2. Show that the following languages are in NP, by providing a non-deterministic algorithm. You are not allowed prove the membership in NP by providing certificate and verifier. • A = {(G, k) | G is k-colorable} • B = {G | G has a dominating set of size < n/2}, where n is the number of vertices of G. For an undirected graph G = (V, E), a set S C V is a dominating set if for every v ¢ S, there is a vertex u E D such that (v, u) e E. %3D

2. Show that the following languages are in NP, by providing a non-deterministic algorithm. You are not allowed prove the membership in NP by providing certificate and verifier. • A = {(G, k) | G is k-colorable} • B = {G | G has a dominating set of size < n/2}, where n is the number of vertices of G. For an undirected graph G = (V, E), a set S C V is a dominating set if for every v ¢ S, there is a vertex u E D such that (v, u) e E. %3D

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Please written by computer source
please send correct answer for part a
True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|. (b) If an A* heuristics is admissible then it satisfies the monotone restriction. (c) Best-first search guarantees optimality in its returned solution. (d) Least-cost-first search guarantees optimality in its returned solution. (e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.
The third-clique problem is about deciding whether a given graph G = (V, E) has a clique of cardinality at least |V |/3.Show that this problem is NP-complete.
The problem Monochomatic-Subgraph-Avoidance takes as input two undirected graphs Fand G. It asks where F can be colored with two colors (say, red and blue) that does not containa monochomatic (all-red or all-blue) G as a subgraph. (Note that when G has two nodes and oneedge between them, this is equivalent to the 2-coloring problem of asking whether F can be coloredso that no neighbors have the same color.)Next, show that Monochomatic-Subgraph-Avoidance is contained in one of the classes inthe second level of the polynomial hierarchy. ALso provide an expression using qualifiers. YOU ALSO NEED TO PROVIDE A CLEAR EXPRESSION USING THE QUALIFIERS.PLEASE GIVE CLEAR EXPLAINATION.
Can you help me solve this exercise? Please note that the greedy approach described in the advice paragraph does not work.
which of the following statment is false? A. a web server is a computer B. a domain name is the numeric version of an IP address
Answer the given question with a proper explanation and step-by-step solution. Answer yes or no and Prove or explain precisely why please1. If you can solve TSP in linear time, you can solve the Hamiltonian path problemin linear time.2. If Graph Isomorphism belongs to NPC then P = NP3. The question if a program stops on an input x within n^3 steps or less belongs toNPC.4. The question does a program stops on an input x (namely there is no infiniteloop) belongs to NPC.
Q6. Given graph G = (V, E), the graph G'= (V', E') is defined such that (u,v) is in E' if and only if G contains a path with at most two edges between u and v. Describe an efficient algorithm for computing G' from G. Once develop the algorithm assuming G has an adjacency-matrix representation and once develop the algorithm assuming adjacency-list representation for the graph. Analyze the running times of your algorithms.
Exercise c. Strict matchingConsider the following generalization of the maximum matching problem, which we callStrict-Matching. Recall that a matching in an undirected graph G = (V, E) is a setof edges such that no distinct pair of edges {a, b} and {c, d} have endpoints that areequal: {a, b} ∩ {c, d} = ∅. Say that a strict matching is matching with the propertythat no pair of distinct edges have endpoints that are connected by an edge: {a, c} ̸∈ E,{a, d} ̸∈ E, {b, c} ̸∈ E, and {b, d} ̸∈ E. (Since a strict matching is also a matching, wealso require {a, b} ∩ {c, d} = ∅.) The problem Strict-Matching is then given a graphG and an integer k, does G contain a strict matching with at least k edges.Prove that Strict-Matching is NP-complete.
Consider an undirected graph on 8 vertices, with 12 edges given as shown below: Q2.1 Give the result of running Kruskal's algorithm on this edge sequence (specify the order in which the edges are selected). Q2.2 For the same graph, exhibit a cut that certifies that the edge ry is in the minimum spanning tree. Your answer should be in the form E(S, V/S) for some vertex set S. Specifically, you should find S.