OVERVIEW 1-st Midterm: 3 problems 2-nd Midterm 3 problems Sorting Quicksort Data structures binary heaps BST Greedy algorithm Prim’s algorithm Dynamic Programming Longest Common subsequence shortest triangulation Shortest Paths Dijkstra Bellman-ford Matrix Multiplication/Floyd/Johnson Computational Geometry Convex hull Closest Pair Voronoi triangulation/graph NP-completeness P, NP, NPC prove that the problem is NP Approximation Algorithms Vertex Cover TSP Steiner tree problem 1-st Midterm: 3 problems 2-nd Midterm 3 problems Only in Finals: 4 problems

NP-Completeness P, NP, NPC Example 1: Example 2: Yes/no for problems in the book: Is Max Independent set is NPC? If Yes then to which NPC problem we reduce it in class? prove that the problem is NP: given a problem, YES can be verified in poly-time with the certificate Example 1: find diameter of the graph (maximum distance) In P since we can use all shortest path Since P is in NP, the problem is in NP Example 2: is there proper k-coloring of graph? Given coloring we can check in poly-time if it is proper

FINALS Be very careful and concentrated Do NOT let yourself stuck with one problem CHECK each answer (leave ~15min at the end)