Project on Graph Theory
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Project on Graph Theory
Covered topics:
• Chapters 3 and 5
Total marks: 10
Exercise 1 (5 marks)
Given a weighted graph G, a minimal cost spanning tree (MCST) T is a tree of G with the smallest weight. We have discussed two algorithms for solving the MCST problem - Kruskal’s algorithm and Prim’s algorithm. Both the algorithms use greedy approaches to solve the problem. Now, do the following steps.
(i) Write programs in C++/java to implementing Kruskal’s and Prim’s algorithms.
(ii) Test your programs on (same for both algorithms) randomly generated test graphs of 50, 100, 150, 200, 250 and 300 vertices.
(iii) For each type of graph (the number of edges is fixed) generate 20 different random problem sets and report your results as in the following table [there will six tables, e.g., Table 1(a-f)].
Table 1 (a): Results for the problem instance of size 50 by Kruskal’s and Prim’s algorithms
Instances Solution Computational Time
Kruskal’s Algo. Prim’s Algo. Kruskal’s Algo. Prim’s Algo.
1
2
………..
Up to 20
Best
Average
Worst
(iv) Summarize your results as in the following table 1(g).
Table 1 (g): Summary of the Results by Kruskal’s and Prim’s algorithms
Size (n) Average Solution Best Time Average Time Worst Time
Kruskal Prim Kruskal Prim Kruskal Prim Kruskal Prim
50
100
150
200
250
300
(v) Draw a figure comparing the average solution and the average computational time.
(vi) Interpret your results, analyze and make comments on your results.
Exercise 2 (5 marks)
Given a weighted graph G, we determine the shortest path between any two fixed pair of vertices of a directed or undirected graph. We have discussed two algorithms for finding shortest path between any two pair of vertices - Dijkstra’s algorithm and Floyd-Warshal’s algorithm. Both the algorithms use greedy approaches to solve the problem. Now, do the following steps.
(i) Write programs in C++/java to implementing Dijkstra’s and Floyd-Warshal’s algorithms.
(ii) Test your programs on (same for both algorithms) randomly generated test graphs of 50, 100, 150, 200, 250 and 300 vertices using ‘vertex 1’ as source and ‘vertex n’ as sink.
(iii) For each type of graph (the number of edges is fixed) generate 20 different random problem sets and report your results as in the following table [there will six tables, e.g., Table 2(a-f)].
Table 2 (a): Results for the problem instance of size 50 by Dijkstra’s and Floyd-Warshal’s
algorithms
Instances Solution Computational Time
Dijkstra’s Algo. Floyd-Warshal’s Algo. Dijkstra’s Algo. Floyd- Warshal’s Algo.
1
2
……..
Up to 20
Best
Average
Worst
(iv) Summarize your results as in the following table 2(g).
Table 2 (g): Summary of the Results by Dijkstra’s and Floyd-Warshal’s algorithms
Size (n) Average Solution Best Time Average Time Worst Time
Dijkstra Floyd- Warshal Dijkstra Floyd- Warshal Dijkstra Floyd- Warshal Dijkstra Floyd- Warshal
50
100
150
200
250
300
(v) Draw a figure comparing the average solution and the average computational time.
(vi) Interpret your results, analyze and make comments on your results.
Nº del proyecto: #10247612
Sobre el proyecto
22 freelancers están ofertando un promedio de $365 por este trabajo
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