Programming and Mathematical Thinking

Game Theory Lecture Notes

2.1 Digraphs on 3 Vertices: There are 64 = 26 distinct graphs on three vertices. The increased number of edges graphs is caused by the fact that the edges are now directed.16 2.2 Two Paths: We illustrate two paths in a digraph on three vertices.16 2.3 Directed Tree: We illustrate a directed tree. Every directed tree has a unique vertex called ...

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Lecture 4: Matching Algorithms for Bipartite Graphs

Figure 4.2: Finding an augmenting path. Direct all edges in G, taking direction from A to B for all unmatched edges, and from B to A for all matched edges. Now all the directed paths in G are alternating, and a free vertex in B can be reached from a …

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Chapter 6: Graph Theory

Leonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find a way to visit every edge of a graph once and only once. This would be useful for checking parking meters along the streets of a city, patrolling the

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Algorithms Graph Search

Graphs have nodes and edges. How many nodes are there? How many edges? Graphs . ... Which explored the most area before finding the target? Do A* and BFS always find the same path? Theorem: If the heuristic function is a lower bound for the ... Do Dijkstra and weighted A* ever find paths of different lengths?

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Euler Paths and Euler Circuits - Jeremy L. Martin

Euler Paths and Euler Circuits An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph

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APPLICATIONS OF GRAPH THEORY IN COMPUTER …

algorithms are used to solve problems that are modeled in the form of graphs. These algorithms are used to solve the graph theoretical concepts which intern used to solve the corresponding computer science application problems. Some algorithms are as follows: 1. Shortest path algorithm in a network 2. Finding a minimum spanning tree 3.

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Control Flow Graph - Cornell University

Control Flow Graph (CFG) A control flow graph(CFG), or simply a flow graph, is a directed graph in which: – (i) the nodes are basic blocks; and – (ii) the edges are induced from the possible flow of the program The basic block whose leader is the first intermediate language statement is called the entry node In a CFG we assume no information about data values

Top Big Data Analytics Use Cases - Oracle

Complex graphs and path analyses are required to identify customer paths and behavior. This data must then be correlated and joined with multiple datasets to correctly analyze store behavior. Pricing analytics and optimization Retailers need to know the true profitability of their customers, how markets can be segmented,

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Graph Theory with Applications to Engineering and Computer ...

2 PATHS AND CIRCUITS 2-1 Isomorphism 2-2 Subgraphs 2-3 A Puzzle With Multicolored Cubes 2-4 Walks, Paths, and Circuits 2-5 Connected Graphs, Disconnected Graphs, and Components 2-6 Euler Graphs 2-7 Operations On Graphs 2-8 More on Euler Graphs 2-9 Hamiltonian Paths and Circuits 2-10 The Traveling Salesman Problem Summary www.TechnicalBooksPDF.com

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