Shortest Path Algorithm with Djikstra

Hi all,
im developing a shortest path searching techniques by using Djikstra's algorithm. My search space is very huge and it is about 100,000 nodes or we can call it Vertex. I store all the nodes and weight of edges in MySql as follows:
From | To | PathCost
A B 2
B A 2
A D 9
D A 9
B C 7
C B 7
B E 5
E B 5
C D 5
D C 9
Whenever the class receive any request from someone who want to go from point A to point Z, it will load the data from mysql by using "Select * FROM table WHERE From='Variable' ", and declare it as new Vertex, and perform the search. The reason i load it from MySql everytime i receive a new request is because any new node can be added to database anytime.
In a nut shell, im developing a system to search for a shortest path in real world, i represent buildings as a Vertex, and road as edges, any idea of what can i improve my current djikstra searching method or any new developement to reduce the running time to lowest??
regards,
howsen

minimal spanning tree != shortest path...
Mr. Pike is indeed correct. Consider this simple example. arrange a bunch of dots around the rim of a circle. Consider the distance between them to be just the standard measure of distance in the plane. Assume that the points are fairly evenly spaced, but not exactly evenly spaced.
The minimal spanning tree, which you got by first joining the two closest points and then the next two, and then by joining more points to that structure, will end up looking like a letter C going around the circle and leaving a gap between the two points that were the furthest apart on the circle.
Every point connects to every other point, possibly by passing through other points and it is minimal because it left out the widest gap.
On the other hand, the quickest way to get from one tip of the C to the other tip is to go straight from the one to the other, not to walk all the way around the circle following a path that goes through every single other point in the system.
Reducing a graph to a minimal spanning tree, gets you a single subgraph of the original grpah that has the least total distance. That, unfortunately, has nothing to do with telling you the fastest way to get from point A to point B traveling along the original graph.
hence minimal spanning tree != shortest path...

Similar Messages

Best shortest path algorithm ??

Hi
I am developing an application to guide a user from one point to another. I need to work out the shortest path between these two points.
Is Dijkstra's algorithm the best to use? or should I be looking for a different one? I am looking for speed.
Thanks

Choosing a "single source shortest path" algorithm depends on if you are going to use a weighted or not weighted graph, if all weights are non-negative or negative etc. If negative -weight edges are allowed, Djikstra's algorithm can not be used. Instead you can use the Bellman-Ford algorithm.
The running time of Djikstra's algorithm is lower than that of the Bellman-Ford algorithm. Runningtime for the Bellman-Ford algorithm is in general O(V^2E). Because Djikstra's algorithm always chooses the "closest" vertex (in a weigthed directed graph G=(V,E)) , we say it uses a greedy strategy. This strategy does not always yield optimal result. How fast the Djiktra algorithm is, depends how the min-priority queue is implemented. f.example: if you use the linear array implementation of the min-priority queue, the runningtime for Djikstra's algorithm is O(v^3) while a binary min-heap implementation of min-priority queue gives a runningtime of O(V E lg V).

Shortest Path Algorithm:

Hi,
I have about 20,000 (double) points and trying to find a shortest path between any two. I know that the best algorithm for doing that is Dijkstra's one. What is the best data structure for this? I read that usually heaps but the time it needs to sort the list is too long, maybe some one knows a better way? Maybe there is another algorithm that solves this problem? Please give me any suggestion about anything that I said above.
Thank you in advance.

I don't know no Dijkstra's algorithm for this problem. The only algorithm of Dijkstra for something like that that I know is to find the shortest path between two nodes in a weight network.
I think that the lower bound for what you are trying to do is the same lower bound for sorting the points, so I think that the best you can do is to apply a good sorting algorithm (like quicksort, mergesort, heapsort or shellsort).
The best data structure depends about how much info do you have previously about the number of points and memory that you have available. If you know that the max number of points that you'll work can be fit in the available memory, then the best data holder to use is an array (it's aways the fastest). If you'll see it as an array or as stack (for example) depends on the algorithm that you'll choose to sort the points.
One last tip: if you choose using a List, prefer the ArrayList over LinkedList. LinkedList is slower than ArrayList for almost all kind of operations. If you'll work with a lot of elemts, do some testing before pick one of the two.
Hope it helps,
RGB

Shortest Path Algorithm. Need help.

