Application of Rough Set for Routing Selection Based on OSPF Protocol

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1 Application of Rough Set for Routing Selection Based on OSPF Protocol Yanbing Liu 1,2, Hong Tang 1, Menghao Wang 1, and Shixin Sun 2 1 Chongqing University of Posts and Telecommunications, Chongqing , P.R. China 2 School of Computer Science, UEST of China, Chengdu , P.R. China liuyb@cqupt.edu.cn Abstract. Attribute reduction is one of the most important issues and the focus of the research on efficient algorithms in rough sets. This paper focus on the routing selection algorithms and application used to compute QoS routes in OSPF protocol that are based on the rough set, which the attribute-value system about the link of network is created from the network topology. The use of rough set method can simplify enormous irregular link QoS attribute and classify the link with the link-status attribute. A illustrative example is employed to show the feasibility and effectiveness that the most excellent routing attribute set is obtained by rough set theory. 1 Introduction IP routing protocols have long been an essential element of IP networks for many years. Recently, this technology has been the focus of new development, as routing has evolved to handle the needs of next generation networks. Traditional IP routing protocols have therefore been substantiallyextendedinanumberof areas. Data Connection provides a full range of high-function portable Unicast IP Routing software products, including BGP, OSPF and RIP for both IPv4 and IPv6 networks. With the development of network and application, the routing needs to satisfy the QoS (Quality of Service) demand. However, because the complication of many solving schemes to QoS Routing is NPC (nondeterministic polynomial time completeness), the node can t maintain the network information timely with the continual change of network state [1][2]. In order to adapt new demand on computer network, it is imperative to apply new feasible and efficient routing scheme to meet increasing demand on network. The theory of rough sets has recently emerged as another major mathematical approach for managing uncertainty that arises from inexact, noisy, or incomplete information. Rough sets can be used for feature reduction, where attributes that do not contribute towards the classification of the given training data can be identified and removed and relevance analysis, where the contribution or significance of each attributes is assessed with respect to the classification task. The problem of finding the minimal subsets (reductions) of attributes that can describe all D. Śl ezak et al. (Eds.): RSFDGrC 2005, LNAI 3642, pp , c Springer-Verlag Berlin Heidelberg 2005

2 Application of Rough Set for Routing Selection Based on OSPF Protocol 655 of the concepts in the given data set is NP-hard. However algorithms to reduce the computation intensity have been proposed. In one method, for example, a discernibility matrix is used to store the differences between attribute values for each pair of data samples. Rather than searching on the entire data set, the matrix is instead searched to detect redundant attributes. The work presented in this paper is to decide the link-rank by a series of the link-state attributes. The application of the rough set theory can solve this problem successfully. Usually, the link is classified by many QoS parameters such as link propagation delay, link available bandwidth, link jitter, possibility of connection and hop-counts et al. Then OSPF can select the best path with the link rank. The instance presented in this paper indicates that the reduction algorithm based on rough set offers an attractive approach to solve the feature subnet selection problem in routing-reduction table. The remaining of this paper is organized as follows. Section 2 describes the related knowledge about OSPF. Application of rough set theory and the algorithm to select the best path are presented in Section 3. Section 4 shows a case to verify the algorithm. A conclusion is drawn in Section 5. 2 Related Knowledge 2.1 OSPF OSPF (Open Shortest Path First) is a link-state routing protocol, which means that the routers exchange topology information with their nearest neighbors. The topology information is flooded throughout the AS, so that every router within the AS has a complete picture of the topology of the AS. This picture is then used to calculate end-to-end paths through the AS, normally using a variant of the Dijkstra algorithm. Therefore, in a link-state routing protocol, the next hop address to which data is forwarded is determined by choosing the best end-to-end path to the eventual destination. OSPF bases its path descriptions on link states that take into account additional network information. OSPF also lets the user assign cost metrics to a given host router so that some paths are given preference. OSPF supports a variable network subnet mask so that a network can be subdivided. The main advantage of a link state routing protocol is that the complete knowledge of topology allows routers to calculate routes that satisfy particular criteria. 2.2 OSPF Routing Algorithm OSPF uses a link-state algorithm in order to build and calculate the shortest path to all known destinations. The algorithm by itself is quite complicated. The following is a very high level, simplified way of looking at the various steps of the algorithm[11]: 1. Upon initialization or due to any change in routing information, a router will generate a link-state advertisement. This advertisement will represent the collection of all link-states on that router.

