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  • Algorithm to shift the car

    - by Simran kaur
    I have a track that can be divided into n number of tracks and a car as GamObject. The track has transforms such that some part of the track's width lies in negative x axis and other in positive. Requirement: One move should cross one track. On every move(left or right), I want the car to reach exact centre of the next track on either sides i.e left or right. My code: Problem: : Because of negative values , somewhere I am missing out something that is making car move not in desirable positions and that's because of negative values only. variable tracks is the number of tracks the whole track is divided in. variable dist is the total width of the complete track. On left movement: if (Input.GetKeyDown (KeyCode.LeftArrow)) { if (this.transform.position.x < r.renderer.bounds.min.x + box.size.x) { this.transform.position = new Vector3 (r.renderer.bounds.min.x + Mathf.FloorToInt(box.size.x), this.transform.position.y, this.transform.position.z); } else { int tracknumber = Mathf.RoundToInt(dist - transform.position.x)/tracks; float averagedistance = (tracknumber*(dist/tracks) + (tracknumber-1)*(dist/tracks))/2; if(transform.position.x > averagedistoftracks) { amountofmovement = amountofmovement + (transform.position.x - averagedistance); } else { amountofmovement = amountofmovement - (averagedistance - transform.position.x); } this.transform.position = new Vector3 (this.transform.position.x - amountofmovement, this.transform.position.y, this.transform.position.z); } }

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  • Pixel alignment algorithm

    - by user42325
    I have a set of square blocks, I want to draw them in a window. I am sure the coordinates calculation is correct. But on the screen, some squares' edge overlap with other, some are not. I remember the problem is caused by accuracy of pixels. I remember there's a specific topic related to this kind of problem in 2D image rendering. But I don't remember what exactly it is, and how to solve it. Look at this screenshot. Each block should have a fixed width margin. But in the image, the vertical white line have different width.Though, the horizontal lines looks fine.

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  • Facebook Graph API - likes returns me an empty set...

    - by Vinch
    When I try to get all my "likes" (formerly fan pages) on Facebook Graph API, sometimes it returns me an empty set: { "data": [ ] } I tried with https://graph.facebook.com/me/likes?access_token=MY_ACCESS_TOKEN and with graph.facebook.com/vinch/likes?access_token=MY_ACCESS_TOKEN but the result is exactly the same (empty). Any idea of what it can be? I need it to know if a user likes (is fan of) a specific page.

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  • Looking for an algorithm to connect dots - shortest route

    - by e4ch
    I have written a program to solve a special puzzle, but now I'm kind of stuck at the following problem: I have about 3200 points/nodes/dots. Each of these points is connected to a few other points (usually 2-5, theoretical limit is 1-26). I have exactly one starting point and about 30 exit points (probably all of the exit points are connected to each other). Many of these 3200 points are probably not connected to neither start nor end point in any way, like a separate net, but all points are connected to at least one other point. I need to find the shortest number of hops to go from entry to exit. There is no distance between the points (unlike the road or train routing problem), just the number of hops counts. I need to find all solutions with the shortest number of hops, and not just one solution, but all. And potentially also solutions with one more hop etc. I expect to have a solution with about 30-50 hops to go from start to exit. I already tried: 1) randomly trying possibilities and just starting over when the count was bigger than a previous solution. I got first solution with 3500 hops, then it got down to about 97 after some minutes, but looking at the solutions I saw problems like unnecessary loops and stuff, so I tried to optimize a bit (like not going back where it came from etc.). More optimizations are possible, but this random thing doesn't find all best solutions or takes too long. 2) Recursively run through all ways from start (chess-problem-like) and breaking the try when it reached a previous point. This was looping at about a length of 120 nodes, so it tries chains that are (probably) by far too long. If we calculate 4 possibilities and 120 nodes, we're reaching 1.7E72 possibilities, which is not possible to calculate through. This is called Depth-first search (DFS) as I found out in the meantime. Maybe I should try Breadth-first search by adding some queue? The connections between the points are actually moves you can make in the game and the points are how the game looks like after you made the move. What would be the algorithm to use for this problem? I'm using C#.NET, but the language shouldn't matter.

