Trade-Offs for Dynamic Graph Problems

Years and Authors of Summarized Original Work

• 2005; Demetrescu, Italiano

Problem Definition

A dynamic graph algorithm maintains a given property ${ \mathcal{P} }$ on a graph subject to dynamic changes, such as edge insertions, edge deletions and edge weight updates. A dynamic graph algorithm should process queries on property ${ \mathcal{P} }$ quickly, and perform update operations faster than recomputing from scratch, as carried out by the fastest static algorithm. A typical definition is given below:

Definition 1 (Dynamic graph algorithm)

Given a graph and a graph property ${ \mathcal{P} }$, a dynamic graph algorithm is a data structure that supports any intermixed sequence of the following operations:

insert(u, v)::

insert edge (u, v) into the graph.

delete(u, v)::

delete edge (u, v) from the graph.

query(...): :

answer a query about property ${ \mathcal{P} }$ of the graph.

A graph algorithm is fully dynamicif it can handle both edge insertions and edge deletions...