Using Graph Theoretical Methods and Traceroute to Visually Represent Hidden Networks

Within the scope of a Wide Area Network (WAN), a large geographical communication network in which a collection of networking devices communicate data to each other, an example being the spanning communication network, known as the Internet, around continents. Within WANs exists a collection of Routers that transfer network packets to other devices. An issue pertinent to WANs is their immeasurable size and density, as we are not sure of the amount, or the scope, of all the devices that exists within the network. By tracing the routes and transits of data that traverses within the WAN, we can identify routers and create both the paths and weights between devices that are communicating. However, there is the issue of hidden routers who transfer data but do not identify themselves to identification requests like Traceroute, and the undocumented edges between Routers. Like a blackbox function that outputs data in a way that we do not know the interior mechanics, we do not know all the internal components that manage the traffic within the WAN. Finding out is called the Anonymous Routing Blackbox Problem, and we will use labelled graphs, vertex and edge coloring, and pathfinding to derive solutions

UNOmaha Problem of the Week (2021-2022 Edition)

The University of Omaha math department\u27s Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester\u27s end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes. Now there are three difficulty tiers to POW problems, roughly corresponding to easy/medium/hard difficulties, with each tier getting twelve problems per semester, and three problems (one of each tier) per week posted online and around campus. The tiers are named after the EPH classification of conic sections (which is connected to many other classifications in math), and in the present compilation they abide by the following color-coding: Cyan, Green, and Magenta. In practice, when creating the problem sets, we begin with a large enough pool of problem drafts and separate out the ones which are most obviously elliptic or hyperbolic, and then the remaining ones fall into parabolic. The tiers don\u27t necessarily reflect workload, though, only prerequisite mathematical background. Ideally, the solutions to elliptic problems, and any parts of solutions to parabolic and hyperbolic problems not covered in standard undergraduate courses, are meant to test participants\u27 creativity. Beware, though, many solutions also include additional commentary which varies wildly in the reader\u27s assumed mathematical maturity

Problem of the Week: A Student-Led Initiative to Bring Mathematics to a Broader Audience

Problem of the Week (POW!) is a weekly undergraduate mathematics competition hosted by two graduate students from the UNO Math Department. It started with the goal to showcase variety, creativity, and intrigue in math to those who normally feel math is dry, rote, and formulaic. Problems shine light on both hidden gems and popular recreational math, both math history and contemporary research, both iconic topics and nontraditional ones, both pure abstraction and real-world application. Now POW! aims to increase availability and visibility in Omaha and beyond. Select problems from Fall 2021 to Spring 2023 are highlighted here: these received noteworthy engagement and praise from participants and observers

OPS Bus Scheduling: A Heuristic Approach to a Three-Tier Multi-Depot Vehicle Routing Problem With Inter-Depot Routes

Omaha Public Schools (OPS) currently uses a Two-Tier Bus Transportation System and is investigating whether switching to a Three-Tier Bus Transportation System would be cost effective by reducing the number of buses and bus drivers OPS uses. This project aims to develop an algorithm that would allow OPS to test whether a Three-Tier system is more cost effective. The Bus Routing Project is composed of two different software components: a geographical analyzer and a heuristic bus route generator