Optimizing Cyclist Parking in a Closed System

Abstract

In this paper, we consider the two different aspects of the bike parking problem; namely the assignment of bike racks to locations, and the selection of the minimal number of bike rack locations satisfying some maximum walking distanced. The first sub-problem considered was the assignment of bike racks to individual buildings in the attempt to satisfy the needs of the total number of cyclists expected to reside within a building during the course of an average day. We show that the case of assigning a finite number of bike racks to all buildings on a campus is NP-Hard, and propose a greedy algorithm to obtain a solution. The case of allowing for additional bike racks to be purchased is shown to bePolynomial-Time solvable. The second sub-problem, finding the minimal number of bike rack locations, is shown to be NP-Hard, and a method to use approximation algorithms for the Maximum Independent Set to find solutions is demonstrated.