In this work we are going to investigate a factorization method that was invented by John Pollard. It makes possible to factorize medium large integers into a product of prime numbers. We will run a C++ program and test how do different parameters affect the results. There will be a connection drawn between the Pollard's rho method, the Birthday paradox and the Floyd's cycle finding algorithm. In results we will find a polynomial function that has the best effectiveness and performance for Pollard's rho method.

A Decision Support model for planning Intercity Railways is presented in this research. The main aim of the model is to generate inputs for the logit model existing in the Virginia Tech Transportation Systems Analysis Model (TSAM). The inputs required by the TSAM logit model are travel time, travel cost and schedule delay. Travel times and travel costs for different rail technologies are calculated using a rail network and actual or proposed rail schedules. The concept of relational databases is used in the development of the network topology. Further, an event graph approach is used for analysis of the generated network. Shortest travel times and their corresponding travel costs between origin-destination pairs are found using Floyd's algorithm. Complete itineraries including transfers (if involved) are intrinsically held in the precedence matrix generated after running the algorithm. A standard mapping technique is used to obtain the actual routes. The algorithms developed, have been implemented in MATLAB. Schedules from the North American Passenger rail system AMTRAK are used to generate the sample network for this study. The model developed allows the user to evaluate what-if scenarios for various route frequencies and rail technologies such as Accelerail, High Speed Rail and Maglev. The user also has the option of modifying route information. Comparison of travel time values for the mentioned technology types in different corridors revealed that frequency of service has a greater impact on the total travel time in shorter distance corridors, whereas technology/line-haul speed has a greater influence on the total travel time in the longer distance corridors. This tool could be useful to make preliminary assessments of future rail systems. The network topology generated by the algorithm can further be used for network flow assignment, especially time-dependent assignment if used with dynamic graph algorithms. / Master of Science