Sociology and CS

1. Sociology and CS Philip Chan

2. How close are people connected? • Are people • closely connected, • not closely connected, • isolated into groups, • …

3. Degree of Separation • The number of connections to reach another person

4. Milgram’s Experiment • Stanley Milgram, psychologist • Experiment in the late 1960’s • Chain letter to gather data • Stockbroker in Boston • 160 people in Omaha, Nebraska • Given a packet • Add name and forward it to another person who might be closer to the stockbroker • Partial “social network”

5. Small World • Six degrees of separation • Everyone is connected to everyone by a few people—about 6 on the average. • Obama might be 6 connections away from you • “Small world” phenomenon

6. Bacon Number • Number of connections to reach actor Kevin Bacon • http://oracleofbacon.org/ • Is a connection in this network different from the one in Milgram’s experiment?

7. Problem Formulation • Given (input) • People • Connections/links/friendships • Find (output) • the average number of connections between two people • Simplification • don’t care about how long/strong/… the friendshipsare

8. Problem Formulation • Formulate it into a graph problem (abstraction) • Given (input) • People • Connections • Find (output) • the average number of connections between two people

9. Problem Formulation • Formulate it into a graph problem (abstraction) • Given (input) • People -> vertices • Connections -> edges • Find (output) • the average number of connections between two people -> ?

10. Problem Formulation • Formulate it into a graph problem (abstraction) • Given (input) • People -> vertices • Connections -> edges • Find (output) • the average number of connections between two people -> average shortest path length

11. Algorithm • Shortest Path • Dijkstra’s algorithm • Limitations?

12. Algorithm • Shortest Path • Dijkstra’s algorithm • This could be an overkill, why?

13. Algorithm • Unweighted edges • Each edge has the same weight of 1 • Simpler algorithm? • Any ideas?

14. Breadth-First Search • Start from the origin • Explore people one link away (dist=1) • Explore people two links away (dist=2) • … • Until the destination is reach

15. Algorithm • Breadth-first search (BFS) • Single origin, all destinations

16. Algorithm • Breadth-first search (BFS) • Single origin, all destinations • Repeat BFS for each origin • ShortestDistance(x,y) = shortestDistance(y,x)

17. Algorithm • Breadth-first search (BFS) • Single origin, all destinations • Repeat BFS for each origin • ShortestDistance(x,y) = shortestDistance(y,x) • Each subsequent BFS can stop earlier

18. BFS Algorithm—A Closer Look • Add origin to the open list • While open list is not empty • Remove the first person from the open list • Mark the person as visited • Add non-visited neighbors of the person to the open list

19. BFS Algorithm—A Closer Look • Add (origin, 0) to the open list • While open list is not empty • Remove the first item (person, dist) from the open list • Mark person as visited • For each non-visited neighbor of person • Add (neighbor, dist + 1) to the open list

20. Implementation • Data Structures • What do we need to keep track of? • Whether we have visited some person before • An ordered list of persons to be visited • Implementation • Boolean visited[person] • Open list of to be visited people • Queue • First in first out (FIFO)

21. Queue Operations • Enqueue • Add an item at the end • Dequeue • Remove an item from the front

22. Queue Implementation 1 • Consider using an array • How to implement the two operations? • Enqueue • Update tail, add item at tail • Dequeue

23. Queue Implementation 1 • Consider using an array • How to implement the two operations? • Enqueue • Update tail, add item at tail • Dequeue • Remove the first item • Shift the rest of the items up, update tail

24. Additional Operations • What do we need to check before Enqueue? • What do we need to check before Dequeue?

25. Additional Operations • What do we need to check before Enqueue? • What do we need to check before Dequeue? • Enqueue: • Is the queue full? • Dequeue • Is the queue empty?

26. Queue Implementation 1(shifting items) • Is the queue empty?

27. Queue Implementation 1(shifting items) • Is the queue empty? • When tail is -1 • Is the queue full?

28. Queue Implementation 1(shifting items) • Is the queue empty? • When tail is -1 • Is the queue full? • When tail is length - 1

29. Number of assignments (Speed of algorithm) • N = number of items on the queue • Count number of assignments • involving items in the queue

30. Number of assignments (Implementation 1) • Enqueue

31. Number of assignments (Implementation 1) • Enqueue • 1 (assign new item at tail) • Dequeue

32. Number of assignments (Implementation 1) • Enqueue • 1 (assign new item at tail) • Dequeue • 1 (assign first item to somewhere else) • N-1 shifts (assignments) • Total N

33. Shifting items in Dequeue • Quite a bit of work • if we have many items in the queue • Can we avoid shifting? • If so, how? Ideas?

34. Queue Implementation 2 • Consider using an array • How to implement the two operations? • Enqueue • Head and tail • Update tail, add at tail • Dequeue

35. Queue Implementation 2 • Consider using an array • How to implement the two operations? • Enqueue • Head and tail • update tail, add at tail • Dequeue • Get item from head • Update head

36. Queue Implementation 2 (head and tail) • Is the queue empty?

37. Queue Implementation 2 (head and tail) • Is the queue empty? • When head is larger than tail • Is the queue full?

38. Queue Implementation 2 (head and tail) • Is the queue empty? • When head is larger than tail • Is the queue full? • When tail is length - 1

39. Number of assignments (Implementation 2) • Enqueue

40. Number of assignments (Implementation 2) • Enqueue • 1 (assign new item at tail) • Dequeue

41. Number of assignments (Implementation 2) • Enqueue • 1 (assign new item at tail) • Dequeue • 1 (assign item at tail to somewhere else)

42. What if tail reaches the end of array • But there is room in the front of the array? • Any ideas to reuse the space in the front?

43. Queue Implementation 3 • Circular queue • Wrap around • If we use head and tail (Implementation 2) • What needs to be changed?

44. Circular Queue Operations • Length = length of array • Enqueue

45. Circular Queue Operations • Length = length of array • Enqueue • If not full • If tail < length • increment tail • Else • tail = 0 • Add item • Dequeue

46. Circular Queue Operations • Length = length of array • Enqueue • If not full • If tail < length • increment tail • Else • tail = 0 • Add item • Dequeue • Similarly for head

47. Queue Implementation 3 (circular queue) • Is the queue empty?

48. Queue Implementation 3 (circular queue) • Is the queue empty? • When head is larger than tail • With wrap-around adjustment • Is the queue full?

49. Queue Implementation 3 (circular queue) • Is the queue empty? • When head is larger than tail • With wrap-around adjustment • Is the queue full? • When head is larger than tail • With wrap-around adjustment • Same!! • How can we distinguish them?

50. Queue Implementation 3 (circular queue) • Is the queue empty? • When head is larger than tail • With wrap-around adjustment • Is the queue full? • When head is larger than tail • With wrap-around adjustment • Same!! • How can we distinguish them? • Keep track of size instead