3 656 Y. Liu et al. 2. All routers will exchange link-states by means of flooding. Each router that receives a link-state update should store a copy in its link-state database and then propagate the update to other routers. 3. After the database of each router is completed, the router will calculate a Shortest Path Tree to all destinations. The router uses the Dijkstra algorithm to calculate the shortest path tree. The destinations, the associated cost and the next hop to reach those destinations will form the IP routing table. 4. In case no changes in the OSPF network occur, such as cost of a link or a network being added or deleted, OSPF should be very quiet. Any changes that occur are communicated via link-state packets, and the Dijkstra algorithm is recalculated to find the shortest path. The OSPF routing algorithm is based on Dijkstra shortest path algorithm. The term Shortest pat is inaccurate because what we really want to find is the Optimum path. To find the optimum path in a network means to find a path with a minimal cost, considering factors like time, money and quality of the received data. The route is not chosen only by the cost, because in every network many constraint-attributes must be considered[11]: - Cost-based routing metrics. - Possibility of connection: Usually in traditional network, the possibility of link connection is high and this metric can be ignored. But in wireless network, it is a very important metric. - Link available bandwidth: As mentioned earlier, we currently assume that most QoS requirements are derivable from bandwidth. We further assume that associated with each link is a maximal bandwidth value, e.g., the link physical bandwidth or some fraction thereof that has been set aside for QoS flows. - Link propagation delay: This quantity is meant to identify high latency links, e.g., satellite links, which may be unsuitable for real-time requests. - Link jitter: This quantity is used as a measure of the change of link delay. A path with a smaller jitter is more stable and typically preferable. - Failure probability: failure probability of a single edge, the number of edges on each path, and the number of all edges shared among paths. The main objective of QoS-based routing is to realize dynamic determination of feasible paths; QoS-based routing can determine a path, from among possibly many choices, that has a good chance of accommodating the QoS of the given flow. 2.3 Related Rough Set Theory Rough set theory is a mathematical approach to imprecision, vague and uncertainty in information analysis [3]. It can be applied to find reduction. An attribute-value system IS is a quadruple (U, C D, V, f), A = C D is the set

4 Application of Rough Set for Routing Selection Based on OSPF Protocol 657 of all attributions which are further classified into two disjoint subsets: the condition attributes C = {a i i =1,,m} and the decision attribution D = {d}, V = a A V a is a set of attribute values, where U = {x 1,x 2,,x n } denotes the set of all objects in the set of all objects in the dataset, V a is the domain of attribute a. a i (x j ) denotes the value of x j on the attribution a i. f : U A V is an information function, which appoints the attribute value of every object x in U. A discernibility matrix is a n n matrix in which the classes are diagonal. In the matrix, the (condition) attributes which can be used to discern between the classes in the corresponding row and column are inserted.the information system s discernibility matrix M(C D (i, j)) with entry C D (i, j) is defined as {a A a(x i ) a(x j )} if d(x i ) d(x j ), φ otherwise, where i, j =1,,n. ThecoreattributesetCore(A) can be defined as the set of all single element where C D (i, j) = 1 [4,5,6]. 3 Routing-Reduction Algorithm to Select the Best Path This paper makes the elucidation of the algorithm to classify link-rank to select the best path. 1) From the historical data of routing table and the QoS information about the links, the attribute-value system about the links can be built. 2) Then we can draw the matrix about the information system and can conclude the routing-reduction table [7,8,9,10]. Step 1: RT = φ, Core = φ; Step 2: for every b A, computing the equivalent class U/b; Step 3: construct discernibility matrix M(A) ={C D (i, j)} n n,where1< i, j < n. Step 4: Do loop, C D (i, j) M(A), if ( C D (i, j) == 1) then Core = Core {C D (i, j)}; Step 5: RT = Core; Step 6: Core, WesetC D (i, j) =φ when a C D (i, j). 3) The decision attribute with excellent routing attributes can be concluded from the routing-reduction table RT. 4) With the knowledge of OSPF, the best path can be obtained. The link state algorithm presented below is known as Dijkstra s algorithm. Initialization: N = set of nodes in the graph; U={source node} for all nodes v if v adjacent to U then D(v) = c(u, v) else D(v) = Infinity

