Lecture 12:

1. Lecture 12: Algorithm Review

2. General Problem Solving Methods Divide & Conquer Greedy Method Dynamic Programming Graph & Tree Traversal Backtracking Branch & BoundConstraint RelaxationReduction Methods

3. Searching & Sorting Binary Search Merge Sort Quicksort Topological sort

4. Graph & Tree Traversal Prim's Algorithm Minimum Spanning Tree Dijkstra's Single-Source Shortest-Path Depth-First Search Hamiltonian Circuits Maximal Matching Graph Coloring algorithm B&B TSP B&B TSP with Constraint Relaxation Max-Flow Min-Cut (Ford-Fulkerson) Dijkstra's Single-Source Shortest-Path (SSSP) Floyd's All-Pairs Shortest-Path (APSP) Natural Clustering (Dendrograms)

5. Greedy Methods Greedy Matching Greedy Coin Changing Prim's Algorithm Minimum Spanning Tree Track Correlation Greedy Euclidean TSP Floyd's All-Pairs Shortest-Path (APSP) Simplex Method

6. Dynamic Programming Dijkstra's Single-Source Shortest-Path Making Change (non-Greedy) Davis-Putnam 3-SAT Algorithm 0/1 Knapsack Problem

7. Constraint Relaxation Methods Augmenting Path Algorithm Maximal Matching Munkres Assignment - Hungarian algorithm Track Correlation B&B TSP with Constraint Relaxation Max-Flow Min-Cut (Ford-Fulkerson) Simplex Method Natural Clustering (Dendrograms)

8. General Combinatorial Algorithms Depth-First Search Hamiltonian Circuits Next Permutation Graph Coloring algorithm Optimal Traveling Salesperson Problem Algorithms Cross & Insert Heuristics for Routing Davis-Putnam 3-SAT Algorithm Solution-Set Enumeration (3-SAT) Sum-of-Subsets N-Queens Problem Methods Backtracking Algorithms

9. Dictionary of Algorithms and Data Structures This web site is hosted in part by the Software and Systems Division, Information Technology Laboratory. This is a dictionary of algorithms, algorithmic techniques, data structures, archetypal problems, and related definitions. Algorithms include common functions, such as Ackermann's function. Problems include traveling salesman and Byzantine generals. Some entries have links to implementations and more information. Index pages list entries by area and by type. The two-level index has a total download 1/20 as big as this page. http://www.itl.nist.gov/div897/sqg/dads/

10. Graph Traversals A D F C H B E G depth-first from node ___ : ___ ___ ___ ___ ___ ___ ___ ___ breadth-first from node ___ : ___ ___ ___ ___ ___ ___ ___ ___ hamiltonian path ___ ___ ___ ___ ___ ___ ___ ___

11. Greedy Tour greedy tour starting from node ___ : ___ ___ ___ ___ ___ ___ ___ ___ lower bound heuristic computing minimum cost to leave each city _______ lower bound heuristic computing minimum cost to enter each city _______

12. Graph Representations edge list B 1 ___ ___ ___ A ___ ___ ___ 1 C 2 ___ ___ ___ 5 2 2 ___ ___ ___ 4 D ___ ___ ___ adjacency matrix 1 2 ___ ___ ___ 3 E ___ ___ ___ G ___ ___ ___ ___ ___ ___ ___ 1 2 ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ F ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

13. Minimal Spanning Tree edge list of MST B 1 ___ ___ ___ A ___ ___ ___ 1 C 2 ___ ___ ___ 5 2 ___ ___ ___ 2 4 D ___ ___ ___ 1 2 ___ ___ ___ 3 E G 1 2 F

14. Single-Source Shortest Path B 1 A 1 C 2 5 2 2 4 D 1 2 from node ____ 3 E G 1 2 F {__} ___ ___ ___ ___ ___ ___ {__ __} ___ ___ ___ ___ ___ ___ {__ __ __} ___ ___ ___ ___ ___ ___ {__ __ __ __} ___ ___ ___ ___ ___ ___ {__ __ __ __ __} ___ ___ ___ ___ ___ ___ {__ __ __ __ __ __} ___ ___ ___ ___ ___ ___