I am working on a graph implementation for a C++ class I am taking. This is what I came up with so far:
struct Edge {
int weight;
Vertex *endpoints[2]; // always will have 2 endpoints, since i'm making this undirected
};
struct Vertex {
int data; // or id
list<Edge*> edges;
};
class Graph {
public:
// constructor, destructor, methods, etc.
private:
list<Vertex> vertices;
};
It's a bit rough at the moment, but I guess I'm wondering... Am I missing something basic? It seems a bit too easy at the moment, and usually that means I'm designing it wrong.
My thought is that a graph is just a list of vertices, which has a list edges, which will have a list of edges, which has two vertex end points.
Other than some functions I'll put into the graph (like: shortest distance, size, add a vertex, etc), am I missing something in the basic implementation of these structs/classes?
Sometimes you need to design stuff like this and it is not immediately apparent what the most useful implementation and data representation is (for example, is it better storing a collection of points, or a collection of edges, or both?), you'll run into this all the time.
You might find, for example, that your first constructor isn't something you'd actually want. It might be easier to have the Graph class create the Vertices rather than passing them in.
Rather than working within the class itself and playing a guessing game, take a step back and work on the client code first. For example, you'll want to create a Graph object, add some points, connect the points with edges somehow, etc.
The ordering of the calls you make from the client will come naturally, as will the parameters of the functions themselves. With this understanding of what the client will look like, you can start to implement the functions themselves, and it will be more apparent what the actual implementation should be
Comments about your implementation:
A graph is a collection of objects in which some pairs of objects are related. Therefore, your current implementation is one potential way of doing it; you model the objects and the relationship between them.
The advantages of your current implementation are primarily constant lookup time along an edge and generalizability. Lookup time: if you want to access the nth neighbor of node k, that can be done in constant time. Generalizability: this represents almost any graph someone could think of, especially if you replace the data type of weight and data with an object (or a Template).
The disadvantages of your current implementation are that it will probably be slower than ideal. Looking across an edge will be cheap, but still take two hops instead of one (node->edge->node). Furthermore, using a list of edges is going to take you O(d) time to look up a specific edge, where d is the degree of the graph. (Your reliance on pointers also require that the graph fits in the memory of one computer; you'd have trouble with Facebook's graphs or the US road network. I doubt that parallel computing is a concern of yours at this point.)
Concerns when implementing a graph:
However, your question asks whether this is the best way. That's a difficult question, as several specific qualities of a graph come in to play.
Edge Information: If the way in which vertices are related doesn't matter (i.e., there is no weight or value to an edge), there is little point in using edge objects; this will only slow you down. Instead, each vertex can just keep a list of pointers to its neighbors, or a list of the IDs of its neighbors.
Construction: As you noticed in the comments, your current implementation requires that you have a vertex available before adding an edge. That is true in general. But you may want to create vertices on the fly as you add edges; this can make the construction look cleaner, but will take more time if the vertices have non-constant lookup time. If you know all vertices before construction the graph, it may be beneficial to explicitly create them first, then the edges.
Density: If the graph is sparse (i.e., the number of edges per vertex is approximately constant), then an adjacency list is again a good method. However, if it is dense, you can often get increased performance if you use an adjacency matrix. Every vertex holds a list of all other vertices in order, and so accessing any edge is a constant time operation.
Algorithm: What problems do you plan on solving on the graph? Several famous graph algorithms have different running times based on how the graph is represented.
Addendum:
Have a look at this question for many more comments that may help you out:
Graph implementation C++
Related
When I look at a book, I only show examples of how to implement graphs in almost every book by adjacent matrix method and adjacent list method.
I'm trying to create a node-based editor, in which case the number of edges that stretch out on each node is small, but there's a lot of vertex.
So I'm trying to implement the adjacent list method rather than the adjacent matrix method.
However, adjacent lists store and use each edge as a connection list.
But, I would like to use the node in the form listed below.
class GraphNode
{
int x, y;
dataType data;
vector<GraphNode*> in;
vector<GraphNode*> out;
public:
GraphNode(var...) = 0;
};
So like this, I want to make the node act as a vertex and have access to other nodes that are connected.