Hey, Im having trouble coming up with an algorithm for a shortest path. I have an NxN weighted matrix and need to get from the upper left corner to the lower right corner. The length of the path must be the shortest possible for the number of moves and total weight (ie. a 3X3 matrix would use 4 moves, a 4X4 uses 6 and a 5X5 uses 8).
im using a 2-dimensional array like matrix[x][y] with the storage at this location being a random integer.
I came up with some guidelines:
1) the path can never move left because it would break the shortest moves requirement.
2) the path can never move up for the same reason.
when traversing through the matrix if x == N then go down to N,N. If y == n go right until N,N.
I can visualize how to do it. Its just putting my algorithm into a program is beyond me right now.
Any help would be appreciated greatly.

Dijkstra's algorithm only works on a weighted graph.
I have a weighted matrix.
Its like a chess board where every square has a
number on it. I have to get from the upper left to
the lower right using as little squares as possible
and then amongst those paths find the one with the
smallest weight or total.So something where individual squares have a certain toughness to get through, then?
Yeah, A* will own that...
I really don't want to write a tutorial on how to find the shortest path. But basically, you need to have a queue of paths. For each iteration until you find your goal, you pop the path with the least cost and you find the four paths you could get from it (move up, down, left, and right).
The key here is the cost function (heuristic). It must approximate the actual cost of a path WITHOUT over-approximating.
For your problem, you should probably factor in cost of the path so far, and the lowest possible expectable distance from the end of the path you're considering to the goal (think "distance formula").
Also, since these are general algorithms, you should probably code them up to work with an arbitrary start/end, instead of concrete values.
~Cheers

Shortest path code

hi
if nyone cud give me the code for finding the shortest path between 2 points but in this case all the paths have equal weights i.e. the shortest path would be the involvement of minimum number of nodes between the start & the end node.
Please am stuck up if anyone can provide me with the code.
Thanks in advance

Related to Dijkstra's shortest path algorithm if all edges have equal
weight, just the heap management (priority queue) will be much simpler.
If the graph to be traversed isn't too big, a simple linear array could do the
job fine where entry i indexes paths of length i. Nothing much else is to
be gained though: it stil will be a permanent graph labeling algoritm.
kind regards,
Jos

Cost Factor in Shortest Path

Hi,
I need a little help.
I am performing routing on geodatic data (i.e., locations with Lat/Long).
I think the AStar shortest path algorithms are finding the shortest path on the basis of distance betwwen two nodes.
I am not quite sure whether they are taking care of the cost column in the link table.
for eg., say A-B-C and A-D-C are two alternative routes from A to C .
such that A-B-C is the shortest path on the basis of geodatic distance between the locations A an C.
But may be the cost-wise A-D-C would have been a shorter path.
So, which path will the algo return?
Also I do not want to implement AStarCostFunction class and provide a distance function.
Please help me out.
Regards.

Hi,
Any/all cost-based analysis in the network data model is done using the cost column. If the cost column contains geodetic distances then that is what will be used.
Hope this helps,
Dan

Fitness for Shortest path using a genetic algorithm

Hi.
I have this problem:
I'm doing a program that has a map and two points. the map has wall that are not valid positions.
I have used a A* algorithm to calculate the shortest path and is working fine.
now i'm implementing a genetic algorithm to solve the problem but i'm not having sucess.
My genetic operator are directions (left, right, up and down).
I'm not being able to find a goodfitness function to solve the problem.
can someone tell me a god function or here I can found information about that?
I have been searching on google and I have not yet had sucess.
I have tryed two diferent fitness tecniques:
- add 1 for each step and if it finds a wall or gets out of the map add the maximum value (mapsize*mapsize).
- the other one is add the valid steps and if it finds a wall or gets out of the map add the number of necessary steps to gets to destination. the valid steps has a weight of 30% and the necessary steps has a weight of 70% (i have tryed to use diferent weight).
Can someone help me?
thanks

How about adapting your TSP code as follows. Your graph G(V, E) has two special vertices: v_s and v_d (start and destination). Let a candidate solution consist of a permutation of V\{v_s, v_d}u{v_m} where v_m is a new marker vertex whose purpose is to allow you to treat part of the candidate solution as irrelevant. Given candidate solution v_0 v_1 v_2 ... v_n v_m v_n+1 ... the weight is c(v_s, v_0) + c(v_0, v_1) + ... + c(v_n-1, v_n) where c(v_a, v_b) is the cost of the edge ab.

