For the weighted shortest path problem, let d, be the cost of reaching the current vertex v, let w be adjacent to v and assume the edge cost is cyw. Suppose that dw Was the costof reaching w prior to examining v. Then under what circumstances is w's distance lowered?A. dw > dyB. dw > dy + CywOC. dw > dy + 1D. dy > dw + Cyw

Answered: For the weighted shortest path problem,…

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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4. For the graph below: a. A snow plow starts at vertex 0 and must return to vertex 0 using a route which visits each edge at least once and repeats a minimum number of edges. Find such a route and how many repeated edges does it have? Assume that the edges all have the length, say length 1.
Find the length of a shortest path between a and zin the given weighted graph. 5. 4. 3 5. bo 2.
For each graph below, state the largest integer weight for directed edge (B,C) that makes the given description true. (Note that the edge weight need not be positive!)
3
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.
Find the shortest path in the graph using the Dijkstra shortest path algorithm?? Please help explain clearly
Please write in detail
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?)
1. Let G = (V, E) be a DAG with weights associated with verticesand edges. Design a Dynamic Programming Algorithm for solvingthe longest path problem.
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 .
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.
Given a directed graph w/ nonnegative edge lengths & two distinct nodes, a and z. Let X denote a shortest path from a to z. If we add 10 to the length of every edge in the graph, then: i) X definitely remains a shortest a-z path. ii) X definitely does not remain a shortest a-z path. iii) X might or might not remain a shortest a-z path (depending on the graph). iv) If X has only one edge, then X definitely remains a shortest a-z path. O i and iv only O iv only O None of the choices O i only O i and iv only O iii only O ii only

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