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

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

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...

CMSC 451 Dave Mount CMSC 451 : Lecture 7 Greedy Algorithms for Scheduling

Interval Scheduling: We continue our discussion of greedy algorithms with a number of problems motivated by applications in resource scheduling. Our first problem is called interval scheduling. We are given a set R of n activity requests that are to be scheduled to use some resource. Each activity has a given start time si and a given finish time fi. For example, these may represent bids to use...

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

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...

Mount CMSC 451 : Lecture 11 Dynamic Programming : Longest Common

Strings: One important area of algorithm design is the study of algorithms for character strings. Finding patterns or similarities within strings is fundamental to various applications, ranging from document analysis to computational biology. One common measure of similarity between two strings is the lengths of their longest common subsequence. Today, we will consider an efficient solution to ...