Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

VIT Unitversity

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Department of Smart Computing

School of Information Technology and Engineering

2017 International Conference on Trends in Electronics and Informatics (ICEI)

Quantitative performance analysis of face recognition system

Sudoku is an interesting number placement puzzle with some simple rules. For some positive integer n, the puzzle involves an n2 × n2 grid partitioned into n2 distinct blocks each of size n × n such that the integers 1 through n2 appear exactly once in each row, each column and each block of the grid. Often some static numbers known as givens are placed according to the difficulty rating in the puzzle and then the rule is to place the numbers from 1 to n2 in the partially filled grid such that the conditions of the puzzle are satisfied. The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size n2. It is based on the concepts of permutations derived from n2 × n2 S-permutation matrices termed as S-permutations. There is a one-to-one correspondence between Sudoku squares and the set of those S-permutation matrices which are mutually disjoint to each other. The proposed algorithm uses the set of all S-permutations generated by some permutation generation algorithm as input and then enumerates all the subsets of cardinality n2 of all S-permutations which are mutually disjoint to each other. The correctness of the algorithm is established. Its worst-case time complexity is O(wn2 +2logw), where w = (n!)2n. A mathematical formula involving the total number of the sets of (n2-1) mutually disjoint S-permutations is also derived. Experimentally, the proposed algorithm is verified for the Sudoku squares of size 9 × 9. It is observed that our algorithm is more systematic and better in terms of computational efficiency. © 2016 World Scientific Publishing Company.

World University root node

Discrete Mathematics, Algorithms and Applications

A new algorithm for enumerating all possible Sudoku squares

In this paper, a new hybrid algorithm (NHA) combining genetic algorithm with local search and using events based on groupings of students is described to solve the university course timetabling problem. A list of events such as lectures, tutorials, laboratories and seminars are ordered and mutually disjoint groups of students taking them are formed in such a way that once a student is selected in any group, he is excluded from further selection in other groups. The union of all the events taken by all the students of each group is formed. The number of events in each group is termed as its group size whose upper bound is restricted by the total number of timeslots and can be reduced to the maximum number of events per student. The above process of forming groups is repeated till the size of each group is reduced within this bound by not choosing those events which are common for all the students in the group. Now, the genetic algorithm with local search (GALS) is applied on a number of benchmark problems. The experimental results show that our algorithm, NHA, is able to produce promising results when compared with the results obtained by using GALS and other existing algorithms. © 2014 Elsevier Ltd. All rights reserved.

Computers and Industrial Engineering

A new hybrid algorithm for university course timetabling problem using events based on groupings of students