Application Of Graph Data Structure

Application Of Graph Data Structure

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  Graph Application PRESENTED BY: JAYDHOLARIYA(15IT024) GAURANG DOBARIYA(15IT025)
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  What is Graph? •Graph Is a Non-linear data structure. • Contain the vertex and edges. • Edges may be directed or undirected. APPLICATION REAL TIME COMPUTER FIELD
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  REAL TIME • Transportationnetworks. Vertices: In road networks vertices are intersections. Edges : Road segments between intersection. • Used by : Google maps, Bing maps and now Apple IOS 9 maps for map programs.
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  Representation of molecular structure •Vertex: molecule • Edges: bond between molecule
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  Map colouring • famousfour colour theorem asserts that it is always possible to properly colour the regions of the map such that no two adjacent regions are assigned the same colour, using at most four distinct colours.
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  Map colouring
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  Three cottage problem •"The three cottage problem is a well-known mathematical puzzle. It can be stated like this: • Three cottages on a plane (or sphere) and each needs to be connected to the gas, water, and electric companies. • Plannar Graph
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  Graph Centre: • Foreach vertex find the length of shortest path to the farthest vertex. Centre of the graph is the vertex for which this value is minimal. • hospital, a fire department, or a police department, should be placed in a city so that the farthest point is as close as possible.
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  Shortest Path • Considersome communications stations (for telephony, cable television, Internet etc.) and a list of possible connections between them, having different costs. • Find the cheapest way to connect these stations in a network. This may be used for example to connect villages to cable television, or to Internet. • The same problem, but instead of connecting communications stations - villages are to be connected with roads.
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  Travelling Salesman Problem Asalesman has to visit a number of cities to deliver items. What is the shortest route that connects all the cities?
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  Airline Network • Graphtheory is already utilised in flight networks. • Airlines want to connect countless cities in the most efficient way, moving the most passengers with the fewest possible trips
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  Minimizing connection inIc • Integrated circuits (ICs) consist of millions of transistors which need to be connected. • it is important to optimise these countless connections to improve the performance of the chip.
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  Computer field • UsingGPS/Google Maps/Yahoo Maps, to find a route based on shortest route. • Finding shortest routes in car navigation systems
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  Computer network • graphtheory used in all types of topology for configure network. • Vertex :each device (Router, pc, etc..) • Edges: connection between the devices.
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  Digital Graph • Documentlink graphs. The best known example is the link graph of the web, • vertex: web page, directed edge: hyperlink • Google any page that is very good will have many other pages linking to it. Pages that are rarely visited, or not very interesting, will be very “lonely” in the internet graph • This gives a way to rank websites and allows Google to display the best results at the beginning.
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  Database • Databases: Forrepresenting ER(Entity Relationship) diagrams in databases, for representing dependency of tables in databases.
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  Social Network • Connectingwith friends on social media, where each user is a vertex, and when users connect they create an edge. • Facebook,Twiter,Instagram etc…