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Great Ideas in Computing Problem mapping

Great Ideas in Computing Problem mapping. Richard Anderson University of Washington. Great Ideas in Computing. Great ideas in computing. What are the underlying ideas of our field Ideas that provide a deep understanding Ideas that give computer scientists intuition

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Great Ideas in Computing Problem mapping

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  1. Great Ideas in ComputingProblem mapping Richard Anderson University of Washington IUCEE: Problem Mapping

  2. Great Ideas in Computing IUCEE: Problem Mapping

  3. Great ideas in computing • What are the underlying ideas of our field • Ideas that provide a deep understanding • Ideas that give computer scientists intuition • Ideas that create excitement? IUCEE: Problem Mapping

  4. Four lectures • Monday – Problem Mapping • Tuesday – Complexity Theory • Wednesday – Average Case Analysis • Thursday – Algorithm Implementation • Convey ideas of theoretical computer science that span disciplines • Long term impact on students is the ideas they internalize • What they remember after they have forgotten the details! IUCEE: Problem Mapping

  5. Mappings: Translations between different levels or domains D1 D2 IUCEE: Problem Mapping

  6. Suppose you have a program to compute the maximum of an array of integers How do you compute the minimum? IUCEE: Problem Mapping

  7. Suppose you have a program to sort positive integers How do you sort arbitrary integers? What is the mapping between problems? How is the mapping used? IUCEE: Problem Mapping

  8. Two well know problems • Traveling Salesman Problem (TSP) • Hamiltonian Circuit Problem (HC) IUCEE: Problem Mapping

  9. Does there exist a Hamiltonian Circuit in this graph? IUCEE: Problem Mapping

  10. Find a minimum cost tour 3 7 7 2 2 5 4 1 1 4 IUCEE: Problem Mapping

  11. How do you map a HC problem into a TSP problem • Imprecise version: • Precise version IUCEE: Problem Mapping

  12. HC to TSP IUCEE: Problem Mapping

  13. Undirected vs. Directed • Hamiltonian Circuit (HC) • Directed Hamiltonian Circuit (DHC) • Traveling Salesman Problem (STSP) • Asymmetric Traveling Salesman Problem (ATSP) IUCEE: Problem Mapping

  14. HC to DHC IUCEE: Problem Mapping

  15. DHC to HC IUCEE: Problem Mapping

  16. TSP to ATSP / ATSP to TSP IUCEE: Problem Mapping

  17. Job shop scheduling • Jobs j1… jn • Single machine • Time to execute job ji is ti • Time to convert from job ji to jk is cik • Cost to start with job ji is c0i • Cost to end with job ji is ci0 IUCEE: Problem Mapping

  18. How is job shop scheduling related to the TSP IUCEE: Problem Mapping

  19. Hamiltonian Path IUCEE: Problem Mapping

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