Question

I’ve implement an adjacency list using the vector of vectors approach with the nth element of the vector of vectors refers to the friend list of node n.

I was wondering if the hash map data structure would be more useful. I still have hesitations because I simply cannot identify the difference between them and for example if I would like to check and do an operation in nth elements neighbors (search,delete) how could it be more efficient than the vector of vectors approach.

Answer 1

A vector<vector<ID>> is a good approach if the set of nodes is fixed. If however you suddenly decide to remove a node, you’ll be annoyed. You cannot shrink the vector because it would displace the elements stored after the node and you would lose the references. On the other hand, if you keep a list of free (reusable) IDs on the side, you can just “nullify” the slot and then reuse later. Very efficient.

A unordered_map<ID, vector<ID>> allows you to delete nodes much more easily. You can go ahead and assign new IDs to the newly created nodes and you will not be losing empty slots. It is not as compact, especially on collisions, but not so bad either. There can be some slow downs on rehashing when a vector need be moved with older compilers.

Finally, a unordered_multimap<ID, ID> is probably one of the easiest to manage. It also scatters memory to the wind, but hey 🙂

Personally, I would start prototyping with a unordered_multimap<ID, ID> and switch to another representation only if it proves too slow for my needs.

Note: you can cut in half the number of nodes if the adjacency relationship is symmetric by establishing than the relation (x, y) is stored for min(x, y) only.