology of an embodiment of the present invention
A schematic diagram of (a);
FIG. 8 is a graph of number of false receptions versus delay constraint;
FIG. 9 is a graph of a number of false rejects versus a delay constraint;
fig. 10 is a graph of number of errors (rejected + received) versus delay constraint.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
In fig. 1, a fully connected graph abstract topology of a symmetric network is shown, with 3 nodes and 3 undirected links, with shortest path weights between nodes of 1 and 2, 10 between nodes 2 and 3, and 20 between nodes 2 and 3, respectively.
In FIG. 2, a full-connectivity abstract topology of an asymmetric network is shown, in which a logical link is constructed between each pair of boundary nodes in the original topology to form a full-connectivity abstract topology of boundary nodes
Fully connected graph abstract topology
The weight of the six logical links on the node is W (1,2) =10, W (1,3) =10, W (2,1) =1,W (3,1) =10, W (2,3) =10, W (3,2) =20.
Compared with a symmetric network, the asymmetric network increases the information quantity, not only doubles the weight number of the associated links with each node pair, but also increases the direction information of the links corresponding to each weight. Thus, the amount of information in an asymmetric network is 3 times that in a symmetric network.
In a symmetric network, only 1 integer 1 representing the link weight needs to be associated with node pairs 1 and 2. However, in an asymmetric network, a three-dimensional vector (1, 10,0) needs to be associated between node pair 1 and 2. Where 1 and 10 represent the weight of the link, and 0 indicates that a greater weight is associated with a link pointing from a small numbered node to a large numbered node.
The steps of generating the tree topology abstraction refer to fig. 3, fig. 4, fig. 5, fig. 6, fig. 7.
Obtaining a full connectivity graph abstract topology from an original topology
The spanning tree topology abstraction step is as follows:
Constructed undirected fully-connected graph abstract topology M u And M l The rule that the partial logic links conform to is that all the edges in the abstract topology of the full connectivity graph meet the rule of a triangle inequality.
In fig. 3 and 4, the weight of each logical link is:
fully connected graph abstract topology
The weight of each logic link in the network is respectively compared with the abstract topology M of the undirected full connectivity graph u 、M l The weights of the corresponding logical links in the network are equal in value.
Step 2, respectively constructing M u And M l Minimum spanning tree topology T of u And T l 。
In the case of figures 5 and 6 of the drawings,
minimum spanning tree topology T u 、T l The weight of each logical link is respectively compared with the undirected full connectivity graph abstract topology M u 、M l The weights of the corresponding logical links in the group are equal in value. For logical links that are not on both minimum spanning tree topologies, a lower bound on their weights may be obtained.
In FIG. 7, there is a directed tree abstraction topology
The weight value of each logic link in the network is respectively abstracted with the full connectivity graph
The weights of the corresponding logical links in the group are equal. The weight value of each logical link is:
And the other routing domain nodes which receive the abstract topology obtain the upper and lower weight bounds of the logical links (2,3) and (3,2) according to the following steps.
Step 4.1, the weight values of the logical links (2,3) and (3,2) whose upper bounds are the unique paths between node pair 2 and 3 and node pair 3 and 2 are obtained according to FIG. 7,
w ub (2，3)＝w(2，1)+w(1，3)＝1+10＝11，
w ub (3，2)＝w(3，1)+w(1，2)＝10+10＝20。
step 4.2, because 2 is less than 3, the lower bound of the weight of the link (2,3) obtained according to fig. 5 is the link weight with the maximum weight on the unique path between nodes 2 and 3,
w lb (u，v)＝max(w(1，2)，w(1，3))＝max(10，10)＝10。
step 4.3, since 3 is greater than 2, the weight lower bound of the link (3,2) obtained according to fig. 6 is the link weight with the largest weight on the unique path between nodes 3 and 2,
W lb (3，2)＝max(w(2，1)，w(3，1))＝max(1，10)＝10。
once the upper and lower bounds of the logic link weight values lost in the tree topology abstraction process are obtained, a single-point approximation algorithm can be applied for decoding.
The performance of the proposed TM method was analyzed by simulation and compared to the AS method proposed in the above-mentioned document. In the simulation, each service request is assumed to have a time delay constraint, and the compared performance indexes are the number of false rejects (w.r.n.), the number of false accepts (w.a.n.), and the number of false rejects (r. + a.) n in the network. The false rejection means that when the estimated delay value of the path is smaller than the delay constraint of the service request and the actual delay value is larger than the delay constraint of the service request, the service request is accepted by the source node, but is finally rejected because it is not feasible in the path establishment process. The false acceptance means that when the estimated delay value of the path is greater than the delay constraint of the service request and the actual delay value is less than the delay constraint of the service request, the service request can be actually supported but rejected by the source node. In the simulation, the false rejection number and the false acceptance number of all service requests after reaching the network are recorded and added to compare the comprehensive performance of the two algorithms.
A randomly generated 300-node network topology was used in the simulation. The network comprises 10 domains, and each domain comprises 30 nodes on average. For each bidirectional link, an integer between 1 and 5 and an integer between 15 and 20 are randomly generated as the delay values of the two directional links. The link direction corresponding to each delay value is randomly selected. The connection arrival rate of the network is poisson distribution, and the connection duration is exponential distribution. The delay constraint for the service request is increased from 4 to 25 at a rate of step 3.
In fig. 8, 9 and 10, the false acceptance number, false rejection number, and false (reject + accept) number of the two abstract algorithms are shown, respectively, where the data bar with horizontal fill lines represents the TM method and the data bar with diagonal fill lines represents the AS method. AS can be seen from the three figures, TM is much smaller than AS regardless of the performance index. This is because the TM algorithm completely preserves the network's asymmetry information by constructing three spanning tree abstract topologies, whereas the AS algorithm completely discards this information. Moreover, partial links in the abstract topology of the symmetrical fully-connected graph constructed by the AS algorithm lose the triangle inequality property, so that the performance of the SP optimization algorithm is influenced, and the TM algorithm thoroughly solves the problem. The asymmetrical network topology abstract method provided by the patent can greatly reduce the number of routing decision errors caused by inaccurate topology information of the source node and improve the performance of the network.
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| US20050187946A1 (en) * | 2004-02-19 | 2005-08-25 | Microsoft Corporation | Data overlay, self-organized metadata overlay, and associated methods |
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