Approximation AlgorithmsCovers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.
Directed Networks & HypergraphsExplores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.
Counting labeled treesExplores counting labeled trees using Prüfer codes and algorithms, providing maps between trees and sequences.
Graph SketchingIntroduces graph sketching, generalizations like multigraphs, and weighted graphs.
AdS/CFT CorrespondenceExplores the AdS/CFT correspondence in various dimensions and its implications for string theory and quantum gravity.
Open ProblemsExplores a variety of open problems in graph theory and computational complexity, challenging students to analyze and solve complex issues.
Prim's and Kruskal's AlgorithmsExplores Prim's and Kruskal's algorithms for finding minimum spanning trees in a graph, covering their correctness, implementation, and analysis.
Linear Programming DualityExplores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.