I've spent hours searching for an answer to this, but in most cases either the
question is about plots/charts (rather than graphs as in "control flow graph"),
or the answer "just use graphviz" is a valid answer.
However I have some constraints and requirements that make "just use graphviz" a
non-answer.
The full graph is large enough that it's not possible to generate a graphviz
for all of it.
Nodes and edges will be dynamically added and removed.
Nodes have lots of information that will be hidden by default and will be
expanded on request (imagine every node as a table with expandable rows/cols)
I want to be able to show only a subset of the graph on request, e.g. for
features like "only show reachable part of the graph from this node" or "show
all simple paths from this node to this node".
Basically I want to be able to start drawing nodes and edges on a 2D plane, and
add new nodes and edges dynamically. It's fine if nodes/edges move around as new
stuff is added. While I don't yet have hard requirements for this, it'd be good
if it looked "nice" -- for example if a node has lots of incoming edges (this is
a directed graph) ideally it'd be in a central place on the plane with all other
nodes around it etc.
Anything that gets me going would be helpful. Thanks.
(I don't know what label to add to this, adding "graph-theory" because I don't know what else to add)
I am trying to solve a modified version of the Traveling Salesmen Problem. This is a modification of the basic TSP so that all nodes have a color property and the optimal path cannot Touch more than four nodes of the same color sequentially. This will be run in a connected graph of no more than 100 nodes. I am trying to run this using Concorde.
Does anyone know how to add the color constraint to a Concorde run?
Thanks
I don't think Concorde is set up to add arbitrary constraints. The solver is highly customized for the classical TSP and can't accommodate new constraints like that. The only way to do it would be if you can figure out a way to convert your problem into a classical TSP by changing the data only (not the constraints), i.e., by coming up with some trick to set the cost matrix so that optimal solutions always satisfy the color constraint, but I can't see a way to do that, off hand.
I'm working on a map that shows different population statistics on a rather granular level in Berlin (447 sub-districts).
https://www.google.com/fusiontables/data?docid=1tIAPGaYK1iEWWLANQOupkAqCcPhVauMjdPS1qOs#map:id=3
For some reason, a small number of polygons (3) is not displayed as soon as you zoom into the map (12 or higher).
As the polygons are displayed at the level before, they should have the proper coordinates. I first thought the shapefiles (kmls provided by the local statistics authority) might be buggy, but that does not seem to be the case.
Can anybody explain to me why this happens?
Thank you very much!
Michael
There are two possibilities that I can think of:
it is a complexity problem or a winding direction issue with the polygon. Thread on Fusion Tables Users Group discussing this issue.
it is a complexity issue with the number of "features" on the tile. See Limits in the documentation, it used to be more clearly defined.
Reversing the winding direction of two of the problem polygons seems to fix the issue:
https://www.google.com/fusiontables/DataSource?snapid=S787935DQC4
I have a tile based map where several tiles are walls and others are walkable. the walkable tiles make up a graph I would like to use in path planning. My question is are their any good algorithms for finding a path which visits every node in the graph, minimising repeat visits?
For example:
map example http://img220.imageshack.us/img220/3488/mapq.png
If the bottom yellow tile is the starting point, the best path to visit all tiles with least repeats is:
path example http://img222.imageshack.us/img222/7773/mapd.png
There are two repeat visits in this path. A worse path would be to take a left at the first junction, then backtrack over three already visited tiles.
I don't care about the end node but the start node is important.
Thanks.
Edit:
I added pictures to my question but cannot see them when viewing it. here they are:
http://img220.imageshack.us/img220/3488/mapq.png
http://img222.imageshack.us/img222/7773/mapd.png
Additionally, in the graphs I need this for there will never be a situation where min repeats = 0. That is, to step on every tile in the map the player must cross his own path at least once.
Your wording is bad -- it allows a reduction to an NP-complete problem. If you could minimize repeat visits, then could you push them to 0 and then you would have a Hamiltonian Cycle. Which is solvable, but hard.
