Final Exam Topics ++++++++++++++++++++++++++++++++++++++++++++ Midterm Topics Minimum Spanning Trees (Chapter 21) ================================= Spanning Trees DFS spanning tree BFS spanning tree Major minimum spanning tree algorithm: 1) Kruskal's algorithm 2) Prim's algorithm Single-Source Shortest Paths (Chapter 22) ================================= Related Algorithms / Variants Challenging Attributes + Negative-weight Edges + Negative-weight Cycles + Cycles Relaxation Bellman-Ford (Section 24.1) + Run-time Single-source shortest paths in DAGs (directed acyclic graphs) (Section 24.2) + Run-time Dijkstra's (Section 24.3) + Run-time Parallel Algorithms (Chapter 26) ================================= Concurrency platform Speedup Amdahl's law Race conditions Example parallelizations Linear Programming (Chapter 29) ================================= Applications Terms Standard Form NP-Completeness (Chapter 34) ================================= Complexity Classes How knowing about complexity can help you Showing a Problem is NP-Complete Decision Problems vs. Optimization Problems Reductions Approximation Algorithms (Chapter 35) ================================= Approximation Ratio (ρ(n) or rho(n)) Approximation Schemes Approximate Vertex Cover Solution Approximate Traveling-salesman Solution Approximate Set-covering Solution