Finding the shortest path router for the router tracking purpose

Hi all,
A Question asking you regarding to routers' tracking information.
We keeps all the router infomation of our subnet in a file name "routers.txt" in this format:
1 2 1
2 4 1
4 3 1
1 3 5
This states there are four routers, the distance between routers 1 and 2 is 1, between 2 and 4 is 1, etc.
I need to write a Java program to keep track the shortest path between routers, I would understand that we can get this done easily in Java, but I am not a Java Savvy. I'm new in Java, would somebody help me to the right direction?
In order to keep track the routers in our subnet easily,the output would look something like:
Router 1
To Router Distance Vector
2 1 2
3 3 2
4 2 2
Thanks very much,
Cait.

Hi kksenji,
Well, because of the webform, it's not obvious to see. The output would be simple. From the input, for router 1 to router 2, the shortest distance is 1. For router 1 to router 3, the shortest distance is 3, for router 1 to router 4, the shortest distance is 2 and so on. The middle vector that it went through is 2 for every route. Hope this makes sense.
Just try to solve the problem with the shortest distance, and I have a hard time to figure out the algorithm for this as well as how to get this started.
Thanks, Cait.

Aco implemenataion for shortest paths.

has anyone used ant colony optimization algorithm for finding shortest paths other than for the tsp? please i need some help and advice. thanks

sorry for not being specific and the insubsequent reply. am just doing some research on aco, i want to try and implement it for best bath planning on a map/graph. I've been looking around for some example on such and noticed that this algorithm is mainly used for tsp problem which got me questioning the possibility of my task. I just want to know if it is definitely possible with aco as i will give it a go in this case. Implementing this algorthm successfully is the main challenge of my project so i cannot contemplate another algorithm option. Thanks for your time.

Shortest path problem

hello,
We have a street-layer (spatial). Now we should calculate the shortest path between two nodes. Does Oracle assist in this? Has anybody some experiences with this problem?
Any help will be appreciated.
regards
Anna

Well, I know there are several algorithms for this problem, but I wanted to know, if and how Oracle assist�s in this point. I get an answer from Oracle, that 10g include such functionality and now I am waiting on it.
Thanks for your try to help.
Monika-Anna

Shortest path which includes all subset

In graphs (V,E) with negative edge weights but with no negative cycles , X <V and s, t in V .I need an algorithm to decide if exist in the graph ,shortest path from s to t with which includes all the nodes from X

Unfortunately the problem you are trying to solve in NP-complete (it means that the best known algorithm for doing this is exponential in time with respect to size of X) so the best solution is to check every possibility. But if your graph has some special form there may be efficient solution for this problem. In general it's special case is finding [Hamiltonian path|http://en.wikipedia.org/wiki/Hamiltonian_path].

Help needed in a shortest path search problem..

Basically the problem is that there is a network of nodes with different paths to other nodes and I am supposed to find a shortest path from a random node to another random node.There are other criteria like weight, capacity etc. but that shouldnt affect the search algorithm... What is the best way to do this type of problem? Example would be great,thanks!

what about Breadth first search? Also for Dijkstra's, it seems to be dependent only on the weight of paths but if the paths have same weight, how do i go back to the previous node if a path wasn't found?

