Algorithms for the visualization and simulation of mobile ad hoc and ...

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25are not actually visualized and presented to the user as a way to help them bettercomprehend the graph data. Instead, a series of progressively simplified graphs areused to guide the positioning of the nodes in a dense, complex graph.Additional simplification algorithms have been proposed to assist in robot pathplanning [37], classifying the topology of surfaces [2], speech recognition [27], andimproving the computational complexity and memory requirements of dense graphprocessing algorithms [25, 40, 13].Simplification may also be accomplished through the use of graph clustering. Girvanand Newman [21] define one such clustering-based algorithm for better visualizingthe community structure of network graphs. The kind of graphs that they are targetingwith this method are those that would have a naturally occurring communitystructure.Rafiei and Curial [35] present another approach to visually simplifying large scalegraphs. They have developed different methods for randomly sampling a graph andusing that sampling to construct the visual representation of the graph. Their generalapproach is similar to ours in that they are using characteristics of the graphs thatfrequently occur, but differs in that they reduce their large graphs down to a handfulof nodes and then “grow” their simplified graph out from those nodes.Gilbert and Levchenko [20] focus on providing metrics for simplifying graphs thatrepresent specific network topologies. The goal of this work is to simplify and visualizecomplex network graphs while maintaining their semantic structures. Although networktopologies are certainly reasonable candidates for these visualization techniques,there are other types of graph data that could greatly benefit from simplification techniquesfor visualization, e.g. the cancer cell graphs produced by Demir et al. [9] andthe citation graphs of Chen [7]. These graphs do not consist of the same propertiesand structures as network topologies, so the metrics of [20] may not be valid for these
26types of graph data. Our goal is to develop importance metrics that are based onthe general topological properties of different types of graphs.This will allow forthe simplification and visualization of any large graph in order for the user to betterunderstand and comprehend its visual representation.3.3 Simplification AlgorithmThe first step of our simplification algorithm performs an importance metric calculationon the graph, generating a scalar weight value for every node in the graph.Several importance metrics have been implemented and evaluated, including numberof N-ring neighbors, number of shortest paths, node eccentricity, distance to thegraph’s center node(s), and distance to a leaf node. It is possible to assign importancevalues to the graph’s nodes based on external factors and calculations not related tothe graph’s topology. In this case the calculations of the first step may be skipped,since pruning (the second step) only needs some type of importance value for thenodes, regardless of its origin.The second step in the algorithm prunes the graph, removing nodes, and associatedlinks, with importance values below a user-specified threshold. If desired bythe user, nodes whose removal would change the graph’s connectivity are not prunedfrom the graph. Adjusting the threshold value allows the user to control the resolutionand complexity of the simplified graph. The higher the threshold, the morenodes are removed, and the coarser the graph becomes.The user may choose toremove nodes from the graph incrementally up to the defined threshold value. Here,a number of pruning steps are applied with successively higher threshold values upto the user defined maximum threshold.
Page 2 and 3: c○ Copyright 2009Daniel Hennessey
Page 4 and 5: iiiTable of ContentsList of Tables
Page 6 and 7: vList of Tables3.1 This table lists
Page 8 and 9: vii2.12 Figures showing OMAN networ
Page 10: ixAbstractAlgorithms for the Visual
Page 13 and 14: 2provement of the simulations. Chap
Page 15 and 16: 4on the clarity, quality, and richn
Page 17 and 18: 6(a)(b)Figure 2.1: Signal radiation
Page 19 and 20: 8(a)(b)Figure 2.3: Acceptable SINR
Page 21 and 22: 10Terrain ClassThe Terrain class is
Page 23 and 24: 12hull operation. In Figure 2.7 the
Page 25 and 26: 14TerrainResolutionChanger ClassDif
Page 27 and 28: 16objects are collapsed together in
Page 29 and 30: 18its results. An example of this w
Page 31 and 32: 20(a)(b)(c)(d)Figure 2.14: Figures
Page 33 and 34: 22library that was implemented in s
Page 35: 24connected at the outset, we ensur
Page 39 and 40: 28metric is similar to the shortest
Page 41 and 42: 30cause the graph to fragment. In o
Page 43 and 44: 323.5 Metric Performance CriteriaOn
Page 45 and 46: # Nodes200 600 1000 Citation 800 12
Page 47 and 48: 36(a)(b)(c)(d)Figure 3.3: Citation
Page 49 and 50: 38(a)(b)(c)(d)Figure 3.5: Citation
Page 51 and 52: 40(a)(b)(c)(d)Figure 3.6: Inet grap
Page 53 and 54: 42(a)(b)(c)(d)Figure 3.8: Inet grap
Page 55 and 56: 44(a)(b)(c)(d)Figure 3.10: Inet gra
Page 57 and 58: 46(a)(b)(c)(d)Figure 3.12: Inet gra
Page 59 and 60: 48sensing algorithms.This chapter i
Page 61 and 62: 50Figure 4.1: Basic diagrams compar
Page 63 and 64: 52Figure 4.3: Graph showing a compa
Page 65 and 66: 54part to the lack of a capable hig
Page 67 and 68: 56in [44]. This method breaks the s
Page 69 and 70: 58L ≤ N ′ /4 in order to provid
Page 71 and 72: 604.5.2 Test DataIn testing the imp
Page 73 and 74: 62MatlabM 512 1024 2048 409625% Ove
Page 75 and 76: 644.6.2 FFT Accumulation MethodThe
Page 77 and 78: 66CUDAN 1024 2048 4096 8192Memory T
Page 79 and 80: 684.7 ConclusionThe computational c
Page 81 and 82: 70Bibliography[1] Ravindra K. Ahuja
Page 83 and 84: 72[25] M.Y. Kao, N. Occhiogrosso, a

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