Reactive Proximity Data Structures for Graphs

TL;DR

This paper introduces new reactive proximity data structures for graphs with small separators, enabling efficient real-time nearest-site queries and updates, with applications in logistics and geographic information systems.

Contribution

The paper presents novel reactive proximity data structures tailored for graphs with polynomial expansion, improving real-time query and update efficiency in such networks.

Findings

Outperforms Dijkstra's algorithm in real-time query scenarios

Effective in applications like emergency dispatching and GIS

Applicable to planar graphs and road networks

Abstract

We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We refer to a data structure that can efficiently react to such updates as reactive. We present novel reactive proximity data structures for graphs of polynomial expansion, i.e., the class of graphs with small separators, such as planar graphs and road networks. Our data structures can be used in several logistical problems and geographic information systems dealing with real-time data, such as emergency dispatching. We experimentally compare our data structure to Dijkstra's algorithm in a system emulating random queries in a real road network.