Finding the shortest path

Hey guys,
Im working on a solution to this problem below is a program to allow a user to draw straight line paths. What i'd like to do is allow the user to select two points on the path he has drawn and find the shortest path among all the interesecting lines.....im going crazy thinking of a solution for this.....im thinking bout steeping down a notch and just try to find just any path first.
Will really appreciate any help.
Thnx in advance,
Vikhyat
import java.applet.*;*
*import java.awt.*;
import java.awt.event.*;*
*import javax.swing.*;
import java.awt.geom.*;
public class Lab11 extends Applet implements MouseListener, MouseMotionListener {
int x0, y0, x1, y1;
int mouseRelease=0;
GeneralPath path = new GeneralPath();
public Lab11()
addMouseListener(this);
addMouseMotionListener(this);
public void mouseDragged(MouseEvent e)
x1 = e.getX();
y1 = e.getY();
repaint();
public void mouseMoved(MouseEvent e) { }
public void mouseClicked(MouseEvent e) { }
public void mouseEntered(MouseEvent e) { }
public void mouseExited (MouseEvent e) { }
public void mousePressed(MouseEvent e) {
x0 = e.getX();
y0 = e.getY();
System.out.println("Mouse pressed at: (" +
x0 + ", " + y0 + ")" );
public void mouseReleased(MouseEvent e) {
x1 = e.getX();
y1 = e.getY();
System.out.println("Mouse released at: (" +
x1 + ", " + y1 + ")" );
mouseRelease = 1;
this.repaint();
public void paint(Graphics g)
Graphics2D g2 = (Graphics2D)g;
g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
//just for show not concerned with saving paths
if(mouseRelease==1)
path.moveTo(x0,y0);
path.lineTo(x1,y1);
mouseRelease = 0;
g2.setPaint(Color.RED);
g2.draw(path);
g.setColor(Color.BLACK);
g.drawLine(x0, y0, x1, y1);
public static void main(String[] argv)
JFrame f = new JFrame("Test");
f.getContentPane().add(new Lab11());
f.setSize(600,600);
f.setVisible(true);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
}Pictorially this is what im trying to do:
User draws a path like so and selects two points as shown in blue
[http://i48.photobucket.com/albums/f236/theforrestgump/select.jpg]
The program should then proceed to highlighting the shortest path
[http://i48.photobucket.com/albums/f236/theforrestgump/sp.jpg]
Edited by: cannonball on Apr 1, 2008 7:58 PM

