**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**6

# Publications

##### 6 Regular Generalized Star Star closed sets in Bitopological Spaces

**Authors:**
K. Kannan,
D. Narasimhan,
K. Chandrasekhara Rao,
R. Ravikumar

**Abstract:**

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

**Keywords:**
τ1τ2-regular closed sets,
τ1τ2-regular open sets,
τ1τ2-regular generalized closed sets,
τ1τ2-regular generalized star
closed sets,
τ1τ2-regular generalized star star closed sets.

##### 5 A Meta-Heuristic Algorithm for Set Covering Problem Based on Gravity

**Authors:**
S. Raja Balachandar,
K. Kannan

**Abstract:**

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving large size set covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the set covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

**Keywords:**
Set covering problem,
velocity,
gravitational force,
Newton's law,
meta heuristic,
combinatorial optimization.

##### 4 An Effective Algorithm for Minimum Weighted Vertex Cover Problem

**Authors:**
S. Balaji,
V. Swaminathan,
K. Kannan

**Abstract:**

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

**Keywords:**
Weighted vertex cover,
vertex support,
approximation algorithms,
NP-complete problem.

##### 3 Optimization of Unweighted Minimum Vertex Cover

**Authors:**
S. Balaji,
V. Swaminathan,
K. Kannan

**Abstract:**

**Keywords:**
vertex cover,
vertex support,
approximation algorithms,
NP - complete problem.

##### 2 Free Convection in an Infinite Porous Dusty Medium Induced by Pulsating Point Heat Source

**Authors:**
K. Kannan,
V. Venkataraman

**Abstract:**

Free convection effects and heat transfer due to a pulsating point heat source embedded in an infinite, fluid saturated, porous dusty medium are studied analytically. Both velocity and temperature fields are discussed in the form of series expansions in the Rayleigh number, for both the fluid and particle phases based on the mean heat generation rate from source and on the permeability of the porous dusty medium. This study is carried out by assuming the Rayleigh number small and the validity of Darcy-s law. Analytical expressions for both phases are obtained for second order mean in both velocity and temperature fields and evolution of different wave patterns are observed in the fluctuating part. It has been observed that, at the vicinity of the origin, the second order mean flow is influenced only by relaxation time of dust particles and not by dust concentration.

**Keywords:**
Pulsating point heat source,
azimuthal velocity,
porous dusty medium,
Darcy's law.

##### 1 Approximating Maximum Weighted Independent Set Using Vertex Support

**Authors:**
S. Balaji,
V. Swaminathan,
K. Kannan

**Abstract:**

**Keywords:**
weighted independent set,
vertex cover,
vertex support,
heuristic,
NP - hard problem.