graph-algorithm

I want to divide a graph with N weighted-vertices and N-1 edges into three parts such that the maximum of the sum of weights of all the vertices in each of the parts is minimized. This is the actual problem i am trying to solve, http://www.iarcs.org.in/inoi/contests/jan2006/Advanced-1.php I considered the following method /*Edges are stored in an array E, and also in an adjacency matrix for depth first search. Every edge in E has two attributes a and b which are the nodes of the edge*/ min-max = infinity for i -> 0 to length(E): for j -> i+1 to length(E): /*Call depth first search on the nodes

Please help me find a good solution for this problem. We have n boxes with 3 dimensions. We can orient them and we want to put them on top of another to have a maximun height. We can put a box on top of an other box, if 2 dimensions (width and lenght) are lower than the dimensions of the box below. For exapmle we have 3 dimensions w*D*h, we can show it in to (h*d,d*h,w*d,d*W,h*w,w*h) please help me to solve it in graph theory. in this problem we can not put(2*3)above(2*4) because it has the same width.so the 2 dimension shoud be smaller than the box Edit: Only works if boxes can not be rotated

I'm new to networkx and actually a bit confused on how to efficiently find the n-degree neighborhood of a node. The n-degree neighborhood of a node v_i is the set of nodes exactly n hops away from v_i. Given a specified n, I need find the n-degree neighborhood for each node in the graph/network. Suppose I have the following graph and I want to find the n=1 neighborhood of node v1. That would be v2 and v3. Next suppose I want to find the n=2 neighborhood of node v1, then that would be v4. import networkx as nx G = nx.Graph() G.add_edges_from([('v1','v2'),('v2','v4'),('v1','v3')]) def

There is a class of algorithms for triangulation between two planar contours. These algorithms try to make a "good triangulation" to fill a space between these contours: One of them ( Optimal surface reconstruction from planar contours ) is based on the dynamic programming technique and uses a cost function for determining which triangulation is acceptable according to the minimum cost. A minimal triangle area as a cost function makes a good result in most of cases ( Triangulation of Branching Contours using Area Minimization ), but, unfortunately, not in all of them. For example when you have

I am looking for an explanation why the AStar / A* algorithm is called AStar. All similar (shortest path problem) algorithms are often named like its developer(s), so what is AStar standing for? There were algorithms called A1 and A2. Later, it was proved that A2 was optimal and in fact also the best algorithm possible, so he gave it the name A* which symbolically includes all possible version numbers. Source: In 1964 Nils Nilsson invented a heuristic based approach to increase the speed of Dijkstra's algorithm. This algorithm was called A1. In 1967 Bertram Raphael made dramatic improvements

I have a directed graph stored in a Map data structure, where the key is the node's ID and the [value] is the array of the nodeIds of the nodes which are pointed by the key node. Map<String, String[]> map = new HashMap<String, String[]>(); map.put("1", new String[] {"2", "5"}); map.put("2", new String[] {"3"}); map.put("3", new String[] {"4"}); map.put("4", new String[] {"4"}); map.put("5", new String[] {"5", "9"}); map.put("6", new String[] {"5"}); map.put("7", new String[] {"6"}); map.put("8", new String[] {"6"}); map.put("9", new String[] {"10"}); map.put("10", new String[] {"5"}); map.put(