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  • How to detect if breaking an edge will make a graph disjoint?

    - by the_graph_guy
    I have a graph that starts off with a single, root node. Nodes are added one by one to the graph. At node creation time, they have to be linked either to the root node, or to another node, by a single edge. Edges can also be created and deleted (one by one, between any two nodes). Nodes can be deleted one at a time. Node and edge creation, deletion operations can happen in any arbitrary order. OK, so here's my question: When an edge is deleted, is it possible do determine, in constant time (i.e. with an O(1) algorithm), if doing this will divide the graph into two disjoint subgraphs? If it will, then which side of the edge will the root node belong? I'm willing to maintain, within reasonable limits, any additional data structure that can facilitate the derivation of this information. Maybe it is not possible to do it in O(1), if so any pointers to literature will be appreciated.

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  • Efficient algorithm for creating an ideal distribution of groups into containers?

    - by Inshim
    I have groups of students that need to be allocated into classrooms of a fixed capacity (say, 100 chairs in each). Each group must only be allocated to a single classroom, even if it is larger than the capacity (ie there can be an overflow, with students standing up) I need an algorithm to make the allocations with minimum overflows and under-capacity classrooms. A naive algorithm to do this allocation is horrendously slow when having ~200 groups, with a distribution of about half of them being under 20% of the classroom size. Any ideas where I can find at least some good starting point for making this algorithm lightning fast? Thanks!

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  • Generic Adjacency List Graph implementation

    - by DmainEvent
    I am trying to come up with a decent Adjacency List graph implementation so I can start tooling around with all kinds of graph problems and algorithms like traveling salesman and other problems... But I can't seem to come up with a decent implementation. This is probably because I am trying to dust the cobwebs off my data structures class. But what I have so far... and this is implemented in Java... is basically an edgeNode class that has a generic type and a weight-in the event the graph is indeed weighted. public class edgeNode<E> { private E y; private int weight; //... getters and setters as well as constructors... } I have a graph class that has a list of edges a value for the number of Vertices and and an int value for edges as well as a boolean value for whether or not it is directed. The brings up my first question, if the graph is indeed directed, shouldn't I have a value in my edgeNode class? Or would I just need to add another vertices to my LinkedList? That would imply that a directed graph is 2X as big as an undirected graph wouldn't it? public class graph { private List<edgeNode<?>> edges; private int nVertices; private int nEdges; private boolean directed; //... getters and setters as well as constructors... } Finally does anybody have a standard way of initializing there graph? I was thinking of reading in a pipe-delimited file but that is so 1997. public graph GenereateGraph(boolean directed, String file){ List<edgeNode<?>> edges; graph g; try{ int count = 0; String line; FileReader input = new FileReader("C:\\Users\\derekww\\Documents\\JavaEE Projects\\graphFile"); BufferedReader bufRead = new BufferedReader(input); line = bufRead.readLine(); count++; edges = new ArrayList<edgeNode<?>>(); while(line != null){ line = bufRead.readLine(); Object edgeInfo = line.split("|")[0]; int weight = Integer.parseInt(line.split("|")[1]); edgeNode<String> e = new edgeNode<String>((String) edges.add(e); } return g; } catch(Exception e){ return null; } } I guess when I am adding edges if boolean is true I would be adding a second edge. So far, this all depends on the file I write. So if I wrote a file with the following Vertices and weights... Buffalo | 18 br Pittsburgh | 20 br New York | 15 br D.C | 45 br I would obviously load them into my list of edges, but how can I represent one vertices connected to the other... so on... I would need the opposite vertices? Say I was representing Highways connected to each city weighted and un-directed (each edge is bi-directional with weights in some fictional distance unit)... Would my implementation be the best way to do that? I found this tutorial online Graph Tutorial that has a connector object. This appears to me be a collection of vertices pointing to each other. So you would have A and B each with there weights and so on, and you would add this to a list and this list of connectors to your graph... That strikes me as somewhat cumbersome and a little dismissive of the adjacency list concept? Am I wrong and that is a novel solution? This is all inspired by steve skiena's Algorithm Design Manual. Which I have to say is pretty good so far. Thanks for any help you can provide.

