TCP/IP: Network Topologies and Set Theory

Interacting with servers and clients within a given network, how does the conceptualization of set theory help people understand the behavior of those servers and clients interacting with one another on that given network? In short, the answer is that set theory allows servers and clients to be modeled in accordance with subsets embedded within the given server's communication-network; this article explores this assertion further.

First and foremost, what is set theory? Albeit, set theory is a specific flavor of mathematics dealing with discrete objects and their placement within a higher dimensional space than the dimension in which those given discreate objects lend themselves to. For example, a set "S" is a made up of "n" elements, where these "elements" (i.e. discrete objects) may be sub-divided into subsets. This being said, how do these statements give rise to distributed application development underlying the TCP/IP abstract programming interface? The answer is related to the importance of minimizing excess computational requirements by subdividing nodes (i.e. servers) on a given server's local area network (i.e. a LAN) to where if a given client application were to contact a server on an arbitrary network where all "nodes" located on that LAN are sub-divided in accordance with a specific subnet mask, the client application's DNS server will map the associated application program's system call to the IP address associated with the given domain name for which the client application is calling relative to the given server delegated to fulfill the client application's request.

Because TCP/IP provides servers and clients with a rich variety of computer networking functionality options, this is to say that specific subnets of the given local area network for which is identified by a given IP address for which a given "remote" client application calls upon, this "call" will be routed internally within the given server's network (i.e. LAN) in accordance with the specific server port relative to the function for which the given client application requests.

Wherefore, subnets can be distinguished in accordance with servers' functionality relative to the client applications calling upon them. Specifically, if a remote client application is requesting a server for a dateTime() function (e.g. a client application is requesting the value for the current date and time), all servers, in general, reserve the capability to supply such a service to a client application. Therefore, the client application will have a minimized wait time in receiving such information due to such a request being handled by potentially any server (i.e. "node") for which the client application specifies as the server's IP address underlying its foregoing communication system call. On the same token, if such a request was not as generic as the one mentioned prior, such as a request to print a document (i.e. a Linux server implementing "CUPS" print-server functionality), the client application-request must be routed to the specific subnet of the given server's local area network that is mapped to the public IP address for which the client application uses to map its request to the given server who may provide such a request. Wherein, the local area network that is mapped to the public IP address-aforementioned then configures the routing of the client application's request to the specific subnet via the mapping of the server's LAN subnet mask.

Here then, because the implementation of subnetting relative to TCP/IP computer networking functionality facilitates parallel processing due to specific classes of nodes located within the given server LAN to be separated into "categorical" subsets in accordance to a server's functionality, this in turn reduces the computational load of the server-LAN as in comparison to the scenario where if no subnetting was to be implemented on that given LAN. Thus, TCP/IP networking communication functionality supports the concept of distributed parallel programming.

The benefit of distributed parallel programming embedded within a server's network topology is that the computational burden from handling concurrent requests by multiple client applications is distributed across the server's LAN. Wherefore, the "computational burden" mentioned-prior will not be placed on the server's network (i.e. LAN) as a whole ergo a specific segment of that whole.