An Improved Proximity Bound for Bike-Dock Reallocation Problem in Bike Sharing System

TL;DR

This paper improves the proximity bound for a nonlinear integer programming problem related to re-allocating bike docks in sharing systems, enabling more efficient algorithms.

Contribution

It derives an enhanced proximity bound for the problem and its scaled variant, refining the algorithmic time bounds for existing polynomial-time solutions.

Findings

Improved proximity bound for the re-allocation problem

Refined time bounds for proximity-scaling algorithms

Enhanced efficiency in solving bike-sharing dock re-allocation

Abstract

We consider a class of nonlinear integer programming problems arising from re-allocation of dock-capacity in a bike sharing system. The main aim of this note is to derive an improved proximity bound for the problem and its scaled variant. This makes it possible to refine the time bound for the polynomial-time proximity-scaling algorithm by Freund et al. (2022).