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  • Better data structure for a game like Bubble Witch

    - by CrociDB
    I'm implementing a bubble-witch-like game (http://www.king.com/games/puzzle-games/bubble-witch/), and I was thinking on what's the better way to store the "bubbles" and to work with. I thought of using graphs, but that might be too complex for a trivial thing. Thought of a matrix, just like a tile map, but that might get too 'workaroundy'. I don't know. I'll be doing in Flash/AS3, though. Thanks. :)

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  • How to represent a graph with multiple edges allowed between nodes and edges that can selectively disappear

    - by Pops
    I'm trying to figure out what sort of data structure to use for modeling some hypothetical, idealized network usage. In my scenario, a number of users who are hostile to each other are all trying to form networks of computers where all potential connections are known. The computers that one user needs to connect may not be the same as the ones another user needs to connect, though; user 1 might need to connect computers A, B and D while user 2 might need to connect computers B, C and E. Image generated with the help of NCTM Graph Creator I think the core of this is going to be an undirected cyclic graph, with nodes representing computers and edges representing Ethernet cables. However, due to the nature of the scenario, there are a few uncommon features that rule out adjacency lists and adjacency matrices (at least, without non-trivial modifications): edges can become restricted-use; that is, if one user acquires a given network connection, no other user may use that connection in the example, the green user cannot possibly connect to computer A, but the red user has connected B to E despite not having a direct link between them in some cases, a given pair of nodes will be connected by more than one edge in the example, there are two independent cables running from D to E, so the green and blue users were both able to connect those machines directly; however, red can no longer make such a connection if two computers are connected by more than one cable, each user may own no more than one of those cables I'll need to do several operations on this graph, such as: determining whether any particular pair of computers is connected for a given user identifying the optimal path for a given user to connect target computers identifying the highest-latency computer connection for a given user (i.e. longest path without branching) My first thought was to simply create a collection of all of the edges, but that's terrible for searching. The best thing I can think to do now is to modify an adjacency list so that each item in the list contains not only the edge length but also its cost and current owner. Is this a sensible approach? Assuming space is not a concern, would it be reasonable to create multiple copies of the graph (one for each user) rather than a single graph?

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  • Graphviz or Dynagraph for Graph-manipulation Program?

    - by noahlavine
    I'm looking into writing a program that will show a graph to the user. The graph will change over time (the user should be able to right-click on a graph item and ask for more detail, which will pop out new bits of the graph), and the user might be able to drag parts of the graph around. I would ideally also like to be able to specify the relative layout of certain parts of the graph myself while leaving the overall layout up to a library, but that's not essential. I'm trying to decide on a graph layout library to use. As far as I can tell, the two leading candidates are Graphviz and Dynagraph. The Dynagraph website suggests that Graphviz is for drawing static graphs, and that Dynagraph was forked from Graphviz and contains algorithms for graphs that will be updated. It has a sample program called Dynasty that does exactly what I want. However, the Graphviz site contains an example program called Lefty which seems to do exactly what I want. Graphviz also seems to be much more widely used, judging by Google (and SO) results. Finally, I'd like to code the GUI part in a language like Python or Scheme, which makes me a bit hesitant to use C++ because I understand it's harder to interface that to interpreters. So my question is, which library is better for what I'm trying to do? Do they both have strong and weak points? Has one of them actually ceased development and is just leaving its website up to confuse me? (I've seen http://stackoverflow.com/questions/464000/simple-dynamic-graph-display-for-c and http://stackoverflow.com/questions/2376987/open-source-libraries-to-design-directed-graphs, but I can't tell whether they're right about the Graphviz or Dynagraph choice because of Lefty and also the language issue.)

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  • Scalable / Parallel Large Graph Analysis Library?