5 658 Y. Liu et al. Loop find w not in N such that D(w) is a minimum add w to N for v adjacent to w and not in N update D(v): D(v) = min{ D(v), D(w)+c(w, v) } until all nodes in N. c(i, j) is the weight of the decision attributes of the link from node i to node j. D(v) is cost of the path from the source node to destination v that has currently (as the iteration of the algorithm) the least cost with the most excellent routing attribute. N is set of nodes whose least-cost path from the source is definitely known. With the help of rough set theory, the simplification of the routing-reduction table is to simplify the condition attributes in routing-reduction table, and after that the routing-reduction possesses the ability of the routing-reduction table before simplification, but possesses more important condition attributes. 4 A Case Analysis Let us take a routing topology of network, which has ten nodes. Figure 1 is a network topology used to illustrate the above arithmetic. The number on the link denotes the link-number (link No.). Routing is determined by the link s QoS attribution parameters, such as: bandwidth, propagation delay, connectionfailure possibility and bit error ratio and so on. All the values in the table 1 denote the w eight (measure) of the attributes that learn from historical records in router, which represents an equivalence class in routing table. Part of the routingattribute conditions in network can be defined as information table IS=(U, C {d},v,f), C = {a 1,a 2,a 3,a 4 } is a routing attribute set, in which a 1 represents the bandwidth of link: 1 denotes enough, 2 denotes available, 3 denotes nonenough. a 2 represents the propagation delay of link: 1 denotes low, 2 denotes normal, 3 denotes high. a 3 represents the failure probability of link: 1 denotes low, 2 denotes normal, 3 denotes under normal. a 4 represents the bit error ratio of the link: 1 denotes low, 2 denotes acceptable, 3 denotes insufferable. The decision attribution D = {d} = {G, N, B}: G denotes good, N denotes normal, B denotes bad (each of their weight is 1,2,3, respectively). The function of the information f can expressed by the table 1. Fig. 1. The Network Topology

6 Application of Rough Set for Routing Selection Based on OSPF Protocol 659 Table 1. Information System Link No. a 1 a 2 a 3 a 4 d G(1) G(1) G(1) N(2) N(2) B(3) B(3) B(3) From Table 1, the discernibility matrix M(C D (i, j)) can be given as follow: φa 3 a 4 a 1 a 3 a 1 a 2 a 2 a 3 a 1 a 2 a 4 a 1 a 2 a 4 a 1 a 2 a 4 φ a 1 a 4 a 1 a 2 a 3 a 4 a 2 a 3 a 4 a 1 a 2 a 3 a 4 a 1 a 2 a 3 a 4 a 1 a 2 a 3 φ a 2 a 3 a 1 a 2 a 3 a 2 a 3 a 4 a 1 a 2 a 3 a 4 a 1 a 2 a 3 a 4 φ a 1 a 3 a 4 a 1 a 4 a 1 a 2 a 4 φ a 1 a 3 a 4 a 1 a 3 a 4 a 1 a 2 a 3 a 4 φ a 1 a 1 a 2 a 4 φ a 2 a 4 φ In the above matrix, C D (4, 6) =1, C D (6, 7) = 1, we can get Core(A) = {a 1,a 4 }. This means that a 1 and a 4 are the most important routing attributes. When C D (i, j) containsa 1 or a 4,thenwesetC D (i, j) =φ. A new simple matrix can be obtained: φφφφa 2 a 3 φφφ φφφ φ φφφ φφ φ φφφ φ φ φ φ φ φ φ φ φ φφφ φφ φ The reduced attribute set can be (a 1 a 2 a 4 ) (a 1 a 3 a 4 ). It means the reduction attributions can be a 1 a 2 a 4 or a 1 a 3 a 4.Wetakea 1 a 2 a 4 as an example. We find that, in the initial information table 1 there are four attributes besides the decision attribute. In general, the router record these attributes by historic data, so there are some attributes that are dispensable to Best Path. After removing the redundant attributes by rough set theory, we get the table 2. The simplification of routing- reduction attributes needn t to select all routing-reduction attributes in the condition of keeping the consistence of routing-reduction table. That is to say, attribute reduction techniques aim at finding minimal subsets of attributes, each of which has the same discriminating

