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MIT6_042JS10_lec18

# MIT6_042JS10_lec18 - Mathematics for Computer Science MIT...

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1 Albert R Meyer, March 15, 2010 Graph Coloring Bipartite Matching lec 7M.1 Mathematics for Computer Science MIT 6.042J/18.062J Albert R Meyer, March 15, 2010 Flight Gates flights need gates, but times overlap. how many gates needed? lec 7M.2 Albert R Meyer, March 15, 2010 Airline Schedule 122 145 67 257 306 99 Flights time lec 7M.3 Albert R Meyer, March 15, 2010 Conflicts Among 3 Flights 99 145 306 Needs gate at same time lec 7M.4 Albert R Meyer, March 15, 2010 Model all Conflicts with a Graph 257 67 99 145 306 122 lec 7M.5 Albert R Meyer, March 15, 2010 Color the vertices so that adjacent vertices have different colors. min # distinct colors needed = min # gates needed Color the vertices lec 7M.6

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2 Albert R Meyer, March 15, 2010 Coloring the Vertices 257, 67 122,145 99 306 4 colors 4 gates assign gates: 257 67 99 145 306 122 lec 7M.7 Albert R Meyer, March 15, 2010 Better coloring 3 colors 3 gates 257 67 99 145 306 122 lec 7M.8 Albert R Meyer, March 15, 2010 Final Exams subjects conflict if student takes both, so need different time slots. how short an exam period? lec 7M.9 Albert R Meyer, March 15, 2010 Model as a Graph 6.042 6.001 18.02 3.091 8.02 M 9am M 1pm T 9am T 1pm assign times: 4 time slots (best possible) lec 7M.10
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MIT6_042JS10_lec18 - Mathematics for Computer Science MIT...

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