The literature review of the clustering algorithm is written to simplify and summarise the investigation and research that has been done in the area of clustering algorithms, while the actual research includes more examinations and modifications in an attempt to employ the existing clustering methods to serve the proposed placement algorithm (see Section "5.8.2. The Design of the Peripheral Clustering Algorithm"). This review of the literature shows only an abstract of most common methods in every clustering direction and focuses on showing why the existing clustering algorithms are excluded. The conclusion summarises the literature review with adding some comparison tables for all methods. Initially, the review describes the requirements of the clustering approach which serves the proposed placement algorithm. Then, the main body of literature review displays the clustering methods as five classes (partitioning,
hierarchical, density-based, grid-based (Lu, 2003) and graph-based (Xu and
WunschII, 2005) methods). On the one hand, the first four classes are reasonably studied, however they are not useful for the proposed placement algorithm due to its intention to cluster the objects according to their similarities with the difficulty of embedding the geometrical position and balancing the clusters. On the other hand, the fifth class is intensively investigated because it relates more to the network and supports the requirements of the proposed placement algorithm. However, it does not provide the complete solution. In addition to the pre-mentioned characteristics of the presented clustering methods, it is essential to present their computation complexity which plays an important role in nominating them to be utilised in a specific implementation. Therefore, the computation complexity of most common clustering algorithms is summarised in Table 2.7:
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Finally, From the pre-mentioned information, it is possible to summarise a general comparison of advantages and disadvantages of clustering methods as shown in Table 2.8.
Clustering Method Computational Complexity References
Partitioning Relocation (K-Means) 𝑂(𝑁𝐾𝑑𝐼) (Xu and WunschII,
2005) Partitioning Relocation (CLARA) 𝑂(𝐾 40 + 𝐾 2+ 𝐾(𝑁 − 𝐾))+ (Xu and WunschII,
2005)
Partitioning Relocation (CLARANS) 𝑂(𝐾𝑁2) (Xu and WunschII,
2005)(Wang et al., 1997)
Partitioning Relocation (EM) Vary widely according
implantation of E- and M-step.
(Dempster et al., 1977)
Hierarchical clustering (Linkage) 𝑂(𝑁2) (Xu and WunschII,
2005)(Olson, 1995)
Hierarchical clustering (BRICH) 𝑂(𝑁) (Xu and WunschII,
2005) Hierarchical clustering (CURE) 𝑂(𝑁𝑠𝑎𝑚𝑝𝑙𝑒2 . 𝑙𝑜𝑔𝑁𝑠𝑎𝑚𝑝𝑙𝑒 ) (Xu and WunschII, 2005) Hierarchical clustering (ROCK) O(𝑁2 + N 𝑚
𝑚𝑚𝑎 + 𝑁2 𝑙𝑜𝑔𝑁) Where 𝑚𝑚: maximum number of neighbour. 𝑚𝑎:average number of neighbour.
(Guha et al., 2000) Hierarchical clustering (CHAMELEON) 𝑂(𝑁𝐾 + 𝑁 𝑙𝑜𝑔𝑁 + 𝐾2𝑙𝑜𝑔𝐾) (Karypis et al.,
1999)
Density-Based (DBSCAN) 𝑂(𝑁 𝑙𝑜𝑔𝑁) (Xu and WunschII,
2005)
Density-Based (OPTICS) 𝑂(𝑁 𝑙𝑜𝑔𝑁) (Patwary et al.,
2013)
Density-Based (DENCLUE) 𝑂(𝑁 𝑙𝑜𝑔𝑁) (Xu and WunschII,
2005)
Grid-Based (STING) 𝑂(𝐺𝑐)Where 𝐺𝑐:Grid cells (Wang et al., 1997)
Grid-Based (WaveCluster) 𝑂(𝑁) (Xu and WunschII,
2005)
Grid-Based (CLIQUE) Linear with number of objects,
Quadratic with the number of dimensions
(Xu and WunschII, 2005)
Graph-Based (BUBBLE
FRAMEWORK) Where O(NE): BFS computational complexity𝑂(𝐾𝐼𝑁𝐸)
(Buluç et al., 2015)
Graph-Based (Spectral Clustering) 𝑂(𝑁3) (Liu et al., 2013)
Graph-Based (Space-Filling Curves) 𝑂(𝑁 𝑙𝑜𝑔𝑁) (Luitjens et al.,
2006)
Graph-Based (CLICK) 𝑂(𝑁𝐸2/3) (Sharan and
Shamir, 2000)
Graph-Based (CAST) 𝑂(𝑁2) (Bellaachia et al.,
2002) General Notations:
N : Number of objects. E : Edges (weight/ similarity) . K : Number of clusters. d : dimensions of attributes. I : Iterations of process.
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Table 2.8: Summary of the pros and cons of each type of clustering algorithms.
Clustering Method Advantages Disadvantages
Partitioning Relocation 1) Easy to modify and implement.
1) Lacks stability and unbalanced clustering. 2) Identify a number of clusters before
clustering (bad for dynamic clustering). 3) Weak against outlier and arbitrary
shapes.
Hierarchical clustering 1) Does not need to identify the number of clusters before clustering. 2) Has dendrogram which
represents the clustering hierarchy.
