Question: Show that it is possible to count the total number of paths in a directed acyclic graph, G , with n vertices and m edges

Show that it is possible to count the total number of paths in a directed acyclic graph, G , with n vertices and m edges using O(n + m) additions. Also, show that there is a graph, G , where this number is at least 2^n/2.

Step by Step Solution

★★★★★

3.32 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER It is possible to count the total number of paths in a directed acyclic graph G with n vertic... View full answer

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 Data Structures Algorithms Questions!

Suppose that we can compute the transitive closure of a directed acyclic graph in f (|V|, |E|) time, where f is a monotonically increasing function of |V| and |E|. Show that the time to compute the...

Give an efficient algorithm to count the total number of paths in a directed acyclic graph. Analyze your algorithm.

Let G = (V, E) be a directed acyclic graph in which there is a vertex 0 V such that there exists a unique path from 0 to every vertex V. Prove that the undirected version of G forms a tree.

Give an efficient algorithm to count the total number of paths in a directed acyclic graph. The count should include all paths between all pairs of vertices and all paths with 0 edges. Analyze your...

Carrying stones. You are given a directed acyclic graph G = (V, E) with n vertices and m edges, along with a node te V. At each vertex v EV, there are a number of stones q[u] (so q[u] is a...

3. (10 Points) Run DAG-SHORTEST-PATHS on the directed graph of Figure 24.5 (Text book], using vertex r as the source. S 2 N OO DO 3 b) 5 2 2 3 c) 1 -2 AN -2 N 6 5 3 2 2 e) 5 - 2 2 6 3 2 (9) Figure...

Consider a directed graph G = ( V , E ) . Given two vertices s and t , design an efficient algorithm to count the total number of paths from s to t that do not share edges. Show your algorithm s...

You have been provided with the description of a programming language, J, intended for scripting applications. Its syntax is similar to a cut-down version of Java in that it consists of function...

Problem 3. Counting Paths (22 points) Let G be a directed acyclic graph with n vertices, and let s, t be two labeled vertices in G. (a) (6 points) Argue that there can be as many as 2n-2 directed...

Problem 1 1 - 5 ( Reaching Far and High ) 1 1 points You are in charge of the Farther and Higher Mountain Guides company. The company owns n guest houses: one at NYC ' s Battery Park, and others at...

Explain the bottom-of-the-pyramid paradigm. From the multinational's perspective, is the BOP a golden opportunity or is it simply a mirage?

Suppose that the Ken-Z Art Gallery has annual sales of $870,000, cost of goods sold of $560,000, average inventories of $244,500, average accounts receivable of $265,000, and an average accounts...

Needing the answers to fill in the blanks for balance sheet for years amount / decrease for 2 0 1 9 / 2 0 2 0 and amount / decrease for years 2 0 1 8 / 2 0 1 9

LO 6.7 29. Nikkie and Jean have two children, Richard (age 4) and Roberta (age 3). For purposes of the parental tax, Richard has net unearned income of $6,000 and Roberta has net unearned income of...

Implement the deque ADT with an array used in a circular fashion.

Implement the queue ADT with a singly linked list.

Suppose we have an nn two-dimensional array A that we want to use to store integers, but we dont want to spend the O(n 2 ) work to initialize it to all 0s, because we already know that we are only...

Filer Manufacturing has 9 , 0 5 6 , 4 8 9 shares of common stock outstanding. The current share price is $ 3 4 . 4 9 , and the book value per share is $ 6 . 9 8 . Filer Manufacturing also has two...

Willow Products expects the following sales of its single product: March April May June July Units 5,600 6,200 7,500 8,000 8,900 Willow Products desires an ending finished goods inventory to be equal...

Drop down #1= go or no-go Drop down #2= go or no-go Drop down #3 = does or doesn't matter Comparing payback period and discounted payback period. Mathew, Inc. is debating using the payback period...