4.5 Small World Phenomenon

Size: px

Start display at page:

Download "4.5 Small World Phenomenon"

Asher Wade
5 years ago
Views:

Small World Phenomenon.5 Small World Phenomenon Small world phenomenon. Six handshakes away from anyone. n experiment to quantify effect. [Stanley Milgram, 960s]!

! Outcome: message delivered with average of 5 intermediaries. Stanley Milgram Kevin acon ntroduction to omputer Science Sedgewick and Wayne opyright 007 http://www.cs.princeton.

1 Small World Phenomenon.5 Small World Phenomenon Small world phenomenon. Six handshakes away from anyone. n experiment to quantify effect. [Stanley Milgram, 960s]! You are given personal info of another person.! oal: deliver message. e.g., occupation and age! Restriction: can only forward to someone you know by first name.! Outcome: message delivered with average of 5 intermediaries. Stanley Milgram Kevin acon ntroduction to omputer Science Sedgewick and Wayne opyright pplications of Small World Phenomenon raph ata Type Sociology applications.! Looking for a job.! Marketing products or ideas.! ormation and spread of fame and fads.! Train of thought followed in a conversation.! efining representative-ness of political bodies.! Kevin acon game (movies, rock groups, facebook, etc.). pplication demands a new data type.! raph = data type that represents pairwise connections.! Vertex = element.! dge = connection between two vertices. Other applications.! lectronic circuits.! Synchronization of neurons. Reference. uncan J. Watts, Small Worlds: The ynamics of Networks between Order and Randomness, Princeton University Press, 999. vertex! nalysis of World Wide Web.! esign of electrical power grids.! Modeling of protein interaction networks. edge! Phase transitions in coupled Kuramoto oscillators.! Spread of infectious diseases and computer viruses.! volution of cooperation in multi-player iterated Prisoner's ilemma. 3

2 raph pplications nternet Movie atabase graph vertices edges nput format. Movie followed by list of performers, separated by slashes. communication telephones, computers fiber optic cables circuits gates, registers, processors wires mechanical joints rods, beams, springs hydraulic reservoirs, pumping stations pipelines financial stocks, currency transactions transportation street intersections, airports highways, airway routes scheduling tasks precedence constraints software systems functions function calls internet web pages hyperlinks games board positions legal moves social relationship people, actors friendships, movie casts neural networks neurons synapses % more movies.txt... Tin Men (987)/eoy, avid/lumenfeld, lan/... /eppi, indy/ershey, arbara Tirez sur le pianiste (960)/eymann, laude/.../erger, Nicole () Titanic (997)Paxton, ill/iaprio, Leonardo/.../Winslet, Kate Titus (999)/Weisskopf, ermann/rhys, Matthew/.../Mcwan, eraldine To ll a ood Night (980)/eorge, Michael ()/.../entile, Linda To e or Not to e (9)/Verebes, rnö ()/.../Lombard, arole () To e or Not to e (983)/rooks, Mel ()/.../ancroft, nne To atch a Thief (955)/París, Manuel/rant, ary/.../kelly, race To ie or (989)/ond, Steve ()/Jones, uane ()/.../Maddalena, Julie To ie or (995)/Smith, Kurtwood/Kidman, Nicole/.../Tucci, Maria To ie Standing (990)/Sacha, Orlando/nthony, erald/.../rose, Jamie To nd ll Wars (00)/Kimura, Sakae/llis, reg ()/.../Sutherland, Kiefer To Kill a lown (97)/lda, lan/lavering, ric/lamberts, eath/anner, lythe To Live and ie in L.. (985)/Mcroarty, Pat/Williams, onnie/.../afoe, Willem... protein networks proteins protein-protein interactions chemical compounds molecules bonds 5 nternet Movie atabase raph P Q. ow to represent the movie-performer relationships?. Use a graph.! Vertex: performer or movie.! dge: connect performer to movie. raph data type. % more tiny.txt // // /// / // /// /// // 3

3 raph Representation Set ata Type raph representation: use a symbol table.! Key = name of vertex (e.g., performer or movie).! Value = set of neighbors. Set data type. Unordered collection of distinct keys. Symbol Table Key Value Q. ow to implement?. dentical to symbol table, but ignore values. String ST 5 raph mplementation raph mplementation (continued) public class raph { private ST<String, ST<String>> st; public raph() { st = new ST<String, ST<String>>(); public void adddge(string v, String w) { if (!st.contains(v)) addvertex(v); if (!st.contains(w)) addvertex(w); st.get(v).add(w); add w to v's set of neighbors st.get(w).add(v); add v to w's set of neighbors Second constructor. To read graph from input stream. public raph(n in) { st = new ST<String, ST<String>>(); while (!in.ismpty()) { String line = in.readline(); String[] names = line.split("/"); for (int i = ; i < names.length; i++) adddge(names[0], names[i]); private void addvertex(string v) { st.put(v, new ST<String>()); add new vertex v with no neighbors public terable<string> adjacentto(string v) { return st.get(v); n in = new n("tiny.txt"); raph = new raph(); % more tiny.txt // // /// / // /// /// // 6 7

raph lient Warmup: Movie inder raph lient Warmup: Movie inder Performer and movie queries.! iven a performer, find all movies in which they appeared.! iven a movie, find all performers.

adjacentto(v)) StdOut.println(v); read in graph from a file process queries % java Movieinder action.

