3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. adi and m GUDD WIT (d) (Harder) Give conditions in terms of k, m, and n such that the algorithm in part (c) is faster than the run time of the algorithm in part (a). (e) (Harder) Similar to part (c), suppose that we use the adaptation of BFS to determine which pairs of agents are connected by a walk of length k ≥ 1. Give conditions in terms of k, m, and n such that this is faster than the run time of the algorithm in part (b).

3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. adi and m GUDD WIT (d) (Harder) Give conditions in terms of k, m, and n such that the algorithm in part (c) is faster than the run time of the algorithm in part (a). (e) (Harder) Similar to part (c), suppose that we use the adaptation of BFS to determine which pairs of agents are connected by a walk of length k ≥ 1. Give conditions in terms of k, m, and n such that this is faster than the run time of the algorithm in part (b).

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

Given an undirected, weighted graph G(V, E) with n vertices and m edges, design an (O(m + n)) algorithm to compute a graph G1 (V, E1 ) on the same set of vertices, where E1 subset of E and E1 contains the k edges with the smallest edge weights , where k < m.
Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm. (Draw the finished shortest path) b. Use Prim to find the MST (Draw the finished MST) c. Use Kruskal to find the MST (Draw the finished MST) d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.
Correct answer will be upvoted else downvoted. We will consider cells of a square network n×n as contiguous in the event that they have a typical side, that is, for cell (r,c) cells (r,c−1), (r,c+1), (r−1,c) and (r+1,c) are nearby it. For a given number n, build a square lattice n×n to such an extent that: Every integer from 1 to n2 happens in this network precisely once; On the off chance that (r1,c1) and (r2,c2) are contiguous cells, the numbers written in them should not be neighboring. Input The principal line contains one integer t (1≤t≤100). Then, at that point, t experiments follow. Each experiment is characterized by one integer n (1≤n≤100). Output For each experiment, output: - 1, if the necessary network doesn't exist; the necessary lattice, in any case (any such network if a significant number of them exist).
Consider eight points on the Cartesian two-dimensional x-y plane. a g C For each pair of vertices u and v, the weight of edge uv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a, h) : V4? + 1? = /17 and dist(a, b) = v2? + 0² = 2. Because many pairs of points have identical distances (e.g. dist(h, c) V5), the above diagram has more than one minimum-weight spanning tree. dist(h, b) = dist(h, f) Determine the total number of minimum-weight spanning trees that exist in the above diagram. Clearly justify your answer.
An unweighted graph G = (V, E) does not have weights associated with its edges asnoted. A simple strategy to find the maximal matching in a greedy way is to randomlyselect an edge in the graph, include it in the matching and remove all of its adjacentedges from the graph as in the steps below.1. Input: An unweighted graph G = (V, E)2. Output: A maximal matching M of G3. M ← Ø4. E ← E5. while E = Ø6. randomly select e ∈ E7. M ← M ∪ {e}8. E ← E \ {e∪ all adjacent edges to e}implement this algorithm in Python
Write a polynomial time algorithm to check if an undirected graph G(V, E), whose maximum degree is 1000, has a clique size of at least k, where 1 ≤ k ≤ |V|.
Correct answer will upvoted else downvoted. You are given a coordinated chart G which can contain circles (edges from a vertex to itself). Multi-edges are missing in G which implies that for every single arranged pair (u,v) exists all things considered one edge from u to v. Vertices are numbered from 1 to n. A way from u to v is a grouping of edges to such an extent that: vertex u is the beginning of the principal edge in the way; vertex v is the finish of the last edge in the way; for all sets of neighboring edges next edge begins at the vertex that the past edge finishes on. We will expect that the unfilled succession of edges is a way from one u to another. For every vertex v output one of four qualities: 0, in case there are no ways from 1 to v; 1, in case there is just a single way from 1 to v; 2, in case there is more than one way from 1 to v and the number of ways is limited; −1, if the number of ways from 1 to v is endless. Input :The first…
Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 3 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm (Would anything change if B to C weight was changed from 3 to 4? To 1? What about 5?)
Use of Matching for Edge ColouringEdges in a matching can share the same colour since matching in a graph is defined as the collection of non-adjacent edges. As a result, we can create an algorithm based on this idea using the below stages. 1. Input: G = (V, E)2. Output: Minimal edge coloring of G3. color ← 04. while G = ∅$5. find maximal matching M of G6. color all M vertices with color7. G ← G − M8. color ← color + 1implementation of Python
Assume that we are given an undirected graph G=(V,E). Consider that Dijkstra's algorithm found a shortest path in G, called SP, between two nodes A and X of V. Is it true or false that if we reverse the nodes on SP, we get a shortest path from X to A? Prove or disprove.
Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm b. Use Prim to find the MST c. Use Kruskal to find the MST d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.
Suppose you are given a directed graph G on n vertices, each of which is assigned a colour. (In this problem, both endpoints of an edge can have the same colour.) Give an efficient algorithm to find the length of the longest monochromatic directed walk in G. (In a walk we can revisit vertices and recross edges, whereas in a path we cannot.) Your algorithm should return "undefined" if there is a directed cycle whose vertices are all the same colour.