Because when I create a node-based editor program, I have to access and process different nodes that are connected to each node.
I want to implement this without using a linked list.
And, I'm going to use graph algorithms in this state.
Is this a bad method?
Lastly, I apologize for my poor English.
Thank you for reading.
You're just missing the point of the difference between adjacency list and adjacency matrix. The main point is the complexity of operations, like finding edges or iterating over them. If you compare a std::list and a std::vector as datatype implementing an adjacency list, both have a complexity of O(n) (n being the number of edges) for these operations, so they are equivalent.
Other considerations:
If you're modifying the graph, insertion and deletion may be relevant as well. In that case, you may prefer a linked list.
I said that the two are equivalent, but generally std::vector has a better locality of reference and less memory overhead, so it performs better. The general rule in C++ is to use std::vector for any sequential container, until profiling has shown that it is a bottleneck.
Short answer: It is probably a reasonable way for implementing a graph.
Long answer: What graph data structure to use is always dependent on what you want to use it for. A adjacency matrix is good for very dense graphs were it will not waste space due to many 0 entries and if we want to answer the question "Is there an edge between A and B?" fast. The iteration over all members of a node can take pretty long, since it has to look at a whole row and not just the neighbors.
An adjacency list is good for sparse graphs and if we mostly want to look up all neighbors of a node (which is very often the case for graph mustering algorithms). In a directed graph were we want to treat ingoing and outgoing edges seperately, it is probably a good idea to have a seperate adjacency list for ingoing and outgoing egdes (as has your code).
Regarding what container to use for the list, it depends on the use case. If you will much more often iterate over the graph and not so often delete something from it, using a vector over a list is a very good idea (basically all graph programms I ever wrote were of this type). If you have a graph that changes very often, you have to delete edges very often, you don't want to have iterator invalidation and so on, maybe it is better having a list. But that is very seldom the case.
A good design would be to make it very easy to change between list and vector so you can easily profile both and then use what is better for your program.
Btw if you often delete one edge, this is also pretty easily done fast with a vector, if you do not care about the order of your edges in adjacency list (so do not do this without thinking while iterating over the vector):
void delte_in_edge(size_t index) {
std::swap(in[i], in.back()); // The element to be deleted is now at the last position,
// the formerly last element is at position i
in.pop_back(); // Delete the current last element
}
This has O(1) complexity (and the swap is probably pretty fast).
I have to model an unweighted graph in C++ and do BFS and DFS. But, I have to create two separate classes: node and edge which would contain the two extremities of type node. I do not understand how would I be able to do any search in the graph using the edge class. If it were me, I would only create the node class and have the neighbours of node X in a list/array inside the class. Is there something I am missing? How could I take advantege of the class edge? Is there any way to do the searches without using an adjacency matrix or list? Thank you!
You can still use adjacency lists. But they will contain not references to other nodes, but rather references to edge instances, which in turn contain both endpoints as node references, as you mention. Of course, that seems kind of redundant because if you have, say source and target nodes in each edge and then you access some edge of a given node using something like node.edges[i].source, then you instantly know that this source is the node itself, otherwise this edge wouldn't even be in this node's adjacency list. But source may still be useful if you pass a reference to edge alone somewhere, where you don't have the source node at hand.
That aside, for the simplest graph this kind of approach seems like an overkill, because edges only store source and destination edges, the former being mostly redundant. But you may need to extend your edge class later with something like weights, labels, auxiliary data like residual flow or something like that. So having such class is a nice idea after all.
Moreover, some algorithms work directly on edges. For example, you may need to search for an edge satisfying some criterion. Having a separate class gives you freedom to create lists of edges without ad-hoc approaches like pair<Node, Node> or something.
You miss the constant of space complexity in storing the edges.
When you store the edges in adjacency matrix/list, you have to store both (node1, node2) and (node2, node1) for each edge.
You double the space, although the big-O complexity stays the same.
However, there're times when such space constant has to be considered.
You can take advantage of the class edge when you would like to save as much space as possible, and you would like to prioritize space over time.
Linear search on all the edge instances is a way.
Linear search is slow but you prioritize space over time.
Maybe parallel search when you have a distributed system is another way, but you have to verify.