7 660 Y. Liu et al. Table 2. Reduction Information System Link No. a 1 a 2 a 4 d G(1) G(1) G(1) N(2) N(2) B(3) B(3) B(3) Fig. 2. The Rank of Link power as the entire attributes. For compatible data table,the most excellent attribute set is selected by rough set theory.the links on the subnet shown Figure 1 are classified to three ranks. Based on the Dijkstra algorithm [11], we can find the best path from A to D in Figure 2 is A B C D according to the link-rank attributes. The routing path is the best on condition that bandwidth is enough and available, bit error ratio is acceptable. After some attributes of the link aren t selected, we investigate that if the condition attribute with same row can decide the same decision value as before. 5 Conclusion and Future Work In this paper, we have proposed a new alternate Best-path-finding algorithm for OSPF. The complication of traditional solving schemes to QoS Routing is NPC. In this paper, the link is classified to different ranks with rough set theory in terms of its QoS attributes, and OSPF based on QoS routing can be realized. Rough set theory can deal with the links with complicated QoS attributes, and can rapidly classify them to different ranks. OSPF based on rough set theory can select a path with the QoS parameters and can offer the QoS-based service in the Internet. The application of rough set theory greatly simplifies the implication of the algorithm. For further work, executing time analysis, when the connectivity and the diameter of graphs change, should be considered. Moreover, future tests in a real network environment should also be performed.

8 Application of Rough Set for Routing Selection Based on OSPF Protocol 661 Acknowledgement The authors would like to thank Dr. Y.Y. Yao and Dr. J.T. Yao for their help when they were in Canada. They also wish to express sincere thanks to their current and past colleagues, especially Dr. Guoyin Wang and Dr. Yu Wu, for their help and discussions. The authors thank the referees for their useful suggestions. The work is supported by the National Natural Science Foundation of China under Grant No , the Natural Science Foundation of CSTC and CQUPT under Grant No. A and the Natural Science Foundation of CQMEC under Grant No. KJ References 1. Bruno, A. (ed.): CCIE # CCIE Routing and Switching Exam Certification Guide. Digit. Libr., 1 (2003) 2. Liu, H.S., Xu, M.W., Ke, X., Cui, Y.: Research on Internetwork Routing Protocol: a Survey. Science of Telecommunications, 19 (2003) Pawlak, Z.: Rough Sets-Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, Netherlands, Li, P., Hong, Z., Saeid, N.: The Application of Rough Set and Kohonen Network to Feature Selection for Object Extraction. Proceedings of the second International Conference on Machine Learning and Cybernetics. November (2003) Crawley, E., Nair, R., et al.: RFC 2386, IETF, August (1998) 6. Apostolopoulos, G., Williams, D., Kamat, S., Guerin, R., et al.: RFC 2676, IETF, August (1999) 7. Li, Y., Xiao, Z., Liu, F.S.: Classification of clients in client relationship management base on rough set theory, Proceedings of the second International Conference on Machine Learning and Cybernetics. November (2003) Wang, Z.L., Meng, W.B., Gu, X.J., et al.: The Research of the Police GIS Spatial Data Classification Technology Based on Rough Set. Proceedings of the 4th Congress on Intelligent Control and Automation. June (2002) Zhang, Y.: Rough Set and Genetic Algorithms in Path Planning of Robot. Proceeding of Second International Conference on Machine Learning and Cybernetics, Xi an, Nov. (2003) Wang, G.Y., Yu, H., Yang, D.C.: Decision table reduction based on information entropy (in Chinese), Chinese Journal computers, 2(7) (2002)