graph-algorithm

For my current project I want to use the graph-tool library since they claim being the fastest: https://graph-tool.skewed.de/performance . I have some algorithms (shortest path, etc.) to run on really large networks, so the faster the better! First question: Is this claim 'being the fastest' true? ;) While trying to build a graph-tool graph fitting my needs, I figured out that its not possible to access vertex properties in a efficient way. Maybe I missed something? My question is now, can the function "getVertexFromGraph(graph, position)" be written in a more efficient way? Or more in general

I have a dependency graph that I have represented as a Map<Node, Collection<Node>> (in Java-speak, or f(Node n) -> Collection[Node] as a function; this is a mapping from a given node n to a collection of nodes that depend on n ). The graph is potentially cyclic*. Given a list badlist of nodes, I would like to solve a reachability problem : i.e. generate a Map<Node, Set<Node>> badmap that represents a mapping from each node N in the list badlist to a set of nodes which includes N or other node that transitively depends on it. Example: (x -> y means node y depends on node x) n1 -> n2 n2 -> n3 n3

Algorithms like the Bellman-Ford algorithm and Dijkstra's algorithm exist to find the shortest path from a single starting vertex on a graph to every other vertex. However, in the program I'm writing, the starting vertex changes a lot more often than the destination vertex does. What algorithm is there that does the reverse--that is, given a single destination vertex, to find the shortest path from every starting vertex? Just reverse all the edges, and treated destination as start node. Problem solved. If this is an undirected graph: I think inverting the problem would give you advantages.

Here's my interpretation of how Dijkstra's algorithm as described by wikipedia would deal with the below graph. First it marks the shortest distance to all neighbouring nodes, so A gets 1 and C gets 7. Then it picks the neighbour with the current shortest path. This is A. The origin is marked as visited and will not be considered again. The shortest (and only) path from the origin to B through A is now 12. A is marked as visited. The shortest path from the origin to the Destination through B is 13. B is marked as visited. The shortest path from the Origin to C through the destination is 14,

If you have a set of ranges, such as the following simple example... [ [12, 25], #1 [14, 27], #2 [15, 22], #3 [17, 21], #4 [20, 65], #5 [62, 70], #6 [64, 80] #7 ] ... how do you compute the maximally intersecting subset (not sure quite how to phrase it, but I mean "the subset of ranges which intersects and has the highest cardinality") and determine the degree of intersection (cardinality of ranges in that subset)? Logically I can work it out, and might be able to translate that to a naive algorithm. Going down the list, we see that 1-5 intersect, and 5-7 intersect, and that #5 intersects both

Algorithm to clone a tree is quite easy, we can do pre-order traversal for that. Is there an efficient algorithm to clone a graph? I tried a similar approach, and concluded we need to maintain a hash-map of nodes already added in the new graph, else there will be duplication of nodes, since one node can have many parents. It suffices to do a depth first search and copy each node as it's visited. As you say, you need some way of mapping nodes in the original graph to corresponding copies so that copies of cycle and cross edges can be connected correctly. This map also suffices to remember nodes