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Sociology and CS

Sociology and CS. Philip Chan. How close are people connected?. Are people closely connected, not closely connected, isolated into groups, …. Degree of Separation. The number of connections to reach another person. Milgram’s Experiment. Stanley Milgram, psychologist

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Sociology and CS

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  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

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