Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Suppose we wish to compute shortest paths in a complete directed graph (a directed graph in which there exists an edge in each direction between

image text in transcribed

Suppose we wish to compute shortest paths in a complete directed graph (a directed graph in which there exists an edge in each direction between every two vertices), with positive edge weights (so that Dijkstra's algorithm may be used). But rather than using a complicated priority queue data structure, we use an unsorted list L of the vertices that have not yet been processed. That is, the simplified version of Dijkstra's algorithm performs the following steps: initialize the dist and prev information used in the original Dijkstra's algorithm initialize L to be a list of all the vertices in the graph while L is not empty {look at all of the vertices in L to find the vertex v with the minimum value of dist. get(v) remove v from L for each edge v rightarrow w relax(v rightarrow w)} You may assume that looking at all vertices in L takes time proportional to the number of vertices examined, and that removing v from L takes constant time. (a) What is the running time of this algorithm, using O-notation, as a function of the number n of vertices and the number m of edges in the input graph? (b) Would this algorithm be a better or worse choice than the more usual form of Dijkstra's algorithm using a binary heap (whose operations are all O(log n), except for make Queue (), which is O(n) to insert n elements), for this type of graph? Explain your

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Intelligent Information And Database Systems 6th Asian Conference Aciids 2014 Bangkok Thailand April 7 9 2014 Proceedings Part I 9 2014 Proceedings Part 1 Lnai 8397

Authors: Ngoc-Thanh Nguyen ,Boonwat Attachoo ,Bogdan Trawinski ,Kulwadee Somboonviwat

2014th Edition

3319054759, 978-3319054759

More Books

Students also viewed these Databases questions