On the Power of Spatial Locality on Online Routing Problems

TL;DR

This paper investigates how limited future spatial information can improve online routing algorithms for TSP and DARP, demonstrating that even small locality knowledge enhances competitive ratios across various metric spaces.

Contribution

It introduces a spatial locality model for online routing problems, showing that limited future spatial information improves competitive ratios for TSP and DARP with multiple servers.

Findings

Spatial locality improves competitive ratios in online routing.

Small locality information is beneficial regardless of metric space.

Enhanced algorithms outperform previous models without spatial locality.

Abstract

We consider the online versions of two fundamental routing problems, traveling salesman (TSP) and dial-a-ride (DARP), which have a variety of relevant applications in logistics and robotics. The online versions of these problems concern with efficiently serving a sequence of requests presented in a real-time on-line fashion located at points of a metric space by servers (salesmen/vehicles/robots). In this paper, motivated from real-world applications, such as Uber/Lyft rides, where some limited knowledge is available on the future requests, we propose the {\em spatial locality} model that provides in advance the distance within which new request(s) will be released from the current position of server(s). We study the usefulness of this advanced information on achieving the improved competitive ratios for both the problems with $k\geq 1$ servers, compared to the competitive results established in the literature without such spatial locality consideration. We show that small locality is indeed useful in obtaining improved competitive ratios irrespective of the metric space.