graph. -traffic modeling maximum flow -shortest (fastest) route shortest path -efficient...
TRANSCRIPT
Graph
• graph is a pair of two sets where– set of elements called vertices (singl. vertex)– set of pairs of vertices (elements of ) called edges
• Example: where
• Notation: – we write for a graph with vertex set and edge set – is the vertex set of , and is the edge set of
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drawing of
- traffic modelingMAXIMUM FLOW
- shortest (fastest) routeSHORTEST PATH
- efficient distribution, logistics, pickup/deliveryHAMILTONIAN PATH/CYCLE,TRAVELLING SALESMAN PROBLEMCHINESE POSTMAN PROBLEM
Network Modeling (rail, road, airline)Applications
- circuit layout, VLSIGRAPH DRAWING PLANARITY
- communication protocolsDIAMETER, RADIUSSPANNING TREEDOMINATING SET
- fault-tolerant networksMINIMUM CUTCONNECTIVITY
ApplicationsNetwork Modeling (electrical, communication)
Applications- Job scheduling / Critical path
GRAPH COLOURINGMAXIMUM CLIQUE
- Job AssignmentMAXIMUM MATCHINGSTABLE MARRIAGE PROBLEM
- Evolutionary trees (Biology)TREE DECOMPOSITION
Modeling conflict / compatibility / relationship