This sounds like it could be mapped onto the traveling salesman problem ... and so likely ends up being NP complete and no efficient deterministic algorithm is known.
Finding a path is fairly straight forward -- find a (or the minimum) spanning subtree and then do a depth/breadth-first traversal. Finding the optimal route is the really difficult bit.
You could use one of the dynamic optimization techniques to try and converge on a fairly good solution.
Unless there is some attribute of the minimum spanning subtree that could be used to generate the best path ... but I don't remember enough graph theory for that.
For instance:
An approach to compute efficiently the first intersection between a viewing ray and a set of three objects: one sphere, one cone and one cylinder (other 3D primitives).
What you're looking for is a spatial partitioning scheme. There are a lot of options for dealing with this, and lots of research spent in this area as well. A good read would be Christer Ericsson's Real-Time Collision Detection.
One easy approach covered in that book would be to define a grid, assign all objects to all cells it intersects, and walk along the grid cells intersecting the line, front to back, intersecting with each object associated with that grid cell. Keep in mind that an object might be associated with more grid-cells, so the intersection point computed might actually not be in the current cell, but actually later on.
The next question would be how you define that grid. Unfortunately, there's no one good answer, and you need to consider what approach might fit your scenario best.
Other partitioning schemes of interest are different tree structures, such as kd-, Oct- and BSP-trees. You could even consider using trees combined with a grid.
EDIT
As pointed out, if your set is actually these three objects, you're definately better of just intersecting each one, and just pick the earliest one. If you're looking for ray-sphere, ray-cylinder, etc, intersection tests, these are not really hard and a quick google should supply all the math you might possibly need. :)
"computationally efficient" depends on how large the set is.
For a trivial set of three, just test each of them in turn, it's really not worth trying to optimise.
For larger sets, look at data structures which divide space (e.g. KD-Trees). Whole chapters (and indeed whole books) are dedicated to this problem. My favourite reference book is An Introduction to Ray Tracing (ed. Andrew. S. Glassner)
Alternatively, if I've misread your question and you're actually asking for algorithms for ray-object intersections for specific types of object, see the same book!
Well, it depends on what you're really trying to do. If you'd like to produce a solution that is correct for almost every pixel in a simple scene, an extremely quick method is to pre-calculate "what's in front" for each pixel by pre-rendering all of the objects with a unique identifying color into a background item buffer using scan conversion (aka the z-buffer). This is sometimes referred to as an item buffer.
Using that pre-computation, you then know what will be visible for almost all rays that you'll be shooting into the scene. As a result, your ray-environment intersection problem is greatly simplified: each ray hits one specific object.
When I was doing this many years ago, I was producing real-time raytraced images of admittedly simple scenes. I haven't revisited that code in quite a while but I suspect that with modern compilers and graphics hardware, performance would be orders of magnitude better than I was seeing then.
PS: I first read about the item buffer idea when I was doing my literature search in the early 90s. I originally found it mentioned in (I believe) an ACM paper from the late 70s. Sadly, I don't have the source reference available but, in short, it's a very old idea and one that works really well on scan conversion hardware.
I assume you have a ray d = (dx,dy,dz), starting at o = (ox,oy,oz) and you are finding the parameter t such that the point of intersection p = o+d*t. (Like this page, which describes ray-plane intersection using P2-P1 for d, P1 for o and u for t)
The first question I would ask is "Do these objects intersect"?
If not then you can cheat a little and check for ray collisions in order. Since you have three objects that may or may not move per frame it pays to pre-calculate their distance from the camera (e.g. from their centre points). Test against each object in turn, by distance from the camera, from smallest to largest. Although the empty space is the most expensive part of the render now, this is more effective than just testing against all three and taking a minimum value. If your image is high res then this is especially efficient since you amortise the cost across the number of pixels.
Otherwise, test against all three and take a minimum value...
In other situations you may want to make a hybrid of the two methods. If you can test two of the objects in order then do so (e.g. a sphere and a cube moving down a cylindrical tunnel), but test the third and take a minimum value to find the final object.