## March 9, 2018:

# Reactive Proximity Data Structures for Graphs

## Nil Mamano

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 e ciently
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 directly 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.

(Based on joint work with David Eppstein and Michael T. Goodrich, to
be presented at LATIN 2018.)