1. Great Ideas in Computing Problem mapping
Richard Anderson
University of Washington
June 30, 2008
IUCEE: Problem Mapping

2. Great Ideas in Computing
June 30, 2008
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?
June 30, 2008
IUCEE: Problem Mapping

4. IUCEE: Problem Mapping
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!
June 30, 2008
IUCEE: Problem Mapping

5. Mappings: Translations between different levels or domains
June 30, 2008
IUCEE: Problem Mapping

6. IUCEE: Problem Mapping
Suppose you have a program to compute the maximum of an array of integers
How do you compute the minimum?
June 30, 2008
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?
June 30, 2008
IUCEE: Problem Mapping

8. IUCEE: Problem Mapping
Two well know problems
Traveling Salesman Problem (TSP)
Hamiltonian Circuit Problem (HC)
June 30, 2008
IUCEE: Problem Mapping

9. Does there exist a Hamiltonian Circuit in this graph?
June 30, 2008
IUCEE: Problem Mapping

10. Find a minimum cost tour3 7 7 2 2 5 4 1 1 4
June 30, 2008
IUCEE: Problem Mapping

11. How do you map a HC problem into a TSP problem
Imprecise version:
Precise version
June 30, 2008
IUCEE: Problem Mapping

12. IUCEE: Problem Mapping
HC to TSP
June 30, 2008
IUCEE: Problem Mapping

13. Undirected vs. Directed
Hamiltonian Circuit (HC)
Directed Hamiltonian Circuit (DHC)
Traveling Salesman Problem (STSP)
Asymmetric Traveling Salesman Problem (ATSP)
June 30, 2008
IUCEE: Problem Mapping

14. IUCEE: Problem Mapping
HC to DHC
June 30, 2008
IUCEE: Problem Mapping

15. IUCEE: Problem Mapping
DHC to HC
June 30, 2008
IUCEE: Problem Mapping

16. IUCEE: Problem Mapping
TSP to ATSP / ATSP to TSP
June 30, 2008
IUCEE: Problem Mapping

17. IUCEE: Problem Mapping
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
June 30, 2008
IUCEE: Problem Mapping

18. How is job shop scheduling related to the TSP
June 30, 2008
IUCEE: Problem Mapping

19. IUCEE: Problem Mapping
Hamiltonian Path
June 30, 2008
IUCEE: Problem Mapping