CMSC 451 : Lecture 21 Clique , Vertex Cover , and Dominating Set Thursday , Nov 30 , 2017

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

NP - Completeness : Clique , Vertex Cover , and Dominating Set Thursday

Vertex Cover (VC): A vertex cover in an undirected graph G = (V,E) is a subset of vertices V ′ ⊆ V such that every edge in G has at least one endpoint in V ′. The vertex cover problem (VC) is: given an undirected graph G and an integer k, does G have a vertex cover of size k? Dominating Set (DS): A dominating set in a graph G = (V,E) is a subset of vertices V ′ such that every vertex in the gra...

CMSC 451 Dave Mount CMSC 451 : Lecture 17 Extensions of Network Flow Thursday , Nov 9 , 2017

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...

CMSC 451 : Lecture 17 Network Flow : Extensions Thursday , Nov 9 , 2017

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...

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...