 Minimum Spanning Tree Update Question in a Connected Graph

Subject Computer Science Data Structures and Algorithms

Question

Let a connected undirected graph G = (V, E) with edge weights and a minimum spanning tree T of G be given. Suppose the weight of an edge (u, v) in G is increased. Describe an O(V + E) algorithm to find a minimum spanning tree with this modification in edge weights.

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Observation – if the edge (u,v) doesn’t belong to T, then MST remains the same as before the modification.
If instead the edge (u,v) belongs to T, then the MST might be updated.
We build a set C1 by marking all vertices that are reachable in T from u but don’t go through v. This task can be achieved using either DFS or BFS....

This is only a preview of the solution. Please use the purchase button to see the entire solution

Related Homework Solutions

Algorithm Design Tracing Using Pseudocode, Desk Check & Desk Checking Table Features \$28.00
Transaction
Commission
Retail Price
Employee
Algorithm Design
Pseudocode
Desk Check
Desk Checking
Expected Results
Record
Item
Sold
Divide & Conquer Algorithm for Finding Anchor (Fixed) Point of Sorted Array \$10.00
Divide
Conquer
Algorithm
Complexity
Pseudocode
Array
Sorted
Anchor
Index
Fixed
Point
Element
Logn
Distinct
Integer
Divide-and-conquer
Logarithmic
Recurrence
Relation
Research Proposal - Applications of Graph Theory in the Study of Community Structures (750 words) \$13.00
Computer Science
Data
Graph
Theory
Community
Structure
Research
Proposal
Objective
Result
Scope
Questions
Social
Network
Algorithm
Dynamic
Node
Edge
NP-Hard
NP-Complete
NP
P
Problem
Approximation
Complexity
Analysis
Topology
Greedy Knapsack 0/1 and Fractional Problem \$15.00
Greedy
Algorithm
Knapsack
0/1
Fractional
Weight
Value
Object
Highest
Lightest
Density
First
Optimal
Solution
Profit
5 Problems Involving Greedy Algorithms \$50.00
Greedy
Algorithm
Analysis
Optimal
Program
Disk
Megabyte
Storage
Capacity
Decimalization
Denomination
Change-making
Half-crown
Florin
Shilling
Sixpence
Threepence
Pence
Coin
Solution
Selection
Sort
Framework
Decomposition
Egyptian
Huffman Coding Java Implementation and Performance Report \$35.00
Huffman
Coding
Report
Symbol
Frequency
Binary
Code
Prefix
Weighted
Length
Chart
Complexity
Java
Algorithm
Path
Tree
Live Chats