Suggestions of the easiest algorithms for some Graph operations

Question

The deadline for this project is closing in very quickly and I don\'t have much time to deal with what it\'s left. So, instead of looking for the best (and probably more complic

Answer 1

This assumes O(E log V) is an acceptable running time, if you're doing something online, this might not be, and it would require some higher powered machinery.

• List all users in the graph network given a distance X

Djikstra's algorithm is good for this, for one time use. You can save the result for future use, with a linear scan through all the vertices (or better yet, sort and binary search).

• List all users in the graph network given a distance X and the type of relation

Might be nearly the same as above -- just use some function where the weight would be infinity if it is not of the correct relation.

• Calculate the shortest path between 2 users on the graph network given a type of relation

Same as above, essentially, just determine early if you match the two users. (Alternatively, you can "meet in the middle", and terminate early if you find someone on both shortest path spanning tree)

• Calculate the maximum distance between 2 users on the graph network

Longest path is an NP-complete problem.

• Calculate the most distant connected users on the graph network

This is the diameter of the graph, which you can read about on Math World.

As for the adjacency list vs adjacency matrix question, it depends on how densely populated your graph is. Also, if you want to cache results, then the matrix might be the way to go.