The Bicycle Thief. CIS 110, Spring 2013
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1 The Bicycle Thief CIS 110, Spring 2013
2 Where to Buy a Bike Since Trophy Bikes moved, someone has been selling used bikes on weekday afternoons out of a basement closet in SEAS Who s been selling them? Where do they come from? How do they get there? 2 CIS 110, Spring 2013
3 The Bicycle Thief One bike disappears from each of these spots every weekday morning! No time to go to each building separately Dangerous to go back to a building twice in one morning What is the shortest route to collect one bike from each building? 3 CIS 110, Spring 2013
4 Traveling Salesman Problem (TSP) Find shortest tour of n cities: visit each exactly once, and return to start? Best known algorithms pretty much test every tour to find shortest If a better algorithm exists, you can do a zillion other interesting things fast too (eg rob a bank) 3 CIS 110, Spring 2013
5 Traveling Salesman Problem (TSP) Find shortest tour of n cities: visit each exactly once, and return to start? Formally: TSP is an N P-complete problem Fast algorithm would mean P = N P* Most famous open question in computer science *Don t worry about what this means 3 CIS 110, Spring 2013
6 Traveling Salesman Problem (TSP) Trying everything is hard: instead use a heuristic (guess) Nearest Insertion: Add point to tour after closest point in tour Smallest Increase: Add point where causes smallest increase in length 3 CIS 110, Spring 2013
7 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour SEAS (distance: 0)
8 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Hill > SEAS (122)
9 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Van Pelt > SEAS (406)
10 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Annenberg > Van Pelt (686)
11 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Huntsman > Annenberg (968)
12 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Steinberg-Dietrich > Annenberg (1084)
13 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour College > Van Pelt (1215)
14 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Houston > College (1278)
15 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Claudia-Cohen > College (1361)
16 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Fagin > Houston (1648)
17 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Penn Museum > Houston (1895)
18 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Education Commons/Stadium > Fagin (2172)
19 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour DRL > SEAS (2311)
20 Traveling Salesman Problem (Nearest Insertion) Add each point after point it is closest to in tour Penn Park > Education Commons/Stadium (2869)
21 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length SEAS (distance: 0)
22 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Hill > SEAS (122)
23 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Van Pelt > SEAS (406)
24 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Annenberg > Van Pelt (686)
25 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Huntsman > Annenberg (968)
26 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Steinberg-Dietrich > Huntsman (1018)
27 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length College > Steinberg-Dietrich (1045)
28 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Houston > Steinberg-Dietrich (1091)
29 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Claudia-Cohen > Steinberg-Dietrich (1093)
30 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Fagin > Steinberg-Dietrich (1313)
31 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Penn Museum > College (1620)
32 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Education Commons/Stadium > Penn Museum (1720)
33 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length DRL > Penn Museum (1731)
34 Traveling Salesman Problem (Smallest Increase) Add each point where it causes smallest increase in tour length Penn Park > Education Commons/Stadium (2174)
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