    - by Joel Hoff
    I am looking for good recommendations for scalable and/or parallel large graph analysis libraries in various languages. The problems I am working on involve significant computational analysis of graphs/networks with 1-100 million nodes and 10 million to 1+ billion edges. The largest SMP computer I am using has 256 GB memory, but I also have access to an HPC cluster with 1000 cores, 2 TB aggregate memory, and MPI for communication. I am primarily looking for scalable, high-performance graph libraries that could be used in either single or multi-threaded scenarios, but parallel analysis libraries based on MPI or a similar protocol for communication and/or distributed memory are also of interest for high-end problems. Target programming languages include C++, C, Java, and Python. My research to-date has come up with the following possible solutions for these languages: C++ -- The most viable solutions appear to be the Boost Graph Library and Parallel Boost Graph Library. I have looked briefly at MTGL, but it is currently slanted more toward massively multithreaded hardware architectures like the Cray XMT. C - igraph and SNAP (Small-world Network Analysis and Partitioning); latter uses OpenMP for parallelism on SMP systems. Java - I have found no parallel libraries here yet, but JGraphT and perhaps JUNG are leading contenders in the non-parallel space. Python - igraph and NetworkX look like the most solid options, though neither is parallel. There used to be Python bindings for BGL, but these are now unsupported; last release in 2005 looks stale now. Other topics here on SO that I've looked at have discussed graph libraries in C++, Java, Python, and other languages. However, none of these topics focused significantly on scalability. Does anyone have recommendations they can offer based on experience with any of the above or other library packages when applied to large graph analysis problems? Performance, scalability, and code stability/maturity are my primary concerns. Most of the specialized algorithms will be developed by my team with the exception of any graph-oriented parallel communication or distributed memory frameworks (where the graph state is distributed across a cluster).

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  • What are some good algorithms for drawing lines between graph nodes?

    - by ApplePieIsGood
    What I'm specifically grappling with is not just the layout of a graph, but when a user selects a graph node and starts to drag it around the screen area, the line has to constantly be redrawn to reflect what it would look like if the user were to release the node. I suppose this is part of the layout algorithm? Also some applications get a bit fancy and don't simply draw the line in a nice curvy way, but also bend the line around the square shaped node in almost right angles. See attached image and keep in mind that as a node is dragged, the line is drawn as marching ants, and re-arranged nicely, while retaining its curved style.

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  • How would you sample a real-time stream of coordinates to create a Speed Graph?

    - by Andrew Johnson
    I have a GPS device, and I am receiving continuous points, which I store in an array. These points are time stamped. I would like to graph distance/time (speed) vs. distance in real-time; however, I can only plot 50 of the points because of hardware constraints. How would you select points from the array to graph? For example, one algorithm might be to select every Nth point from the array, where N results in 50 points total. Code: float indexModifier = 1; if (MIN(50,track.lastPointIndex) == 50) { indexModifier = track.lastPointIndex/50.0f; } index = ceil(index*indexModifier); Another algorithm might be to keep an array of 50 points, and throw out the point with the least speed change each time you get a new point.

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  • Excel Graph: How can I turn data below in to a 'time based' graph

    - by Mike
    In my spreadsheet I am collecting time periods when certain values have been changed. The user is restricted to 4 time periods. I would like to show the data based on thos time periods. I've included a mock up' of the data and the type of graph I would like to create. I've tried to create it for the last hour but am obviously missing something so thought I'd ask around. http://i48.tinypic.com/55lezr.jpg Many thanks for any help Mike P.S How do I make this image appear in the message and not as a link?

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  • Can I use a plaintext diff algorithm for tracking XML changes?

