GRAPHS § § § § § § Elements – line segments in a graph that represent network components. Nodes – the terminals of the line segment. Incident node and element – if the node is terminal of the element. Graph – shows the geometrical interconnection of the elements of a network. Subgraph – any subset of elements of a graph. Path – a subgraph of connected elements with no more than two elements connected to any one node. § Connected graph – if and only if there is a path between every pair of nodes.
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and be as concise as possible. • Graph • Vertex/node (point) • Edge/arc (line) • Multiple arc • Loop Connected graph Graph where can travel from any point to any other point somehow Simple graph No multiple arcs or loops Complete graph Simple graph where every node connected to every other node by exactly one arc Network Weighted graph Degree/order of node Number of arcs joined to node • Complete simple graph with n nodes has arcs. Graphs as matrices: adjacency matrix vs. distance/weighted
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1 Multi-Channel Scheduling and Spanning Trees: Throughput-Delay Trade-off for Fast Data Collection in Sensor Networks ¨ Amitabha Ghosh‚ Ozlem Durmaz Incel‚ V. S. Anil Kumar‚ and Bhaskar Krishnamachari Two primary factors that affect the data collection rate (throughput) and timeliness (delay) are: (i) efficiency of the link scheduling protocol‚ and (ii) structure of the routing tree in terms of its node degrees and radius. In this paper‚ we utilize multiple frequency channels and design an
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Plot a graph <y> versus t (plot t on the abscissa‚ i.e.‚ x-axis). Results 2: Task 3. Plot a graph <y> versus t2 (plot t2 on the abscissa‚ i.e.‚ x-axis). The equation of motion for an object in free fall starting from rest is y = ½ gt2‚ where g is the acceleration due to gravity. This is the equation of a parabola‚ which has the general form y = ax2. Results 3: Task 4. Determine the slope of the line and compute an experimental value of g from the slope value. Remember‚ the slope of this graph represents
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uncertainty about the real value of the respective cost‚ which can take any value in the interval‚ independently from the costs associated with the other edges of the graph. Adopting the model described above‚ the classic optimality criterion of the minimum spanning tree problem (where a fixed cost is associated with each edge of the graph) does not apply anymore‚ and
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References: of Mathematics and Statistics ‚The University of Melbourne‚ 2006 [2] E. W. Dijkstra. A note on two problems in connexion with graph[J]‚ Numerische Mathematic‚ 1959 Engineering‚ Petra Christian University‚ 2005 [4] Liang Dai‚ Fast Shortest Path Algorithm for Road Network and Implementation‚ Carleton University School of Computer Science‚ 2012 [5] Xiang Liu‚ Daoxiong Gong‚ A comparative
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Origami : Kusudama. One important point to be made on assembling modular origami is the color arrangement‚ where the planar graph theory‚ polyhedral‚ and also a coloring-theorem potentially as notorious as the Four Color Theorem‚ come into play. A planar graph is‚ by definition‚ on which edges intersect at vertex points only. And in modular origami‚ such graphs are often “capped”—meaning they would have pyramid shapes capped on each face‚ resulting in a spiky surface. To find a way to color
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Algorithmic Thinking: The Key for Understanding Computer Science Gerald Futschek Vienna University of Technology Institute of Software Technology and Interactive Systems Favoritenstrasse 9‚ 1040 Vienna‚ Austria futschek@ifs.tuwien.ac.at Abstract. We show that algorithmic thinking is a key ability in informatics that can be developed independently from learning programming. For this purpose we use problems that are not easy to solve but have an easily understandable problem definition. A proper
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Pajek Program for Analysis and Visualization of Large Networks Reference Manual List of commands with short explanation version 2.00 Vladimir Batagelj and Andrej Mrvar Ljubljana‚ September 26‚ 2010 c 1996‚ 2010 V. Batagelj‚ A. Mrvar. Free for noncommercial use. PdfLaTex version October 1‚ 2003 Vladimir Batagelj Department of Mathematics‚ FMF University of Ljubljana‚ Slovenia http://vlado.fmf.uni-lj.si/ vladimir.batagelj@fmf.uni-lj.si Andrej Mrvar Faculty of Social Sciences University
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Minimum Spanning Tree MST. Given connected graph G with positive edge weights‚ find a min weight set of edges that connects all of the vertices. Minimum Spanning Tree 24 4 23 6 9 18 • • • • • • • 5 introduction Weighted graph API cycles and cuts Kruskal’s algorithm Prim’s algorithm advanced algorithms clustering 11 16 8 10 14 7 21 G References: Algorithms in Java (Part 5)‚ Chapter 20 Intro to Algs and Data Structures‚ Section 5.4
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