import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import javax.swing.*;
public class ShortPath extends JPanel {
    Path2D.Double path;
    Path2D.Double shortPath = new Path2D.Double();
    Point p1 = new Point();
    Point p2 = new Point();
    final double PROXIMITY = 5.0;
    public ShortPath() {
        path = new Path2D.Double();
        path.moveTo(145,80);
        path.lineTo(125,170);
        path.lineTo(190,200);
        path.lineTo(240,340);
        path.lineTo(285,220);
        path.lineTo(145,80);
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                            RenderingHints.VALUE_ANTIALIAS_ON);
        g2.setPaint(Color.blue);
        g2.draw(path);
        g2.setPaint(Color.green);
        g2.setStroke(new BasicStroke(2f));
        g2.draw(shortPath);
        g2.setPaint(Color.red);
        g2.fill(new Ellipse2D.Double(p1.x-2, p1.y-2, 4, 4));
        g2.setPaint(Color.orange);
        g2.fill(new Ellipse2D.Double(p2.x-2, p2.y-2, 4, 4));
    private void findShortPath() {
        if(!isPointOnLine(p1) || !isPointOnLine(p2)) {
            System.out.println("a point is not on the path");
            return;
        double d1 = getDistanceToPoint(p1);
        double d2 = getDistanceToPoint(p2);
        double pathLength = getDistanceToPoint(new Point());
        Point2D.Double start = new Point2D.Double();
        Point2D.Double end   = new Point2D.Double();
        if((d1 < d2 && d2 - d1 < pathLength - d2 + d1) ||
           (d1 > d2 && d1 - d2 > pathLength - d1 + d2)) {
            start.setLocation(p1);
            end.setLocation(p2);
        } else {
            start.setLocation(p2);
            end.setLocation(p1);
        generatePath(start, end);
    //                        145,80
    // leg distance = 92.2    125,170
    // leg distance = 71.6    190,200   163.8
    // leg distance = 148.7   240,340   312.5
    // leg distance = 128.2   285,220   440.7
    // leg distance = 198.0   145,80    638.7
    private double getDistanceToPoint(Point p) {
        PathIterator pit = path.getPathIterator(null);
        double[] coords = new double[2];
        double distance = 0;
        Point2D.Double start = new Point2D.Double();
        Point2D.Double end = new Point2D.Double();
        Line2D.Double line = new Line2D.Double();
        while(!pit.isDone()) {
            int type = pit.currentSegment(coords);
            switch(type) {
                case PathIterator.SEG_MOVETO:
                    start.setLocation(coords[0], coords[1]);
                    pit.next();
                    continue;
                case PathIterator.SEG_LINETO:
                    end.setLocation(coords[0], coords[1]);
            line.setLine(start, end);
            boolean onLine = line.ptSegDist(p) < PROXIMITY;
            if(onLine) { // point is on this line
                distance += start.distance(p);
                break;
            } else {
                distance += start.distance(end);
            start.setLocation(end);
            pit.next();
        return distance;
    private void generatePath(Point2D.Double first, Point2D.Double second) {
        Point2D.Double p = new Point2D.Double(first.x, first.y);
        Point2D.Double start = new Point2D.Double();
        Point2D.Double end = new Point2D.Double();
        Line2D.Double line = new Line2D.Double();
        boolean pathStarted = false;
        for(int j = 0; j < 2; j++) {
            PathIterator pit = path.getPathIterator(null);
            double[] coords = new double[2];
            while(!pit.isDone()) {
                int type = pit.currentSegment(coords);
                switch(type) {
                    case PathIterator.SEG_MOVETO:
                        start.setLocation(coords[0], coords[1]);
                        pit.next();
                        continue;
                    case PathIterator.SEG_LINETO:
                        end.setLocation(coords[0], coords[1]);
                        line.setLine(start, end);
                        boolean onLine = line.ptSegDist(p) < PROXIMITY;
                        if(onLine) {            // found point on line
                            Point2D.Double linePt = getClosestPoint(line, p);
                            Line2D.Double segment;
                            if(!pathStarted) { // found first point
                                                // both points on line
                                if(line.ptSegDist(second) < PROXIMITY) {
                                    Point2D.Double secPt =
                                        getClosestPoint(line, second);
                                    segment = new Line2D.Double(linePt, secPt);
                                    shortPath.append(segment, false);
                                    return;
                                } else {        // first point only
                                    segment = new Line2D.Double(linePt, end);
                                    shortPath.append(segment, false);
                                    p.setLocation(second);
                                    pathStarted = true;
                            } else {            // found second point
                                segment = new Line2D.Double(start, linePt);
                                shortPath.append(segment, false);
                                return;
                        } else if(pathStarted) {
                                                // add intermediate lines
                            Line2D.Double nextLine =
                                new Line2D.Double(start, end);
                            shortPath.append(nextLine, false);
                start.setLocation(end);
                pit.next();
    private Point2D.Double getClosestPoint(Line2D.Double line,
                                           Point2D.Double p) {
        double minDist = Double.MAX_VALUE;
        Point2D.Double closePt = new Point2D.Double();
        double dy = line.getY2() - line.getY1();
        double dx = line.getX2() - line.getX1();
        double theta = Math.atan2(dy, dx);
        double length = line.getP2().distance(line.getP1());
        int limit = (int)(length+.05);
        for(int j = 0; j < limit; j++) {
            double x = line.getX1() + j*Math.cos(theta);
            double y = line.getY1() + j*Math.sin(theta);
            double distance = p.distance(x, y);
            if(distance < minDist) {
                minDist = distance;
                closePt.setLocation(x, y);
        return closePt;
    private boolean isPointOnLine(Point p) {
        Point2D.Double start = new Point2D.Double();
        Point2D.Double end = new Point2D.Double();
        Line2D.Double line = new Line2D.Double();
        PathIterator pit = path.getPathIterator(null);
        double[] coords = new double[2];
        while(!pit.isDone()) {
            int type = pit.currentSegment(coords);
            switch(type) {
                case PathIterator.SEG_MOVETO:
                    start.setLocation(coords[0], coords[1]);
                    pit.next();
                    continue;
                case PathIterator.SEG_LINETO:
                    end.setLocation(coords[0], coords[1]);
                    line.setLine(start, end);
                    if(line.ptSegDist(p) < PROXIMITY) {
                        return true;
            start.setLocation(end);
            pit.next();
        return false;
    public static void main(String[] args) {
        ShortPath test = new ShortPath();
        test.addMouseListener(test.ml);
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(test);
        f.setSize(400,400);
        f.setLocation(200,200);
        f.setVisible(true);
    private MouseListener ml = new MouseAdapter() {
        boolean oneSet = false;
        public void mousePressed(MouseEvent e) {
            Point p = e.getPoint();
            if(oneSet) {
                p2 = p;
                findShortPath();
            } else {
                p1 = p;
                shortPath.reset();
            oneSet = !oneSet;
            repaint();
}