Your homework question may have an artificial constraint of the design of the edge class. Artificial constraint idea comes from https://meta.stackexchange.com/questions/10811/how-do-i-ask-and-answer-homework-questions
I'm new in using C++ boost library in particularly the boost graph library which a needed to try coding some algorithms where i commonly check the adjacency of two vertices and dealing with other graph concepts like computing graph invariants.
What i know is that we can iterate through adjacent vertices with the function : adjacent_vertices(u, g) but i'm searching for an efficient way to test if two vertices u, v are adjacent or not without doing linear search
The AdjacencyMatrix concept gives a complexity guarantee that the edge() function must return in constant time.
To check if two vertices v and w are adjacent in G, you write edge(v, w, G).second, since the function returns a pair where the second value indicates if the edge exists.
The edge() function is implemented for other graph representations as well. Here is a graph that shows how different representations compare with regard to performance of checking vertex adjacency:
Here is the code used to generate the data for this plot. Each data point is 100 random graphs of medium density, with 100 random edge checks per each graph. Note the logarithmic y axis.
What is the best choice will eventually depend on your particular application, because for other operations the ordering of structures by speed is different. In other words, avoid premature optimization.
BGL is a highly generic library. You can adapt most any datastructure for use with its algorithms.
You can vary the edge container. You don't mention it, but I'm assuming you've been looking at the interface/complexity guarantees for boost::adjacency_list.
Indeed the edge membership test will be O(n) even if you use setS for the edge container selector. This is mostly because adjacency lists store outgoing edges are per vertex. So in worst case, each vertex contains at most one outgoing edge and the search is practically O(n) [1]
In this case you simply want to select another graph implementation.
The documentation page on Graph Concepts is a good starting point to find out about which concepts are expected. As well as, which models supply those concepts.
In the worst case you can adapt your data structure for use with Boost Graph algorithms. E.g. you could store all edges in a simple std::[unordered_]set<std::pair<VID, VID> > and adapt it to model the EdgeListGraph concept.
That way you will have performant lookups.
[1] of course this also means, in best case the search is whatever your set implementation affords: O(log n) because all edges could originate from the same vertex...
I've been thinking about creating a class in C++ on graph theory. The idea is it'll be a class to hold indefinite number of vertices and edges for a simple graph (at most one edge between a pair of vertices). The problem is how'd I store this indefinite number of vertices/edges in the most efficient way.
I came up with the idea of having dynamic pointer to array of vertices as a member in the class. However, it'd be inefficient, and I also encounter problem of how to determine the connection of vertices (I wouldn't be able to determine which vertices connect with which), if I use this method. The alternative is to create a class Vertex that suppose to contain information of its connectivity. However, because of indefinite number of edges, I cannot think of other way around other than to use dynamic variables inside Vertex. It'd make my code efficiency worse with this approach.
So is there a better approach?
If you do not plan to frequently add and remove items from inside the collections, I'd use STL vectors. They're fast for iterating through, but not terrible for inserts and removes in the middle.
If you want to add / remove anywhere frequently, I'd use STL lists. They're slower for iterating, but insertion / removal is O(1).
You can then define your vertex and edge as something like:
class Edge;
class Vertex
{
// ...
public:
std::list<Edge> incomingEdges;
std::list<Edge> outgoingEdges;
}
class Edge
{
// ...
public:
Vertex startpoint;
Vertex endpoint;
}
You'll pretty quickly find yourself wanting both a Vertex and Edge class -- there are too many algorithms that depend on coloring, or weighting, or marking edges, and it's also simpler to mix directed and undirected edges. The odds are good that you aren't going to really care a lot about storing the appropriate references dynamically, because that can be reduced to a vector of pointers.
Another issue to think about is if you will want to store this thing persistently.
Suggestion: try the Simplest Thing That Can Possibly Work first. Assuming an Array class that resizes itself as needed, that will look something like
class Vertex {
Array<Edge> edges ;
VertexData vd ; // define this for the task.
public:
// ctor etc; quiz: what operations?
}
class Edge {
Vertex v1, v2;
EdgeData ed;
public:
// ctor etc
}
Construct all the vertices and edges with new, don't worry about performance,and write some code against these classes.
