CMSC 451 Dave Mount CMSC 451 : Lecture 13 All - Pairs Shortest Paths and the Floyd - Warshall Algorithm Tuesday

CMSC 451 : Lecture 13 All - Pairs Shortest Paths and the Floyd - Warshall Algorithm

All-Pairs Shortest Paths: Earlier, we saw that Dijkstra’s algorithm and the Bellman-Ford algorithm both solved the problem of computing shortest paths in graphs from a single source vertex. Suppose that we want instead to compute shortest paths between all pairs of vertices. We could do this applying either Dijkstra or Bellman-Ford using every vertex as a source, but today we will consider an a...

CMSC 451 Dave Mount CMSC 451 : Lecture 19 NP - Completeness : Reductions Tue , Nov 21 , 2017

CMSC 451 Dave Mount CMSC 451 : Lecture 10 Dynamic Programming : Weighted Interval Scheduling

Dynamic Programming: In this lecture we begin our coverage of an important algorithm design technique, called dynamic programming (or DP for short). The technique is among the most powerful for designing algorithms for optimization problems. Dynamic programming is a powerful technique for solving optimization problems that have certain well-defined clean structural properties. (The meaning of t...

CMSC 451 : Lecture 5 Graph Shortest Paths : Dijkstra and Bellman - Ford Tuesday , Sep 12 , 2017

Shortest Paths: Today we consider the problem of computing shortest paths in a directed graph. We are given a digraph G = (V,E) and a source vertex s ∈ V , and we want to compute the shortest path from s to every other vertex in G. This is called the single source shortest path problem. The algorithms we will present work for undirected graphs as well, by simply assuming that each undirected ed...

CMSC 451 Dave Mount CMSC 451 : Lecture 12

Chain matrix multiplication: This problem involves the question of determining the optimal sequence for performing a series of operations. This general class of problem is important in compiler design for code optimization and in databases for query optimization. We will study the problem in a very restricted instance, where the dynamic programming issues are easiest to see. Suppose that we wis...