I know how KD-Tree works.
But I can't figure out how to apply that to improve DBSCAN performance.
Can you give me some ideas on how I should apply KD-Tree?
p.s I've found that it has something to do with the NearstNeibors Algorithm, but I still can't figure out what to do with it.
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What is SAS decomposition algorithm. SAS documentation for decomposition algorithm. I don't understand this and can someone please explain it in simple terms? Can I use that algorithm to solve ATM optimization problem as explained here and how optimal is the solution? Are there any better algorithms to solve this ATM optimization problem?
Please do bear with me if you find my query a little stupid. But I am currently doing a high school research project on how Fourier transformation can be used in recognizing human speech(similar to how Shazam works). But I need to two different Fast Fourier Transformation algorithms for this project. One of the algorithms I am using would definitely be the Cooley-Tukey FTT algorithm. However, I am unsure of another FTT algorithm I should use. Thus, what would be a good algorithm to use and is there any pseudo code/source code for that particular algorithm? I was only able to find algorithms for Cooley-Tukey thus far.
Thanks!
If you don't need speed (due to some performance constraints), then a DFT (straight matrix multiply) should produce very similar results (differing due to rounding noise) using a very different algorithm.
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I am trying to implement a solution to a problem using Integer linear programming (ILP). As the problem is NP-hard , I am wondering if the solution provided by Simplex Method would be optimal ? Can anyone comment on the optimality of ILP using Simplex Method or point to some source. Is there any other algorithm that can provide optimal solution to the ILP problem?
EDIT: I am looking for yes/no answer to the optimality of the solution obtained by any of the algorithms (Simplex Method, branch and bound and cutting planes) for ILP.
The Simplex Method doesn't handle the constraint that you want integers. Simply rounding the result is not guaranteed to give an optimal solution.
Using the Simplex Method to solve an ILP problem does work if the constraint matrix is totally dual integral.
Some algorithms that solve ILP (not constrained to totally dual integral constraint matrixes) are Branch and Bound, which is simple to implement and generally works well if the costs are reasonably uniform (very non-uniform costs make it try many attempts that look promising at first but turn out not to be), and Cutting Plane, which I honestly don't know much about but it's probably good because people are using it.
The solution set for a linear programming problem is optimal by definition.
Linear programming is a class of algorithms known as "constraint satisfaction". Once you have satisfied the constraints you have solved the problem and there is no "better" solution, because by definition the best outcome is to satisfy the constraints.
If you have not completely modeled the problem, however, then obviously some other type of solution may be better.
Clarification: When I write above "satisfy the constraints", I am including maximization of objective function. The cutting plane algorithm is essentially an extension of the simplex algorithm.
Can anybody tell me, how can I compare TSP Optimal and heuristics? I have implemented TSP but don't know how can I compare them. Infact, how can I find the optimal cost of the TSP? Any method or guess?
Thanks
Check the optimal solution with well-known benchmark instances:
Download the data from TSPLIB here and compare your solutions with the optimal values here
Solving the TSP to optimality is an NP-hard problem.
To assess the quality of a heuristic solution, you have several options:
Compare it to heuristic solutions produced by other algorithms. This will give you an idea of which heuristics work better on the given instance, but obviously won't tell you anything about how close you are to the optimal solution.
Compare to the optimal solution. Concorde is probably your best bet for computing this.
Compute a lower bound for the TSP instance, and compare the heuristic solution to that. The two standard approaches are the Held-Karp lower bound and the assignment problem relaxation.
Use instances with known optimal solutions, such as those in TSPLIB.
I was looking at the problem Magic Square
I am sure with some loop and if condition this problem can be solve, but I am interested to know if there is any know algorithm / datastructure to solve this problem. I am not interested in exact solution, but any hint toward algorithm/datastructure would help.
That is a description of sudoku, generalized to squares of different size. There are several known sudoku solvers; you would have to adapt them.
There is nice algorithm from Donald Knuth: Algorithm X, Dancing Links
As I know it is one of the fastest algorithms to solve Sudoku.
And here is quite readable and through paper with nice pictures: http://arxiv.org/abs/cs/0011047