    - by rinogo
    Hi all! Interesting question for you here. I'm working in Flex/AS3 on (for simplicity) an XML editor. I need to provide undo/redo functionality. Of course, one solution is to store the entire source text with each edit. However, to conserve memory, I'd like to store the diffs instead (these diffs will also be used to transmit updates to the server for auto-saving). My question is - can I use a plaintext diff algorithm for tracking these XML changes? My research on the internet indicates that I cannot do so. However, I'm obviously missing something. Plaintext diff provides functionality that is purportedly: diff(text, text') - diffs patch(text, diffs) - text' XML is simply text, so why can't I just use diff() and patch() to transform the text reliably? For example: Let's say that I'm a poet. When I write poetry, I use lots of funky punctuation... You know, like <, /, and . (You might see where I'm going with this...) If I'm writing my poetry in an application that uses diffs to provide undo/redo functionality, does my poetry become garbled when I undo/redo my edits? It's just text! Why does it make a difference to the algorithm? I obviously don't get something here...Thanks for explaining! :) -Rich

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  • Enumerate all paths in a weighted graph from A to B where path length is between C1 and C2

    - by awmross
    Given two points A and B in a weighted graph, find all paths from A to B where the length of the path is between C1 and C2. Ideally, each vertex should only be visited once, although this is not a hard requirement. I supose I could use a heuristic to sort the results of the algorithm to weed out "silly" paths (e.g. a path that just visits the same two nodes over and over again) I can think of simple brute force algorithms, but are there any more sophisticed algorithms that will make this more efficient? I can imagine as the graph grows this could become expensive. In the application I am developing, A & B are actually the same point (i.e. the path must return to the start), if that makes any difference. Note that this is an engineering problem, not a computer science problem, so I can use an algorithm that is fast but not necessarily 100% accurate. i.e. it is ok if it returns most of the possible paths, or if most of the paths returned are within the given length range.

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  • O(log n) algorithm for computing rank of union of two sorted lists?

    - by Eternal Learner
    Given two sorted lists, each containing n real numbers, is there a O(log?n) time algorithm to compute the element of rank i (where i coresponds to index in increasing order) in the union of the two lists, assuming the elements of the two lists are distinct? I can think of using a Merge procedure to merge the 2 lists and then find the A[i] element in constant time. But the Merge would take O(n) time. How do we solve it in O(log n) time?

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  • O(log n) algorithm to find the element having rank i in union of pre-sorted lists

    - by Eternal Learner
    Given two sorted lists, each containing n real numbers, is there a O(log?n) time algorithm to compute the element of rank i (where i coresponds to index in increasing order) in the union of the two lists, assuming the elements of the two lists are distinct? I can think of using a Merge procedure to merge the 2 lists and then find the A[i] element in constant time. But the Merge would take O(n) time. How do we solve it in O(log n) time?

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  • How is this algorithm, for finding maximum path on a Directed Acyclical Graph, called?

    - by Martín Fixman
    Since some time, I'm using an algorithm that runs in complexity O(V + E) for finding maximum path on a Directed Acyclical Graph from point A to point B, that consists on doing a flood fill to find what nodes are accessible from note A, and how many "parents" (edges that come from other nodes) each node has. Then, I do a BFS but only "activating" a node when I already had used all its "parents". queue <int> a int paths[] ; //Number of paths that go to note i int edge[][] ; //Edges of a int mpath[] ; //max path from 0 to i (without counting the weight of i) int weight[] ; //weight of each node mpath[0] = 0 a.push(0) while not empty(a) for i in edge[a] paths[i] += 1 a.push(i) while not empty(a) for i in children[a] mpath[i] = max(mpath[i], mpath[a] + weight[a]) ; paths[i] -= 1 ; if path[i] = 0 a.push(i) ; Is there any special name for this algorithm? I told it to an Informatics professor, he just called it "Maximum Path on a DAG", but it doesn't sound good when you say "I solved the first problem with a Fenwick Tree, the second with Dijkstra, and the third with Maximum Path".

