SLET: Computer Sciences

Elective—Ill
Linear Programming Problem (LPP) in the standard form, LPP in Canonical form. Conversion of LPP in Standard form to LPP in Canonical form. Simplex—Prevention of cyclic computations In Simplex and Tableau, Big-M method, dual simplex and revised simplex.

Complexity of simplex algorithm(s). Exponential behaviour of simplex. Ellipsoid method and Karmakar’s method for solving LPPs. Solving simple LPPs through these methods. Comparison of complexity of these methods.

Assignment and Transportation Problems : Simple algorithms like Hungarian method, etc. Shortest Path Problems : Dijkstra’s and Moore’s method. Complexity.

Network Flow Problem : Formulation. Max-Flow Min-Cut theorem. Ford and Fulkerson’s algorithm. Exponential behaviour of Ford and Fulkerson’s algorithm. Malhotra- Pramodkumar-Maheshwari (MPM) Polynomial algorithm for solving Network flow problem. Bipartite Graphs and Matchlngs; Solving matching problems using Network flow problems.

Matroids : Definition. Graphic and Cographic matrolds. Matroid Intersection problem. Non-linear Programming : Kuhn-Tucker conditions. Convex functions and Convex regions.

Convex programming problems. Algorithms for solving convex programming problems—Rate of convergence of Iterative methods for solving these problems.

Elective—IV
Neural Networks : Perceptron model Linear separability and XOR problem. Two and three layered neural nets, Backpropagatlon—Convergence. Hopfleld nets Neural net learning, Applications.

Fuzzy Systems : Definition of a Fuzzy set Fuzzy relations. Fuzzy functions, Fuzzy measures. Fuzzy reasoning, Applications of Fuzzy systems.

Elective—V
Unix : Operating System, Structure of Unix Operating System, Unix Commands, Interfacing with Unix, Editors and Compilers for Unix. LEX and YACC, File system System calls, Filters. Shell programming.

Windows : Windows environment, Unicode, Documents and Views, Drawing In a window. Message handling. Scrolling and Splitting views. Docking toolbars and Status bars Common dialogs and Controls. MDI, Multithreading, OLE, Active X controls, ATL. Database access Network programming.