Question: 3. Consider the following algorithm for the vertex cover problem for trees. Pick an edge (u, v), where u is a leaf. Include v in

3. Consider the following algorithm for the vertex cover problem for

3. Consider the following algorithm for the vertex cover problem for trees. Pick an edge (u, v), where u is a leaf. Include v in the cover, delete all edges incident to v, and repeat until there are no edges left. Show that this algorithm finds a smallest cover. Hint: you may argue using matchings as in the analysis of the 2-approximation algorithm

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!

t1=1, for i=1 to 9 Answer the following questions: (a) Show that the construction can be done in polynomial time. (b) Show that if the 3DM problem instance is a yes-instance, then the constructed...

4 In the class, we have discussed a Greedy - Based algorithm for weighted Vertex Cover Problem ( VCP ) . Below is a formal statement. 2 Algorithm 2 : ALG - B Input: An undirected graph G = ( V , E )...

we have discussed a Greedy - Based algorithm for weighted Vertex Cover Problem ( VCP ) . Below is a formal statement. 2 Algorithm 2 : ALG - B Input: An undirected graph G = ( V , E ) and a cost...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

Consider the following algorithm for the weighted vertex cover problem. For each vertex v, t(v) is initialized to its weight, and when t(v) drops to 0, v is picked in the cover. c(e) is the amount...

(a) A user complains that their web application Times Out after successfully connecting to a remote host, yet, an investigation with ping indicates the remote host is alive. Propose a cause of this...

3. A balanced bipartition of set X splits X into two parts A and B so that the sizes of A and B differ by at most 1. In particular, when X is even, A=B=X/2; when X is odd, A=B1=X/2. We refer to the...

Return to the cardinality Vertex Cover problem (VCover) of Exercise 14-7(a). One algorithm to construct an approximately optimum set VQ ! 5i V: xi = 16 for the problem can be stated as follows: (i)...

Graph theory. Please do PROBLEM 3 and show step by step. 2: Suppose that T and T are both spanning tree of a connected graph G on n vertices. Lete E E(T)E(T) and let X and Y be a partition of V(G)...

The minimum vertex cover problem is stated as follows: Given an undirected graph G = (V,E) with N vertices and M edges. Find a minimal size subset of vertices X from V such that every edge (u,v) in E...

When might a supertype/subtype hierarchy be useful?

A compressor is surrounded by cold R-134a so it works as an isothermal compressor. The inlet state is 0C, 100 kPa and the exit state is saturated vapor. Find the specific heat transfer and...

In his private office, just down the hall from his conference room, the Chief Financial Officer ( CFO ) of Theriot Technologies is meeting with his newly hired assistant, Julie. CFO: Before our next...

Down Under Boomerang, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.43 million. The fixed asset will be depreciated straight-line to...

3. Should participants be incentivized to attend? If so, how would you suggest?

1. Using Allisons (1971) model, what lens(es) do you believe Chief Jackson used to make these decisions?

2. How much time should be allocated to the focus group?