Computing of the shortest path using a custom cost function in Oracle NDM

Hi to all,
I have Oracle 10g R2, I'm working on Oracle Network Data Model. I created a Network (named ITALIA_NET) based on links table (named ITALIA_LINK$) and nodes table (named ITALIA_NODE$).
Until now I computed the shortest path between two nodes using the 10gR2 NDM Java API, in particular I used the shortestPath() method.
I know that this method computes the shortest path between two nodes on the base of the values of a field that can be the lenght OR the travel time of the links.
What I wish to do is compute the shortest path between two nodes with a function that considers ( at the same time ) more parameters and on the base of them returns a path. For example, I want compute the shortest path taking into account these parameters for the links:
travel times of links
gradient links
tortuosity links
Infact, I have for each link the costs of: travel time (for example 3 minuts for cross the link), gradient (for example, the link has 2% of gradient) and tortuosity (for example, the link has two curves of 60° of angle).
Do you have any idea how I can implement this?
Are there other ways for reach this objective?
I hope I explained well my objective.
Thank you very much to all in advance.

_1) If I convert the values of the other cost columns into the values of the primary cost column (time is ok), what is the formulation for do this conversion?_
The modeling part is the most difficult part. I am not sure if there is a universal conversion formula between two different costs.
One recommendation is to use time as your primary cost.
For any other secondary costs, collect some data (or from some published statistics) on how these costs affect the travel time (based on the actual speeds wrt to gradients and tortuosity).
I am not an expert on this. Maybe asking questions like,
Q. how will a road of gradient = 10 deg affect the speed, uphill and downhill compared to the speed limit?
Once you have a good estimates on the speeds, you can compute the travel times as the distance/length of the link is known. The same applies to tortuosity,
Q. how will roads with 30/60/90 deg angles affect the travel speeds compared to the speed limit?
Assuming you are using something like the speed limit as you normal travel speed to compute your travel time.
_2) After conversion, how can I combine these columns?_
Say if you have done the conversion part in Step 1, you have 3 costs,
cost1, cost2, and cost3
You can create a view on the link table with the combined link cost as (cost1+cost2+cost4) or
you can create a new column that sums up the costs you want and use it as the link cost.
hope it helps!
jack

Shortest path problem in ABAP

Hi experts,
Is it possible to write the code for the "Shortest path problem" in ABAP?If yes, what is the code?
Moderator Message: Don't expect members to spoon-feed you
Edited by: Suhas Saha on Jul 25, 2011 11:13 AM

Hi munish,
I dont think there is any thing wrong with the ABAP code.
Try testing your ABAP mapping using transaction code SXI_MAPPING_TEST in XI.
Enter the Details asked and then enter TEst data in XML format..
Also, you can make use of the Trace element to find out if there is any thing wrong with the code.
Include the following Statements after every step in the ABAP code to ensure that the particular step is completed successfully.
data : l_trace type string.
concatenate l_trace '<Message you want to display>' into l_trace.
trace->trace(level = '<level>'
message =l_trace).
The trace is visible in SXMB_MONI (click on "Trace" in the left pane to view).
using this you will get to know i the code is functioning as desired.
Regards,
Yashaswee.

Shortest Path Algorithm with Djikstra

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