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  • Problem: Munin Graph

    - by Pablo
    I've been trying to install Munin for 15 days, I looked for information, analized logs, I even deleted and reinstalled Munin using YUM. I'm hosted at Media Temple on a VPS with CentOS. The problem is still there and It's driving me nuts. Graphics are shown as following: http://imageshack.us/photo/my-images/833/capturadepantalla201106u.png/ This is the configuration of my munin.conf file dbdir /var/lib/munin htmldir /var/www/munin logdir /var/log/munin rundir /var/run/munin [localhost] address **.**.***.*** #IP VPS This is the configuration of my munin-node.conf file log_level 4 log_file /var/log/munin/munin-node.log port 4949 pid_file /var/run/munin/munin-node.pid background 1 setseid 1 # Which port to bind to; host * user root group root setsid yes # Regexps for files to ignore ignore_file ~$ ignore_file \.bak$ ignore_file %$ ignore_file \.dpkg-(tmp|new|old|dist)$ ignore_file \.rpm(save|new)$ allow ^127\.0\.0\.1$ Thanks so much, I appreciate all the answers UPDATE munin-graph.log Jun 22 16:30:02 - Starting munin-graph Jun 22 16:30:02 - Processing domain: localhost Jun 22 16:30:02 - Graphed service : open_inodes (0.14 sec * 4) Jun 22 16:30:02 - Graphed service : sendmail_mailtraffic (0.10 sec * 4) Jun 22 16:30:02 - Graphed service : apache_processes (0.12 sec * 4) Jun 22 16:30:02 - Graphed service : entropy (0.10 sec * 4) Jun 22 16:30:02 - Graphed service : sendmail_mailstats (0.14 sec * 4) Jun 22 16:30:02 - Graphed service : processes (0.14 sec * 4) Jun 22 16:30:03 - Graphed service : apache_accesses (0.27 sec * 4) Jun 22 16:30:03 - Graphed service : apache_volume (0.15 sec * 4) Jun 22 16:30:03 - Graphed service : df (0.21 sec * 4) Jun 22 16:30:03 - Graphed service : netstat (0.19 sec * 4) Jun 22 16:30:03 - Graphed service : interrupts (0.14 sec * 4) Jun 22 16:30:03 - Graphed service : swap (0.14 sec * 4) Jun 22 16:30:04 - Graphed service : load (0.11 sec * 4) Jun 22 16:30:04 - Graphed service : sendmail_mailqueue (0.13 sec * 4) Jun 22 16:30:04 - Graphed service : cpu (0.21 sec * 4) Jun 22 16:30:04 - Graphed service : df_inode (0.16 sec * 4) Jun 22 16:30:04 - Graphed service : open_files (0.16 sec * 4) Jun 22 16:30:04 - Graphed service : forks (0.13 sec * 4) Jun 22 16:30:05 - Graphed service : memory (0.26 sec * 4) Jun 22 16:30:05 - Graphed service : nfs_client (0.36 sec * 4) Jun 22 16:30:05 - Graphed service : vmstat (0.10 sec * 4) Jun 22 16:30:05 - Processed node: localhost (3.45 sec) Jun 22 16:30:05 - Processed domain: localhost (3.45 sec) Jun 22 16:30:05 - Munin-graph finished (3.46 sec)

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  • Improving the running time of Breadth First Search and Adjacency List creation

    - by user45957
    We are given an array of integers where all elements are between 0-9. have to start from the 1st position and reach end in minimum no of moves such that we can from an index i move 1 position back and forward i.e i-1 and i+1 and jump to any index having the same value as index i. Time Limit : 1 second Max input size : 100000 I have tried to solve this problem use a single source shortest path approach using Breadth First Search and though BFS itself is O(V+E) and runs in time the adjacency list creation takes O(n2) time and therefore overall complexity becomes O(n2). is there any way i can decrease the time complexity of adjacency list creation? or is there a better and more efficient way of solving the problem? int main(){ vector<int> v; string str; vector<int> sets[10]; cin>>str; int in; for(int i=0;i<str.length();i++){ in=str[i]-'0'; v.push_back(in); sets[in].push_back(i); } int n=v.size(); if(n==1){ cout<<"0\n"; return 0; } if(v[0]==v[n-1]){ cout<<"1\n"; return 0; } vector<int> adj[100001]; for(int i=0;i<10;i++){ for(int j=0;j<sets[i].size();j++){ if(sets[i][j]>0) adj[sets[i][j]].push_back(sets[i][j]-1); if(sets[i][j]<n-1) adj[sets[i][j]].push_back(sets[i][j]+1); for(int k=j+1;k<sets[i].size();k++){ if(abs(sets[i][j]-sets[i][k])!=1){ adj[sets[i][j]].push_back(sets[i][k]); adj[sets[i][k]].push_back(sets[i][j]); } } } } queue<int> q; q.push(0); int dist[100001]; bool visited[100001]={false}; dist[0]=0; visited[0]=true; int c=0; while(!q.empty()){ int dq=q.front(); q.pop(); c++; for(int i=0;i<adj[dq].size();i++){ if(visited[adj[dq][i]]==false){ dist[adj[dq][i]]=dist[dq]+1; visited[adj[dq][i]]=true; q.push(adj[dq][i]); } } } cout<<dist[n-1]<<"\n"; return 0; }

