1. Application of greedy method:Prim’s Algorithm 2. Greedy Method ???A greedy method is an method that followsthe problem solving technique of making thelocally optimal…

Slide 1 Probabilistically Checkable Proofs (and inapproximability) Irit Dinur, Weizmann open day, May 1 st 2009 Slide 2 How Efficiently Can Proofs Be Checked ? P  NP (12…

Graphs Graphs Applications of Depth-First Search Undirected graphs: Connected components, articulation points, bridges, biconnected components Directed graphs: Cyclic/acyclic…

PCP and Inapproximability Irit Dinur NEC Example: the Minimum Vertex Cover function Facts: 1. Best algorithm runs in time (1.21)n [Robson ‘86] 2. VC is NP-hard. [Karp ’72]…

Probabilistically Checkable Proofs (and inapproximability) Irit Dinur, Weizmann open day, May 1st 2009 How Efficiently Can Proofs Be Checked? (slide by Madhu Sudan) our real…

Slide 1 Applications of graph traversals [CLRS] – problem 22.2 - Articulation points, bridges, and biconnected components [CLRS] – subchapter 22.4 Topological sort Slide…

Prims’ spanning tree algorithm Given: connected graph (V, E) (sets of vertices and edges) V1= {an arbitrary node of V}; E1= {}; //inv: (V1, E1) is a tree, V1 ≤ V, E1…