[4] **viXra:1608.0250 [pdf]**
*replaced on 2016-12-03 19:20:21*

**Authors:** Atul Mehta

**Comments:** 5 Pages.

In this paper, we explore the connections between graphs and Turing machines. A method to construct Turing machines from a general undirected graph is provided. Determining whether a Hamiltonian cycle does exist is now shown to be equivalent to solving the halting problem. A modified version of Turing machines is now developed to solve certain classes of computational problems.

**Category:** Data Structures and Algorithms

[3] **viXra:1608.0230 [pdf]**
*submitted on 2016-08-21 11:20:24*

**Authors:** Fu Yuhua

**Comments:** 5 Pages.

Based on creating generalized and hybrid set and library with neutrosophy and quad-stage method, this paper presents the concept of "computer information library clusters" (CILC). There are various ways and means to form CILC. For example, CILC can be considered as the "total-library", and consists of several "sub-libraries". As another example, in CILC, a "total-library" can be set up, and a number of "sub-libraries" are side by side with the "total-library". Specially, for CILC, the operation functions can be added; for example, according to "natural science computer information library clusters" (natural science CILC), and applying "variation principle of library (or sub-library)", “partial and temporary unified theory of natural science so far” with different degrees can be established. Referring to the concept of “natural science CILC”, the concepts of “social science CILC”, “natural science and social science CILC”, and the like, can be presented. While, referreing to the concept of “computer information library clusters”, the concepts of “computer and non-computer information library clusters”, “earth information library clusters”, “solar system information library clusters”, “Milky Way galaxy information library clusters”, “universe information library clusters”, and the like, can be presented.

**Category:** Data Structures and Algorithms

[2] **viXra:1608.0098 [pdf]**
*replaced on 2016-08-11 23:42:15*

**Authors:** Leorge Takeuchi

**Comments:** 16 Pages. Two link addresses (URI) were wrong.

Quicksort, invented by Tony Hoare in 1959, is one of the fastest sorting algorithms. However, conventional
implementations have some weak points, including the following: swaps to exchange two elements are redundant,
deep recursive calls may encounter stack overflow, and the case of repeated many elements in input data is a well-
known issue. This paper improves quicksort to make it more secure and faster using new or known ideas in C
language.

**Category:** Data Structures and Algorithms

[1] **viXra:1608.0044 [pdf]**
*submitted on 2016-08-04 22:35:27*

**Authors:** Sidharth Ghoshal

**Comments:** 10 Pages.

Documented is an algorithm,
It is intimately related to a question about piecewise linear cobordisms. IF the conjecture is true then this algorithm is polynomial time. IF it is not, the this algorithm "might be" but probably won't be. Contact a local topologist for updates in this computational crisis.

**Category:** Data Structures and Algorithms