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  • Cross-platform DirectShow alternatives for real life graph

    - by Ole Jak
    Today I have such graph. I run it on windows I need some easy crossplatform DirectShow like alternative where to reconstruct such graph will not be a hard task. Where can I get such alternative? *(and If you can presenta way to reconstruct such graph in It It would be grate!) BTW: By crossplatform I mean Linux Mac and Windows compatible, By using SampleGrabber I ment I need to be able to get data from that step of graph from my programm and I use VirtualCamera from here soundmorning.com/download.php

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  • What is the most efficient way to determine if a directed graph is singly connected?

    - by zebraman
    I am working on an assignment where one of the problems asks to derive an algorithm to check if a directed graph G=(V,E) is singly connected (there is at most one simple path from u to v for all distinct vertices u,v of V. Of course you can brute force check it, which is what I'm doing right now, but I want to know if there's a more efficient way. Could anyone point me in the right direction?

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  • How can I find the shortest path between two subgraphs of a larger graph?

    - by Pops
    I'm working with a weighted, undirected multigraph (loops not permitted; most node connections have multiplicity 1; a few node connections have multiplicity 2). I need to find the shortest path between two subgraphs of this graph that do not overlap with each other. There are no other restrictions on which nodes should be used as start/end points. Edges can be selectively removed from the graph at certain times (as explained in my previous question) so it's possible that for two given subgraphs, there might not be any way to connect them. I'm pretty sure I've heard of an algorithm for this before, but I can't remember what it's called, and my Google searches for strings like "shortest path between subgraphs" haven't helped. Can someone suggest a more efficient way to do this than comparing shortest paths between all nodes in one subgraph with all nodes in the other subgraph? Or at least tell me the name of the algorithm so I can look it up myself? For example, if I have the graph below, the nodes circled in red might be one subgraph and the nodes circled in blue might be another. The edges would all have positive integer weights, although they're not shown in the image. I'd want to find whatever path has the shortest total cost as long as it starts at a red node and ends at a blue node. I believe this means the specific node positions and edge weights cannot be ignored. (This is just an example graph I grabbed off Wikimedia and drew on, not my actual problem.)

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  • What is the relaxation condition in graph theory

    - by windopal
    Hi, I'm trying to understand the main concepts of graph theory and the algorithms within it. Most algorithms seem to contain a "Relaxation Condition" I'm unsure about what this is. Could some one explain it to me please. An example of this is dijkstras algorithm, here is the pseudo-code. 1 function Dijkstra(Graph, source): 2 for each vertex v in Graph: // Initializations 3 dist[v] := infinity // Unknown distance function from source to v 4 previous[v] := undefined // Previous node in optimal path from source 5 dist[source] := 0 // Distance from source to source 6 Q := the set of all nodes in Graph // All nodes in the graph are unoptimized - thus are in Q 7 while Q is not empty: // The main loop 8 u := vertex in Q with smallest dist[] 9 if dist[u] = infinity: 10 break // all remaining vertices are inaccessible from source 11 remove u from Q 12 for each neighbor v of u: // where v has not yet been removed from Q. 13 alt := dist[u] + dist_between(u, v) 14 if alt < dist[v]: // Relax (u,v,a) 15 dist[v] := alt 16 previous[v] := u 17 return dist[] Thanks

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