graph-theory

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

I am reading Introduction to Algorithms. In 22.5 Strongly Connected Component, the algorithm STRONGLY-CONNECTED-COMPONENT(G) is defined as: Call DFS(G) to compute finishing times u.f for each vertex u Compute G transpose Call DFS(G transpose), but in the main loop of DFS, consider the vertices in order of decreasing u.f(as computed in line 1) Output the vertices of each tree in the depth-first forest formed in line 3 as a separate strongly connected component If I change the alogrithm to just using G, without calculating G transpose. Also consider the vertices in order of Increasing u.f

I'm writing a bit of JavaScript code which should select a random item from a canvas if the item meets certain requirements. There are different kinds of items (circles, triangles, squares etc.) and there's usually not the same number of items for each kind. The items are arranged in a hierarchy (so a square can contain a few circles, and a circle can contain other circles and so on - they can all be nested). Right now, my (primitive) approach at selecting a random item is to: Recursively traverse the canvas and build a (possibly huge!) list of items Shuffle the list Iterate the shuffled list

For example, two simple vertices in an OrientDB Graph: orientdb> CREATE DATABASE local:/databases/test admin admin local graph; Creating database [local:/databases/test] using the storage type [local]... Database created successfully. Current database is: local:/graph1/databases/test orientdb> INSERT INTO V (label,in,out) VALUES ('vertexOne',[],[]); Inserted record 'V#6:0{label:vertexOne,in:[0],out:[0]} v0' in 0.001000 sec(s). orientdb> INSERT INTO V (label,in,out) VALUES ('vertexTwo',[],[]); Inserted record 'V#6:1{label:vertexTwo,in:[0],out:[0]} v0' in 0.000000 sec(s). Is there a way to

Given: A Set (for the sake of discussion we will call it S ), which is an unordered collection of line segments. Each line segment is defined as two Longitude-Latitude end-points. While all of the line segments follow an implied curve, there are "gaps" between each of the segments, of various sizes. We refer to this curve as "implied" because it is not explicitly defined anywhere. The only information that we have available are the line segments contained within S . Desired Result: A sequence (for the sake of discussion we will call it R ), which is an ordered collection of line segments. Each