graph-theory

I'm playing around with networkx (graph library in python) and I found documentation saying the PageRank algorithm takes edge weights into account when scoring, but I was wondering if larger edge weights were better or lower weights better? Shortly, large weights are better for incoming nodes. PageRank works on a directed weighted graph. If page A has a link to page B, then the score for B goes up, i.e. the more input the page B (node) have, the higher is its score. Wikipedia article on PageRank for further details. Edit : let's make an experiment. Create a directed graph with 3 nodes and two

I'm looking for a way to allocate local variables to registers. I'm aware of a couple of serious methods for doing it (namely, those mentioned on Wikipedia ), but I'm stuck on how "spilling" is accomplished. Also, the relevant literature is quite intimidating. I'm hoping there's something simpler that will satisfy my priorities: Correctness -- an algorithm that will generate correct code regardless of how many local variables there are. Simplicity -- something I can understand without having to read too much literature. Efficiency -- it needs to be better than the current method, which is:

I read it is ideal to represent sparse graphs by adjacency lists and dense graphs by an adjacency matrix. But I would like to understand the main difference between sparse and dense graphs. Dense graph is a graph in which the number of edges is close to the maximal number of edges. Sparse graph is a graph in which the number of edges is close to the minimal number of edges. Sparse graph can be a disconnected graph . As the names indicate sparse graphs are sparsely connected (eg: Trees). Usually the number of edges is in O(n) where n is the number of vertices. Therefore adjacency lists are

if given a graph problem how do we know whether we need to use bfs or dfs algorithm??? or when do we use dfs algorithm or bfs algorithm. What are the differences and advantages of one over other? BFS is going to use more memory depending on the branching factor... however, BFS is a complete algorithm... meaning if you are using it to search for something in the lowest depth possible, BFS will give you the optimal solution. BFS space complexity is O(b^d) ... the branching factor raised to the depth (can be A LOT of memory). DFS on the other hand, is much better about space however it may find a

the current GPU threads are somehow limited (memory limit, limit of data structures, no recursion...). do you think it would be feasible to implement a graph theory problem on GPU. for example vertex cover? dominating set? independent set? max clique?.... is it also feasible to have branch-and-bound algorithms on GPUs? Recursive backtracking? Pratik Deoghare You will be interested in Exploring the Limits of GPUs With Parallel Graph Algorithms Accelerating large graph algorithms on the GPU using CUDA . This is tangentially related to your question, but I've implemented a "recursive"

Can some one tell me the difference between hamiltonian path and euler path. They seem similar! Chris Diver An Euler path is a path that crosses every edge exactly once without repeating, if it ends at the initial vertex then it is a Euler cycle. A Hamiltonian path passes through each vertex (note not each edge), exactly once, if it ends at the initial vertex then it is a Hamiltonian cycle. In a Euler path you might pass through a vertex more than once. In a Hamiltonian path you may not pass through all edges. Eulerian path must visit each edge exactly once, while Hamiltonian path must visit

First of all, let me say I'm using LyX, though I have no problem using ERT. Secondly, what is the most simplest way to draw a simple graph like this in Latex? I've seen some documents with graphs and I've seen some examples, but I couldn't figure out how to just draw a simple graph - what packages do I need, etc? TikZ can do this. A quick demo: \documentclass{article} \usepackage{tikz} \begin{document} \begin{tikzpicture} [scale=.8,auto=left,every node/.style={circle,fill=blue!20}] \node (n6) at (1,10) {6}; \node (n4) at (4,8) {4}; \node (n5) at (8,9) {5}; \node (n1) at (11,8) {1}; \node (n2)

I have this algorithm that is pseudocode for the dijkstra algorithm for graph theory. The first thing that goes on is a basic for loop. visitedSet[0] = true //visitedSet is a array of bools for (int i = 1; i <= numberNodes; ++i) { distanceArray[i] = adjacencyMatrix[0,i]; //distanceArray is 1D with size of fifty //adjacencyMatrix is 2D with size of fifty //Both arrays hold values of unsigned ints } Here are the array definitions enum GraphLimit300 {MAX_NODES = 50}; unsigned int adjacencyMatrix[MAX_NODES][MAX_NODES]; unsigned int distanceArray[MAX_NODES]; Visual studio is giving me an array