Authors: Vaclav Kosar
Comments: 6 Pages. my name with special characters in latex form: V\' aclav Ko\v sa\v r
This article should be easy to understand for anybody and is meant to prove that I proposed new kind of operation system based on wiki-like or graph-like structure is
1-more natural, thus easier to learn
2-more efficient on existing tasks in terms of human time spent
3-can handle new kind of tasks
Computer task is data transformation. It is improbable that current paper-like handling of data is the best way. I would like to show that current computers provide a much more natural and useful way of handling all-purpose data. The main idea is that one should store information in a structure as natural as possible, so that user does not have to give efforts to transform the information (express more, search naturally, write once then just reference ...).
I am not sure if I can claim any authorship of following ideas, since one can never be sure whether an idea existed before and what actually helped one to come up with this idea. The only purpose of this paper is thus the pure desire to make progress of thought, by starting the discussion and construction of crowd sourced operation system based entirely on idea of graph databases.
I cannot provide the reader with infinite detais and precision, thus I leave some uncertainties to be cleared by the reader himself for pleasure.
My main inspirations for this more natural operation system were: Graph database, Wikipedia, brain, Lisp, mind-mapping, QED manifesto, CSS 3, WikiOS.
Category: Data Structures and Algorithms
Authors: Matthias Mueller
Comments: 45 Pages.
Four different polynomial 3-SAT algorithms named "Algorithm A/B/C/D[M]" are provided:
|v1: "Algorithm A":||Obsolete, please ignore.|
|v2: "Algorithm B":||Obsolete. Published in December 2013. Never failed for millions of test runs. Proof of correctness needs to be improved. Mr. M. Prunescu's paper 'About a surprizing computer program of Matthias Mueller' is about this Algorithm B.|
|v3: "Algorithm C":||Obsolete, please ignore.|
|v4: "Algorithm D‑1.0":||Newest and best algorithm. Never failed in tests. Related paper v4 contains a detailed description of this polynomial 3-SAT solving algorithm, an extensive proof of correctness and a link where you can download my compiled demo C++ implementation (with source code) for Windows and Linux, an alternative polynomial solver version, and an additional tool program.|
|v5: "Algorithm D‑1.1":||Very same algorithm as v4, but better explained and with a re-written, completely new part of the proof of correctness.|
|v6: "Algorithm D‑1.1":||Some helpful improvements (compared to v5).|
|v7: "Algorithm D‑1.2":||Paper from May 22nd, 2016.|
|v8: "Algorithm D‑1.3":||Parts of the proof of correctness have been replaced by a completely re-written, more detailed variant.|
|v9: "Algorithm D‑1.3":||Please read this version for a figurative, linguistic description of the algorithm. Another part of the proof of correctness has been made more detailed.|
|vA: "Algorithm DM‑1.0":||Completely re-written document. Still describes algorithm D, but as short as possible and in mathematical notation.|
|vB: "Algorithm DM‑2.0":||Heavily revised and extended vA document. A much more precise notation is used (compared to vA) and most formulas are now comprehensively commented and explained. Might be easier to understand for learned readers, while others prefer v9 (D-1.3).|
|vC: "Algorithm DM‑2.1":||Please read this version for a precise, mathematical description of the algorithm. Best paper of all. Compared to DM-2.0, three substantial extensions have been added: Why the algorithm does NOT have the restrictions of a logical resolution, that the polynomial solver correctly solved the pigeon hole problem for n=6 ("PH6"), and what the ideas behind the three rules of the polynomial algorithm are.|
Authors: Dhananjay P. Mehendale
Comments: 6 Pages. Presented and Published in the Proceedings of International Conference on Perspectives of Computer Confluence with Sciences 2012, ICPCCS 12.
In this paper we propose a new algorithm for linear programming. This new algorithm is based on treating the objective function as a parameter. We transform the matrix of coefficients representing this system of equations in the reduced row echelon form containing only one variable, namely, the objective function itself, as a parameter whose optimal value is to be determined. We analyze this matrix and develop a clear method to find the optimal value for the objective function treated as a parameter. We see that the entire optimization process evolves through the proper analysis of the said matrix in the reduced row echelon form. It will be seen that the optimal value can be obtained 1) by solving certain subsystem of this system of equations through a proper justification for this act, or 2) By making appropriate and legal row transformations on this matrix in the reduced row echelon form so that all the entries in the submatrix of this matrix, obtained by collecting rows in which the coefficient of so called unknown parameter d whose optimal value is to be determined, become nonnegative and this new matrix must be equivalent to original matrix in the sense that the solution set of the matrix equation with original matrix and matrix equation with transformed matrix are same. We then proceed to show that this idea naturally extends to deal with nonlinear and integer programming problems. For nonlinear and integer programming problems we use the technique of Grobner bases since Grobner basis is an equivalent of reduced row echelon form for a system of nonlinear equations, and the methods of solving linear Diophantine equations respectively.
Category: Data Structures and Algorithms