Conjested Networks Given a connected computer network (bidirectional communicati
ID: 3601802 • Letter: C
Question
Conjested Networks Given a connected computer network (bidirectional communication) we want to find two different nodes u and v such that we can maximize the congestion between u and v with a continuously sent virus being sent between the pair. We define the congestion level as the maximum number of edge-disjoint paths between nodes u and v. For example, the network shown in the following figure has three different paths between nodes 0 and 6 such that each edge is only part of one of the paths. Note that two paths are allowed to go through the same node, such as node 7. No other pair of nodes has a higher congestion evel. 6 7 Input Specification We will be given a sequence of connected computer networks each with n nodes, n 40, labeled (0,1, , n-1). The last input case will be followed by a network of n = 0 nodes, which should not be processed. The specification for a computer network will be as follows: the first line contains a single non-negative value n, denoting the number of nodes. This is then followed by n lines of integers, separated by spaces, denoting the neighbors (zero indexed) of each node. Expect up to 2000 test cases. Output Specification For each input case output one integer on a line by itself denoting the maximum congestion level possible for some pair of its network nodes.Explanation / Answer
we have explained how reliable protocols allow hosts to exchange data reliably even if the underlying physical layer is imperfect and thus unreliable. Connecting two hosts together through a wire is the first step to build a network. However, this is not sufficient. Hosts usually need to interact with remote hosts that are not directly connected through a direct physical layer link. This can be achieved by adding one layer above the datalink layer : the network layer.
The main objective of the network layer is to allow endsystems, connected to different networks, to exchange information through intermediate systems called router. The unit of information in the network layer is called a packet.here are three main types of datalink layers. The simplest datalink layer is when there are only two communicating systems that are directly connected through the physical layer. Such a datalink layer is used when there is a point-to-point link between the two communicating systems. The two systems can be endsystems or routers. PPP, defined in RFC 1661, is an example of such a point-to-point datalink layer. Datalink layers exchange frames and a datalink frame sent by a datalink layer entity on the left is transmitted through the physical layer, so that it can reach the datalink layer entity on the right. Point-to-point datalink layers can either provide an unreliable service (frames can be corrupted or lost) or a reliable service (in this case, the datalink layer includes retransmission mechanisms). .. The unreliable service is frequently used above physical layers (e.g. optical fiber, twisted pairs) having a low bit error ratio while reliability mechanisms are often used in wireless networks to recover locally from transmission errors.
The second type of datalink layer is the one used in Local Area Networks (LAN). Conceptually, a LAN is a set of communicating devices such that any two devices can directly exchange frames through the datalink layer. Both endsystems and routers can be connected to a LAN. Some LANs only connect a few devices, but there are LANs that can connect hundreds or even thousands of devices. In this chapter, we focus on the utilization of point-to-point datalink layers. We will describe later the organisation and the operation of Local Area Networks and their impact on the network layer.
Even if we only consider the point-to-point datalink layers, there is an important characteristics of these layers that we cannot ignore. No datalink layer is able to send frames of unlimited size. Each datalink layer is characterized by a maximum frame size. There are more than a dozen different datalink layers and unfortunately most of them use a different maximum frame size. This heterogeneity in the maximum frame sizes will cause problems when we will need to exchange data between hosts attached to different types of datalink layers.
As a first step, let us assume that we only need to exchange small amount of data. In this case, there is no issue with the maximum length of the frames. However, there are other more interesting problems that we need to tackle. To understand these problems, let us consider the network represented in the figure below.
This network contains two types of devices. The end hosts, represented as a small workstation and the routers, represented as boxes with three arrows. An endhost is a device which is able to send and receive data for its own usage in contrast with routers that most of the time forward data towards their final destination. Routers have multiple links to neighboring routers or endhosts. Endhosts are usually attached via a single link to the network. Nowadays, with the growth of wireless networks, more and more endhosts are equipped with several physical interfaces. These endhosts are often called multihomed. Still, using several interfaces at the same time often leads to practical issues that are beyond the scope of this document. For this reason, we will only consider single-homed hosts in this ebook.
To understand the key principles behind the operation of a network, let us analyse all the operations that need to be performed to allow host A in the above network to send one byte to host B. Thanks to the datalink layer used above the A-R1 link, host A can easily send a byte to router R1 inside a frame. However, upon reception of this frame, router R1 needs to understand that the byte is destined to host B and not to itself. This is the objective of the network layer.
The network layer enables the transmission of information between hosts that are not directly connected through intermediate routers. This transmission is carried out by putting the information to be transmitted inside a data structure which is called a packet. Like a frame that contains useful data and control information, a packet also contains useful data and control information. An important issue in the network layer is the ability to identify a node (host or router) inside the network. This identification is performed by associating an address to each node. An address is usually represented as a sequence of bits. Most networks use fixed-length addresses. At this stage, let us simply assume that each of the nodes in the above network has an address which corresponds to the binary representation on its name on the figure.
To send one byte of information to host B, host A needs to place this information inside a packet. In addition to the data being transmitted, the packet must also contain either the addresses of the source and the destination nodes or information that indicates the path that needs to be followed to reach the destination.
There are two possible organisations for the network layer :
The datagram organisation
The first and most popular organisation of the network layer is the datagram organisation. This organisation is inspired by the organisation of the postal service. Each host is identified by a network layer address. To send information to a remote host, a host creates a packet that contains :