CMSC 451 Dave Mount CMSC 451 : Lecture 19 NP - Completeness : Reductions Tue , Nov 21 , 2017
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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...
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Extensions of Network Flow: Network flow is an important problem because it is useful in a wide variety of applications. We will discuss two useful extensions to the network flow problem. We will show that these problems can be reduced to network flow, and thus a single algorithm can be used to solve both of them. Many computational problems that would seem to have little to do with flow of flu...
متن کاملCMSC 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...
متن کاملCMSC 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...
متن کاملCMSC 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...
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