Homework Assignment 7

In the following illustration of a graph, the vertices are denoted by circles and the edges are denoted by lines. Each vertex contains a letter that can be used to identfy it. Each edge has a number next to it indicating its "length". Most edges are undirected; directed edges have an arrow on them indicating their directionality.

Calculate the shortest path from vertex a to vertex j using Dijkstra's algorithm. Show all of your work in the following table. (Note: More or fewer than 13 iterations may be required.)

Iter.	Label of a	Label of b	Label of c	Label of d	Label of e	Label of f	Label of g	Label of h	Label of i	Label of j	Perm.
0	0,*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	\(\infty\),*	a
1
2
3
4
5
6
7
8
9
11
12
13

Using your work from the previous question, what is the shortest path from vertex a to vertex i?

Suppose a netmask of 255.255.255.240 is applied to a class C network address. How many (mathematically feasible) possible host addresses are there in each subnet? (Show your work.)
Consider the IP address 199.239.136.200.
1. Convert this address to binary.
2. Identify the network and host portion of this address.
3. Is this a class A, B, C, or D address?
Determine the subnetwork for the device with CIDR address 212.43.43.33/27 Show all of your work.
Consider a datagram network that uses 5-bit host addresses and suppose that a router in that network uses longest prefix matching and has the following forwarding table:
```
    Prefix Match            Interface
        00                      0
        010                     1
        011                     2
        10                      2
        11                      3
    
```
1. What destination host addresses are associated with each interface?
2. How many host addresses are associated with each interface? (Note: Do not list them all and count them to find the answer, use simple arithmetic.)
As you know, the TCP header contains a number of bit flags. These bits are often read in as a single 8-bit integer (in which the two leading/most-significant bits are 0).
Suppose the decimal value of the mask for the ACK and SYN bits (indicating a SYNACK also known as an ACKofSYN) is 18. Suppose in addition, that, for a particular TCP packet, this 8-bit int has the value of 50. Are the ACK and SYN bits both 1 for this packet? Show all of your work. Hint: You can answer this question using the same techniques you have used to manipulate network masks.