1) Difficult to select correct parameters which grantee the required clustering (find balanced clusters).
2) Almost has high computational complexity.
Density-Based 1) Does not need to identify the number of clusters. 2) Can discover arbitrary
shapes.
3) Acceptable complexity.
1) Not accurate clustering and creating unbalanced clusters.
2) Quality of clustering depends on the identified threshold.
3) Not much informative therefore using an indexing technique (R*-tree).
Grid-Based 1) For clustering large dataset. 2) Can discover arbitrary
shapes resist outliers. 3) Low complexity.
1) Not accurate clustering and creating unbalanced clusters.
2) Quality of clustering depends on the grid resolution.
Graph-Based
Most of them modified to support geometrical attributes and graph edges which are needed in the clustering requirements of the proposed placement algorithm.
Driven by different classes and has different characteristics.
Graph-Growing Methods
(Bubble Framework)
1) Considering the nodes and links in clustering.
1) Beginning K nodes should be well
distributed over the graph, while controllers positions consternate in the centre of graph.
Flows Method 1) Maximize reliability. 1) Used as subroutine inside another
algorithm because it is generated unbalance clusters.
Spectral Partitioning
Methods 1) Using the nodes connectivity to cluster the graph.
1) It can only partition the graph into four or eight clusters.
2) Cannot guarantee a balance clustering. Recursive Graph
bisection (RGB) Method
1) Using the nodes connectivity to cluster the graph.
1) Can only create 𝟐𝒌 balanced clusters,
where k=1,2,3...etc. Geometric-Partitioning
Methods 1) Utilize the geometrical attribute of nodes in clustering.
1) Cannot produce the required clustering: A) RCB only 𝟐𝒌 clusters.
B) Space-filling: Not accurate clustering. 2) Does not considering the connectivity of the graph nodes.
Gene Expression Data
Clustering 1) The nodes (genes) similarities are represented as weighted edges.
Page | 37 As demonstrated in the literature review of the clustering algorithm and previous tables there is no single clustering algorithm which could partition according to the geographical location and create balanced clusters of connected nodes in low computational complexity.
In addition to the review of clustering algorithms that are presented in section 3.3, the literature relates to the placement algorithms in section 3.2 showing some research that exploits many clustering algorithms to generate controllers domains, which are displayed in Table 2.9.
The studies presented in the table perform a different type of controller placement, however, their clustering algorithms encounter the problem of high computational complexity and cannot guarantee balanced clusters.
No. Research Clustering algorithm 1 (Zhang et al., 2011) Minicut clustering
2 (Xiao et al., 2014)
(Xiao et al., 2016) Spectral clustering K-self-adaptive clustering
3 (Yao et al., 2014) Capacitated K-center
4 (Aoki et al., 2015) Minimum cut clustering Conductance clustering Distance-k cliques clustering
5 (Aoki and Shinomiya,2015) Conductance clustering, Spectral clustering,
Betweenness centrality clustering Repeated bisection clustering
6 (Liu et al., 2016) Reliability Factor (K-Mean)
7 (Sanner et al., 2016) Adapted the K-Mean Hierarchical clustering
8 (Zhu et al., 2017) Adapted K-Mean
9 (Zhao et al., 2017) Exemplar-clustering
10 (Liao et al., 2017) Density-based clustering
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CHAPTER
THREE
OPTIMISATION METRICS OF CONTROLLER
PLACEMENT
3.1. Introduction
The previous research did not provide a view about the effect of the controller placement on the bandwidth utilisation. Also, they focus only on measuring the effect of the controller placement on the switch-controller latency and the flow-setup latency, which is just one portion (control-plane latency) of the first connection latency. According to the researcher, the optimisation ratio of the control-plane latency is not enough to determine if the achieved improvement really optimises the SD-WAN latency to a considerable level. Therefore, this research firstly examines the effect of the controller placement on the SD-WAN bandwidth using the old and proposed routing algorithm on the control packets. After that, it monitors the process of creating a full connection between two hosts in SD-WAN in order to: 1) construct the formula that contains all latencies, which are required when creating this connection; 2) measure the value of every latency component in this formula. The formula of the complete connection latency and the values of its components leads to determine the effect of the controller placement on the latency of creating a connection between two hosts in the SD-WAN.
This chapter demonstrates the mentioned objectives as three contributions, which are: the design of novel routing algorithm for SD-WAN; and the two new techniques to measure and evaluate the latency of the control plan and data plan of SD-WAN.
In the beginning, the chapter provides a complete review of the novel routing algorithm, by covering: its literature review; its design; its results; and its effect on SD-WAN bandwidth. Then, in a similar structure, the chapter explains the two different techniques, which used to measure the latency metrics of the SD-WAN. The first technique employs the computers (nodes in the data-plan) to measure the control plan latency metrics (all the components of the connection flow-setup latency) and the data plan latency metrics. While, the second technique employs the controller itself to measure the control path latency, which improves the validity of the previous
Page | 39 measurements of the first technique. Finally, performing this measurement is essential for determining the range of latency values of every latency metric. Also, it is the fundamental process for generating the formula, which is used to compute the latency metrics of the SD-WAN inside the COVN simulator.