Assignment Instructions

CS515 Homework 8.

CS515, Fall 2020
Homework 8
Due: November 11, 2020
1. (16 pts.) Let e1 and e2 be two lowest-weight edges in a connected and weighted graph G. Show that
e1 and e2 belong to some MST in G.
2. (16 pts.) Consider this statement: If e1, e2 and e3 are three lowest-weighted edges in a connected
and weighted graph G, then e1, e2 and e3 belong to some MST in G. Is this statement true? Either
prove it or show a counterexample.
3. (16 pts.) Show that every MST in a connected, weighted graph G is returned by Kruskal’s algorithm
for some sorted order of the edges of G.
4. (16 pts.) Let G be a connected, weighted graph G and let e be an edge in G. Is it possible for e to
be a part of every MST in G? If so, describe a general condition that guarantees it.
5. (20 pts.) Let G be a connected, weighted graph G and let e be a highest-weight edge in G. Is it
possible for e to be a part of some MST in G? If you think the answer is no, explain why. If you
think the answer is yes, formulate a possibly general conditions under which e is included in some
6. (16 pts.) Suppose all edge weights in a graph are integers in the range 1 to V . How fast can you
make Kruskal’s algorithm run? Explain.
7. (Bonus: 30 pts.) A directed graph G = (V; E) is semi-connected if for all pairs of vertices u; v 2 V ,
u is reachable from v or v is reachable from u. Describe a O(jV j + jEj) algorithm to determine
whether or not G is semi-connected. A precise narrative is acceptable. Explain why your algorithm
is correct and justify the running time.

CS515 Homework 8

Calculate Price

Price (USD)

This assignment has been solved!

Place your order for a custom solution to this or a similar paper.

Why Choose Us For Your Assignment?


We value all our customers' privacy. For that reason, all information stays private and confidential and will never be shared with third parties.


With our service you will never miss a deadline. We use strict follow-ups with our writers to ensure that all papers are submitted on time.


We have no tolerance for plagiarism. All papers go through thorough checking to ensure that no assignments contain plagiarism.

Money Back

You feel unsatisfied with your results? No worries. We offer refunds to our customers if any paper is not written according to the instructions.

Clients Love Us

Client #121678
Client #121678
Read More
This is by far the best I have ever scored in a custom essay. I am surprised the writer handled this assignment so well despite the short notice. I will definitely use your service next time.
Client #21702
Client #21702
Read More
When I was recommended to you by my friends, I wasn't sure you could deliver excellent results for Masters research papers until I submitted my first order. I am all yours now.
Client #20730
Client #20730
Read More
Excellent Services! You are the only assignment helper I can rely on. I have worked with many before and your services are exceptional. I have recommended you to my friends and the results are similar.
Client #20387
Client #20387
Read More
I rarely write reviews online but your services are worth promoting. My paper was so urgent I was sure I was gonna miss the deadline but you turned things around. You are awesome!
Client #20189
Client #20189
Read More
I am a satisfied customer. I know I should have given a 5 star because you deserve it but I will give 4.6 because I almost missed a deadline because of a revision. Luckily it was minor and the writer acted promptly.
Client #20187
Client #20187
Read More
Great paper but there is still some room for improvement. I am impressed by your fast responses and how you tacked my concerns professionally. Thank you for being among the few genuine essay writing service providers.
Client #19783
Client #19783
Read More
I can't thank you enough for being a great part of my college life. I recommended you to two more of my friends. I am sure they will be making their orders soon. I love the fact that you offer free pages for referrals. I will be referring a few more and maybe I won't have to pay for my next two paper, LOL.