Graduate Courses





  • CSE 5101 - Advanced Algorithms

    Topics:

    Randomized Algorithms: Las Vegas and Monte Carlo Algorithms; Randomized Data Structures: Skip Lists; Amortized Analysis: Different methods, Applications in Fibonacci Heaps; Lower Bounds: Decision Trees, Information Theoretic Lower Bounds, Adversary Arguments; Approximation Algorithms: Approximation Schemes, Hardness of Approximation; Fixed Parameter Tractability: Parameterized Complexity, Techniques of designing Fixed Parameter Algorithms, Examples; Online Algorithms: Competitive Analysis, Online Paging Problem, k-server Problem; External Memory Algorithms; Advanced Data Structures: Linear and Non-linear Methods

  • CSE 5102 - Combinatorial Optimization

    Topics:

    Introduction to Optimization; Linear Programming: Different forms, Simplex Method, Primal-Dual theory; Max-Flow: The Max-Flow-Min-Cut Theorem, Ford-Fulkerson Labeling Algorithm, Dijkstra's Algorithm, The Floyd-Warshall Algorithm; Some Network Flow Algorithms: The Minimum Cost Network Flow Method, Transportation Problem; Capacitated Transportation Problem, Assignment Problem; Integer Linear Programming; Relaxation; Cutting-Plane Algorithm; Branch and Bound Technique; Dynamic Programming; NP-Completeness; TSP and Heuristics; Approximation.

  • CSE 5103 - Graph Theory

    Topics:

    Introduction, Fundamental concepts, Trees, Spanning trees in graphs, Distance in graphs, Eulerian graphs, Digraphs, Matching and factors, Cuts and connectivity, k-connected graphs, Network flow problems, Graph coloring: vertex coloring and edge coloring, Line graphs, Hamiltonian cycles, Planar graphs, Perfect graphs.

  • CSE 5104 - Computational Geometry

    Topics:

    Searching and Geometric Data Structures: Balanced binary search trees, Priority-search trees, Range searching, Interval trees, Segment trees, Algorithms and complexity of fundamental geometric objects: Polygon triangulation and art gallery theorem, Polygon partitioning, Convex-hulls in 2-dimension and 3-dimension, Dynamic convex-hulls; Geometric intersection: Line segment intersection and the plane-sweep algorithm, Intersection of polygons; Proximity: Voronoi diagrams, Delunay triangulations, closest and furthest pair; Visualization: Hidden surface removal and binary space partition (BSP) trees; Graph Drawings: Drawings of rooted trees (Layering, Radial drawings, HV-Drawings, Recursive winding), Drawings of planar graphs (Straight-line drawings, Orthogonal drawings, Visibility drawings); Survey of recent developments in computational geometry.

  • CSE 5105 - Bioinformatics Algorithms

    Topics:

    Introduction; Molecular biology basics: DNA, RNA, genes, and proteins; Restriction mapping algorithm; Motif in DNA sequences, motif finding algorithms; Genome rearrangements, sorting by reversals and breakpoints; DNA sequence alignments; Gene prediction; Space-efficient sequence alignments, sub-quadratic alignment; DNA sequencing, genome sequencing, protein sequencing, spectrum graphs; Combinatorial pattern matching: Exact pattern matching, heuristic similarity search algorithms, approximate string matching, BLAST, FASTA; Clustering: Microarrays, hierarchical clustering, K-means clustering, corrupted cliques problem, CAST clustering algorithm; Evolutionary trees.

  • CSE 5106 - Stringology

    Topics:

    Introduction to Stringology: Notations, Problems and Naive Solutions, Motivations, Applications, Basic string searching algorithms; Data structures for String Matching: Suffix Tree, Suffix Array, Aho-Corasick Automaton, Applications of these data structures; Approximate Pattern Matching: Edit distance, Dynamic programming, Similarity measures for DNA and protein sequences, q-gram methods, Bit-parallel methods, Algorithms for degenerate/indeterminate strings; Sequence Analysis: Longest Common subsequence (LCS) Problem, Advanced Algorithms for LCS, Variants of LCS and algorithms; Text Compression: Shannon-Fano and Huffman codes, Arithmetic coding, Lempel-Ziv family of compression techniques, Burrows-Wheeler Transformation.

  • CSE 5107 - Mathematical Programming

    Topics:

    Basic concept of Mathematical Programming, Concepts of linear and quadratic programming, Convexity, Convex sets and convex functions, Concept of integer programming, Some examples of integer programming problems, Linear programming techniques, Graphical solution of linear programming problems, Simplex method, Dual simplex method, Different integer programming techniques, Revised simplex method.

  • CSE 5108 - Petri Net Theory and Modeling of Systems

    Topics:

    Introduction to Petri Nets, Elementary Net Systems, Place/Transition Nets, Definition and types of Petri nets, Terms and notations marking, Importance of net theory, Transition firings, Practical modeling examples, Introduction to workflow, workflow modeling using Petri Nets, Liveness and safeness, Behavioral properties, Deadlocks and siphons, Structural properties, Colored Petri Nets, Time Petri Nets, Timed Petri Nets, Stochastic Petri Nets.

  • CSE 5151 - Cryptography

    Topics:

    Classical Cryptography; Data Encryption Standard, Advance Encryption Standard; Public-key cryptography: RSA cryptosystem, ElGamal cryptosystem; Signature Schemes: ElGamal signature schemes, Digital signature standard; Hash Functions: Collision-free Hash functions; Key Distribution and Key Agreement: Key pre-distribution, Diffie-Hellman key exchange; Identification Schemes: Schnorr identification scheme, Okamoto identification schemes; Algorithm to compute discrete logs; Chinese Remainder method, Polards rho method; Attacks: Brute Force attack, Birthday attack; Cryptanalysis: Linear cryptanalysis, Differential cryptanalysis; Elliptic Curves; Quantum cryptography;

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