Question

A social network graph (SNG) is a graph where each vertex is a person and each edge represents an acquaintance. In other words, an SNG is a graph showing who knows who. For example, in the graph shown on Figure 2, George knows Mary and John, Mary knows Christine, Peter and George, John knows Christine, Helen and George, Christine knows Mary and John, Helen knows John, Peter knows Mary. The degrees of separation measure how closely connected two people are in the graph. For example, John has 0 degrees of separation from himself, 1 degree of separation from Christine, 2 degrees of separation from Mary, and 3 degrees of separation from Peter. i. From among breadth-first search, depth-first search, iterative deepening search, and uniform cost search, which one(s) guarantee finding the correct number of degrees of separation between any two people in the graph? ii. For the SNG shown in Figure 2, draw the first three levels of the search tree, with John as the starting point (the first level of the tree is the root). Is there a one- to-one correspondence between nodes in the search tree and vertices in the SNG? Why, or why not? In your answer here, you should assume that the search algorithm does not try to avoid revisiting the same state. iii. Draw an SNG containing exactly 5 people, where at least two people have 4 degrees of separation between them. iv. Draw an SNG containing exactly 5 people, where all people have 1 degree of separation between them. v. CSE 5360 Only (5 point EC for CSE 4308): In an implementation of breadth-first search for finding degrees of separation, suppose that every node in the search tree takes 1KB of memory. Suppose that the SNG contains one million people. Outline (briefly but precisely) how to make sure that the memory required to store search tree nodes will not exceed 1GB (the correct answer can be described in one-two lines of text). In your answer here you are free to enhance/modify the breadth-first search implementation as you wish, as long as it remains breadth-first (a modification that, for example, converts breadth-first search into depth-first search or iterative deepening search is not allowed).

Answer 1

a) Breadth first search is the algorithm which gaurantees us in finding the correct number of degrees of separation between any two people in a SNG.

b)

john

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|                      |                   |

George     Christine      Helen

|                      |                   |

Mary           Mary

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Peter

Yes, the tree is in one one correspondance with the diagram.

c)

Simply remove the helen as it is connected to John and connect it to Peter. Hence the degree between John and Helen will become 4.