What are good examples of problems that graphs can solve better than the alternative? [closed]

Answer 1

Profiling and/or Benchmarking algorithms and implementations in code.

Answer 2

You can utilise graphs anywhere you can define the problem domain objects into nodes and the solution as the flow of control and/or data amongst the nodes.

Considering the fact that trees are indeed connected-acyclic graphs, there are even more areas you can use the graph theory.

Answer 3

To find out if two molecules can fit together. When developing drugs one is often interested in seeing if the drug molecules can fit into larger molecules in the body. The problem with determining whether this is possible is that molecules are not static. Different parts of the molecule can rotate around their chemical bindings so that a molecule can change into quite a lot of different shapes.

Each shape can be said to represent a point in a space consisting of shapes. Solving this problem involves finding a path through this space. You can do that by creating a roadmap through space, which is essentially a graph consisting of legal shapes and saying which shape a shape can turn into. By using a A* graph search algorithm through this roadmap you can find a solution.

Okay that was a lot of babble that perhaps wasn't very understandable or clear. But my point was that graphs pop up in all kinds of problems.

Answer 4

IMHO most of the domain models we use in normal applications are in some respect graphs. Already if you look at the UML diagrams you would notice that with a directed, labeled graph you could easily translate them directly into a persistence model. There are some examples of that over at Neo4j

Cheers

/peter

Answer 5

Your source code is tree structured, and a tree is a type of graph. Whenever you hear people talking about an AST (Abstract Syntax Tree), they're talking about a kind of graph.

Pointers form graph structures. Anything that walks pointers is doing some kind of graph manipulation.

The web is a huge directed graph. Google's key insight, that led them to dominate in search, is that the graph structure of the web is of comparable or greater importance than the textual content of the pages.

State machines are graphs. State machines are used in network protocols, regular expressions, games, and all kinds of other fields.

It's rather hard to think of anything you do that does not involve some sort of graph structure.

Answer 6

OCR. Picture a page of text scanned at an angle, with some noise in the image, where you must find the space between lines of text. One way is to make a graph of pixels, and find the shortest path from one side of the page to the other, where the difference in brightness is the distance between pixels.

This example is from the Algorithm Design Manual, which has lots of other real world examples of graph problems.