4 raph lient Warmup: Movie inder raph lient Warmup: Movie inder Performer and movie queries.! iven a performer, find all movies in which they appeared.! iven a movie, find all performers. public class Movieinder { public static void main(string[] args) { n in = new n(args[0]); raph = new raph(in); while (!Stdn.ismpty()) { String v = Stdn.readLine(); for (String w :.adjacentto(v)) StdOut.println(v); read in graph from a file process queries % java Movieinder action.txt acon, Kevin eath Sentence (007) River Wild, The (99) Tremors (990) Roberts, Julia lood Red (989) Love Trouble (99) Mexican, The (00) Ocean's leven (00) Tilghman, Shirley % java Movieinder mpaa.txt acon, Kevin ir reathe, The (007) ir Up There, The (99) nimal ouse (978) pollo 3 (995) alto (995) eauty Shop (005) ig Picture, The (989) Sleepers (996) Starting Over (979) Stir of choes (999) Telling Lies in merica (997) Trapped (00) Tremors (990) We Married Margo (000) Where the Truth Lies (005) White Water Summer (987) Wild Things (998) Woodsman, The (00) 8 9 Kevin acon ame Kevin acon Numbers ame. iven a performer, find (shortest) chain of movies connecting them to Kevin acon. Performer Kevin Kline Meg Ryan Tom anks Kevin acon Was in rench Kiss Sleepless in Seattle pollo 3 With Meg Ryan Tom anks Kevin acon 0

5 omputing acon Numbers Path inder P ow to compute. ind shortest path in performer-movie graph. Path finder P. public class Pathinder (data type to compute shortest paths) int void Pathinder(raph, String s) distanceto(string v) showpath(string v) process graph with source s return shorest distance between s and v print shortest path between s and v esign principles.! ecouple graph algorithm from graph data type.! void feature creep. 3 omputing acon Numbers: Java mplementation omputing Shortest Paths public class acon { public static void main(string[] args) { n in = new n(args[0]); raph = new raph(in); String s = "acon, Kevin"; Pathinder finder = new Pathinder(, s); while (!Stdn.ismpty()) { String actor = Stdn.readLine(); finder.showpathrom(actor); % java acon top-grossing.txt Stallone, Sylvester Rocky (98) Tamburro, harles. Terminator : Judgment ay (99) erkeley, Xander pollo 3 (995) acon, Kevin read in the graph from a file create object to return shortest paths process queries % java acon top-grossing.txt oldberg, Whoopi Sister ct (99) rodénchik, Max pollo 3 (995) acon, Kevin Tilghman, Shirley To compute shortest paths:! Source vertex is at distance 0.! ts neighbors are at distance.! Their remaining neighbors are at distance.! Their remaining neighbors are at distance 3.! 0 3 5

6 readth irst Search readth irst Searcher: Preprocessing oal. iven a vertex s, find shortest path to every other vertex v. S from source vertex s Put s onto a O queue. Repeat until the queue is empty:! dequeue the least recently added vertex v! add each of v's unvisited neighbors to the queue, and mark them as visited. Key observation. Vertices are visited in increasing order of distance from s because we use a O queue. public class Pathinder { private ST<String, String> prev = new ST<String, String>(); private ST<String, nteger> dist = new ST<String, nteger>(); public Pathinder(raph, String s) { Queue<String> q = new Queue<String>(); q.enqueue(s); dist.put(s, 0); while (!q.ismpty()) { String v = q.dequeue(); for (String w :.adjacentto(v)) { if (!dist.contains(w)) { q.enqueue(w); dist.put(w, + dist.get(v)); prev.put(w, v); 6 7 readth irst Searcher: Printing the Path Running Time nalysis To print shortest path: follow prev[] from vertex v back to source s.! Print v, prev[v], prev[prev[v]],, s. nalysis. S scales to solve huge problems.! x: shortest path from to : data ile movies performers edges read input build graph S show null key prev dist.txt,88,77 8K 0.6 sec 0.5 sec 0.3 sec source P3.txt action.txt mpaa.txt,538,938,86 70,35 39,86 80,6 00K 70K 60K 0.3 sec 0.7 sec. sec 0.99 sec.8 sec 7.5 sec 0.7 sec. 5.5 sec all.txt 85,6 933,86 3.3M 5 sec 56 sec 39 sec 3 60M data as of pril 9, 007 public void showpath(string v) { while (prev.contains(v)) { StdOut.println(v); v = prev.get(v); symbol tables 8 9

ata nalysis pplications of readth irst Search xercise. ompute histogram of Kevin acon numbers. nput. 85,6 movies, 933,86 actors. acon # 0 requency,9 More S applications.! Particle tracking.

7 ata nalysis pplications of readth irst Search xercise. ompute histogram of Kevin acon numbers. nput. 85,6 movies, 933,86 actors. acon # 0 requency,9 More S applications.! Particle tracking.! mage processing.! rawling the Web.! Routing nternet packets.!... 8,088 uzz Mauro, Jessica rizd, Pablo apussi rgentine short film Sweet reams (005) ,6,9 7,905 xtensions. oogle maps red Ott, solo actor in red Ott olding a ird (89) 8! 3,9 data as of pril 9, onclusions Linked list. Ordering of elements. inary tree. ierarchical structure of elements. raph. Pairwise connections between elements. ata structures.! Queue: linked list.! Set: binary tree.! Symbol table: binary tree.! raph: symbol table of sets.! readth first searcher: graph + queue + symbol table. mportance of data structures.! nables us to build and debug large programs.! nables us to solve large problems efficiently. 3

4.5 Small World Phenomenon

Small World Phenomenon 4.5 Small World Phenomenon Small world phenomenon. Six handshakes away from anyone. n experiment to quantify effect. [Stanley Milgram, 960s] You are given personal info of another