Question: In a directed graph, the indegree of a node is the number of incoming edges and the outdegree is the number of outgoing edges. Show

In a directed graph, the indegree of a node is the number of incoming edges and the outdegree is the number of outgoing edges. Show that the following problem is NP-complete. Given an undirected graph G and a designated subset C of Gs nodes, is it possible to convert G to a directed graph by assigning directions to each of its edges so that every node in C has indegree 0 or outdegree 0, and every other node in G has indegree at least 1?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

In a directed graph, the indegree of a node is the number of incoming edges and the outdegree is the number of outgoing edges. Show that the following problem is NP-complete. Given an undirected...

Exercises Let's provide some more functionality for our Graph interface, in a library of graph analysis methods. These will be static methods in the GraphLib class ( as in Math. random ) , and will...

The purpose of these exercises is to get you started with network analysis and the SNAP software. For this homework, you need to install and try out the SNAP network analysis tools. We strongly...

java numVertices( ): Returns the number of vertices of the graph. vertices ( ): Returns an iteration of all the vertices of the graph. numEdges( ): Returns the number of edges of the graph. edges( ):...

Please write code in Java Programming: Directed Graphs Implement a method to compute the average out-degree for a graph, use the method signature below. The out-degree of a node is the number of...

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Provide an ecient algorithm that given a directed graph G with n vertices and m edges as input, nds the outdegree of each vertex in G. Note that outdegree of a vertex u is the number of edges...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Repeat the previous problem and then remove one edge from the graph. Show that now there is a single (nonsimple) path that includes all the edges of your graph. Data from in Previous Problem Draw a...

( 3 mark ) ( Page Rank Algorithm ) PageRank is the basis of Google's ranking of web pages in search results. Given a directed graph where pages are nodes and the links between pages are edges, the...

Supermart Food Stores (SFS) has experienced net operating losses in its frozen food products line in the last few periods. Management believes that the store can improve its profitability if SFS...

What is the difference between economic income and accounting income?

What is the present value of a series of infinite future cash flows ( C F t ) that continue in perpetuity? Multipite Choice P V = C F t r P V = C F t r - g P V = C F 1 ( 1 + r ) 2 P V = C F t ( 1 + r...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

6. Vanguard

6. Training identified the Top 125 companies for training (see Training, February 2009). The top ten ranked companies were:

1. PricewaterhouseCoopers