Select all of the following statements that are true A knot is a strongly connected subgraph of a directed graph. The banker's algorithm is defined for consumable resources. In an expedient system, the resource allocation graph will never contain any satisfiable request edges. In order to show that a system state is safe, the Maximum Claim Graph mus completely reducible. A knot is a necessary condition for a deadlock. A process p is unblocked in a resource allocation graph if there is no request edge starting at

Select all of the following statements that are true A knot is a strongly connected subgraph of a directed graph. The banker's algorithm is defined for consumable resources. In an expedient system, the resource allocation graph will never contain any satisfiable request edges. In order to show that a system state is safe, the Maximum Claim Graph mus completely reducible. A knot is a necessary condition for a deadlock. A process p is unblocked in a resource allocation graph if there is no request edge starting at

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

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Consider a connected graph G with at least 4 edges that has all distinct edge weights. Which of the following properties must be true of a Minimum Spanning Tree (MST) of G? I. The MST must contain the shortest edge of G. II. The MST must contain the second-shortest edge of G. III. The MST can never contain the longest edge of G. None I Only I and II Only I and III Only O1, II, and III
Algorithm : (1. Single-destination Shortest Path, 2. Bellman-Ford, 3. Negative-Weight Cycles), Dynamic Programming Define and prove a recurrence for the following problem: Given a directed graph G = (V, E) with edge weight function w : E → R and a source vertex s ∈ V , find a shortest path from s to v for every vertex v ∈ V .
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3. 4. Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient algorithm that computes the number of different directed paths from s to t. Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix with rows indexed by vertices, column indexed by edges such that Bij = -1 1 0 if edge j leaves vertex i, if edge jenters vertex i, otherwise. Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.
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.
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.
Square graph. The square of a directed graph G = (V,E) is the graph G^2 =(V,E^2)suchthat(u,w)∈E^2 if and only iff or some v∈V both(u,v)∈E and (v, w) ∈ E; that is, there is a path of exactly two edges. (i) Suppose that G is represented by an adjacency list. Describe an efficient algorithm for computing G^2 from G. (ii) Suppose that G is represented by an adjacency matrix. Describe an efficient algorithm for computing G^2 from G.
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Let G = (V, E) be an undirected graph and each edge e ∈ E is associated with a positive weight ℓ(e).For simplicity we assume weights are distinct. Is the following statement true or false? Let T be a minimum spanning tree for the graph with the original weight. Suppose we replace eachedge weight ℓ(e) with ℓ(e)^2, then T is still a minimum spanning tree.
Write a boolean function, called universalSink, to determine weather a directed graph has a universal sink. A universal sink is a vertex which has no outgoing edges, and all other vertices have an incoming edge to the sink vertex.
5. Consider the following modification of the independent set problem. As input, you receive an undirected graph G = (V, E). As output, you must decide if G contains an independent set UCV such that U contains at least 99% of the vertices in V (that is, JU| > 0.99|V|). Prove that this modification of the independent set problem is NP-Complete.