Pre-requisite : EE635 Applied Linear Algebra or equivalent.;Brief Overview of Linear and Nonlinear Programming. Kuhn-Fourier Elimination Scheme, Farkas Lemma, Constrained Optimization through Lagrange multipliers for equation and inequality based systems, Karush-Kuhn-Tucker Theorem, Strong Duality Theorem of Linear Programming.;Network Flows.Max-flow Mincut Theorem, Algorithms for maximizing flows, min cost flow Problem and its electrical equivalent, Menger's Theorems.;Graph Optimization Problems.Maximum spanning tree, matching and covering, shortest path problem, graph colouring problems.;Introduction to Matroids.Axioms for matroids, The greedy algorithm and the related characterization of matroids.
Douglas B. West, Introduction to Graph Theory Second edition: Prentice Hall 2001.
A.Schrijver, Theory of Linear and Integer Programming, Wiley, Chichester, 1986
C.H. Papadimitriou, K.Steiglitz, Combinatorial optimization: algorithms and complexity, Dover Pubns, July 1998.
H.Narayanan, Submodular functions and Electrical Networks, (vol 54) Annals of Discrete Maths, North Holland,1997, 2nd edition at http://www.ee.iitb.ac.in/~hn/book/ 2009.