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Question 3+ Who plays the tambourine? child preferences Year 2 kids George, Huan, Indira, Jiba and Kwang join a music club. They can't yet read George lagerphone, tambourine music, so are offered percussion instruments. Huan bongos, cymbal, tambourine Available are bongos, cymbal, lagerphone, Indira maracas, tambourine maracas and tambourine, but only one of Jiba bongos, maracas, tambourine each. The teacher asks for their preferences, Kwang cymbal, lagerphone, maracas listed at right. Use the matching algorithm to find how to give each child one of their preferences. [For a small set of preferences like this it is easy to solve the problem by eye'. The purpose is to demonstrate how the max flow algorithm works on a matching problem.] The diagrams all show the children's preferences. A 'supersource and a 'supertarget' have been introduced. Step through from flow Fo to F5, showing all levels and labels. Mark existing non-zero flows in heavy black and incremental flows in heavy red. The first diagram (with all zero flows) has been completed to indicate the style. B ( V F. with fi F with $2 A o M F2 with f: F3 with f4 So F4 with fo F5 = Fmax showing all mathchings. T T plays tambourine Question 3+ Who plays the tambourine? child preferences Year 2 kids George, Huan, Indira, Jiba and Kwang join a music club. They can't yet read George lagerphone, tambourine music, so are offered percussion instruments. Huan bongos, cymbal, tambourine Available are bongos, cymbal, lagerphone, Indira maracas, tambourine maracas and tambourine, but only one of Jiba bongos, maracas, tambourine each. The teacher asks for their preferences, Kwang cymbal, lagerphone, maracas listed at right. Use the matching algorithm to find how to give each child one of their preferences. [For a small set of preferences like this it is easy to solve the problem by eye'. The purpose is to demonstrate how the max flow algorithm works on a matching problem.] The diagrams all show the children's preferences. A 'supersource and a 'supertarget' have been introduced. Step through from flow Fo to F5, showing all levels and labels. Mark existing non-zero flows in heavy black and incremental flows in heavy red. The first diagram (with all zero flows) has been completed to indicate the style. B ( V F. with fi F with $2 A o M F2 with f: F3 with f4 So F4 with fo F5 = Fmax showing all mathchings. T T plays tambourine