Then go back, think how you'd have liked to write the code, and re-implement the classes to have that interface.
I'm a little prejudiced, since I used to teach the book and worked for Marshall Cline and Mike Girou, but I think one of the best C++ books for someone trying to really use it effectively is The C++ FAQBook, by Cline, Girou, and Lomow.
Greetings code-gurus!
I am writing an algorithm that connects, for instance node_A of Region_A with node_D of Region_D. (node_A and node_D are just integers). There could be 100k+ such nodes.
Assume that the line segment between A and D passes through a number of other regions, B, C, Z . There will be a maximum of 20 regions in between these two nodes.
Each region has its own properties that may vary according to the connection A-D. I want to access these at a later point of time.
I am looking for a good data structure (perhaps an STL container) that can hold this information for a particular connection.
For example, for connection A - D I want to store :
node_A,
node_D,
crosssectional area (computed elsewhere) ,
regionB,
regionB_thickness,
regionB other properties,
regionC, ....
The data can be double , int , string and could also be an array /vector etc.
First I considered creating structs or classes for regionB, regionC etc .
But, for each connection A-D, certain properties like thickness of the region through which this connection passes are different.
There will only be 3 or 4 different things I need to store pertaining to a region.
Which data structure should I consider here (any STL container like vector?) Could you please suggest one? (would appreciate a code snippet)
To access a connection between nodes A-D, I want to make use of int node_A (an index).
This probably means I need to use a hashmap or similar data structure.
Can anyone please suggest a good data structure in C++ that can efficiently
hold this sort of data for connection A -D described above? (would appreciate a code snippet)
thank you!
UPDATE
for some reasons, I can not make use of pkgs like boost. So want to know if I can use any libraries from STL
You should try to group stuff together when you can. You can group the information on each region together with something like the following:
class Region_Info {
Region *ptr;
int thickness;
// Put other properties here.
};
Then, you can more easily create a data structure for your line segment, maybe something like the following:
class Line_Segment {
int node_A;
int node_D;
int crosssectional_area;
std::list<Region_Info>;
};
If you are limited to only 20 regions, then a list should work fine. A vector is also fine if you would prefer.
Have you considered a adjacency array for each node, which stores the nodes it is connected to, along with other data?
First, define a node
class Node
{
int id_;
std::vector<AdjacencyInfo> adjacency_;
}
Where the class AdjacencyInfo can store the myriad data which you need. You can change the Vector to a hashmap with the node id as the key if lookup speed is an issue. For fancy access you may want to overload the [] operator if it is an essential requirement.
So as an example
class Graph
{
std::map<int, Node> graph_;
}
boost has a graph library: boost.graph. Check it out if it is useful in your case.
Well, as everyone else has noticed, that's a graph. The question is, is it a sparse graph, or a dense one? There are generally two ways of representing graphs (more, but you'll probably only need to consider these two) :
adjacency matrix
adjacency list
An adjacency matrix is basically a NxN matrix which stores all the nodes in the first row and column, and connection data (edges) as cells, so you can index edges by vertices. Sorry if my English sucks, not my native language. Anyway, you should only consider adjacency matrix if you have a dense graph, and need to find node->edge->node connections really fast. However, iterating through neighbours or adding/removing vertices in an adjacency matrix is slow, the first requiring N iterations, and the second resizing the array/vector you use to store the matrix.
Your other option is to use an adjacency list. Basically, you have a class that represents a node, and one that represents an edge, that stores all the data for that edge, and two pointers that point to the nodes it's connected to. The node class has a collection of some sort (a list will do), and keeps track of all the edges it's connected to. Then you'll need a manager class, or simply a bunch of functions that operate on your nodes. Adding/connecting nodes is trivial in this case as is listing neighbours or connected edges. However, it's harder to iterate over all the edges. This structure is more flexible than the adjacency matrix and it's better for sparse graphs.
I'm not sure that I understood your question completely, but if I did, I think you'd be better off with an adjacency matrix, seems like you have a dense graph with lots of interconnected nodes and only need connection info.
Wikipedia has a good article on graphs as a data structure, as well as good references and links, and finding examples shouldn't be hard. Hope this helps :
Link