Online Carpooling using Expander Decompositions
Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, and Sahil Singla

TL;DR
This paper introduces efficient online algorithms for the carpooling problem that maintain low discrepancy in edge orientations, achieving polylogarithmic bounds in stochastic settings on general graphs.
Contribution
It extends discrepancy bounds from complete graphs to general expander graphs using expander decompositions and analyzes the greedy algorithm's effectiveness in this context.
Findings
Achieves polylogarithmic discrepancy bounds for online carpooling on expander graphs.
Extends previous bounds from complete graphs to general graphs using expander decompositions.
Demonstrates the effectiveness of the greedy algorithm in stochastic settings on expanders.
Abstract
We consider the online carpooling problem: given vertices, a sequence of edges arrive over time. When an edge arrives at time step , the algorithm must orient the edge either as or , with the objective of minimizing the maximum discrepancy of any vertex, i.e., the absolute difference between its in-degree and out-degree. Edges correspond to pairs of persons wanting to ride together, and orienting denotes designating the driver. The discrepancy objective then corresponds to every person driving close to their fair share of rides they participate in. In this paper, we design efficient algorithms which can maintain polylog maximum discrepancy (w.h.p) over any sequence of arrivals, when the arriving edges are sampled independently and uniformly from any given graph . This provides the first polylogarithmic…
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