Question

In a graph class I need to handle nodes with integer values (1-1000 mostly). In every step I want to remove a node and all its neighbors from the graph. Also I want to always begin with the node of the minimal value. I thought long about how to do this in the fastest possible manner and decided to do the following:

• The graph is stored using adjancency lists
• There is a huge array std::vector<Node*> bucket[1000] to store the nodes by its value
• The index of the lowest nonempty bucket is always stored and kept track off
• I can find the node of minimal value very fast by picking a random element of that index or if the bucket is already empty increase the index
• Removing the selected node from the bucket can clearly done in O(1), the problem is that for removing the neighbors I need to search the bucket bucket[value of neighbor] first for all neighbor nodes, which is not really fast.

Is there a more efficient approach to this?

I thought of using something like std::list<Node*> bucket[1000], and assign every node a pointer to its “list element”, such that I can remove the node from the list in O(1). Is this possible with stl lists, clearly it can be done with a normal double linked list that I could implement by hand?

Answer 1

I recently did something similar to this for a priority queue implementation using buckets.

What I did was use a hash tables (unordered_map), that way, you don’t need to store 1000 empty vectors and you still get O(1) random access (general case, not guaranteed). Now, if you only need to store/create this graph class one time, it probably doesn’t matter. In my case I needed to create the priority queue tens/hundreds of time per second and using the hash map made a huge difference (due to the fact that I only created unordered_sets when I actually had an element of that priority, so no need to initialize 1000 empty hash sets). Hash sets and maps are new in C++11, but have been available in std::tr1 for a while now, or you could use the Boost libraries.

The only difference that I can see between your & my usecase, is that you also need to be able to remove neighboring nodes. I’m assuming every node contains a list of pointers to it’s neighbors. If so, deletion of the neighbors should take k * O(1) with k the number of neighbors (again, O(1) in general, not guaranteed, worst case is O(n) in an unordered_map/set). You just go over every neighboring node, get its priority, that gives you the correct index into the hash map. Then you find the pointer in the hash set which the priority maps to, this search in general will be O(1) and removing the element is again O(1) in general.

All in all, I think you got a pretty good idea of what to do, but I believe that using hash maps/sets will speed up your code by quite a lot (depends on the exact usage of course). For me, the speed improvement of an implementation with unordered_map<int, unordered_set> versus vector<set> was around 50x.