Decremental All-Pairs Shortest Paths

Years and Authors of Summarized Original Work

• 2004; 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. An algorithm is fully dynamic if it can handle both edge insertions and edge deletions. A partially dynamic algorithm can handle either edge insertions or edge deletions, but not both: it is incremental if it supports insertions only, and decremental if it supports deletions only.

This entry addressed the decremental version of the all-pairs shortest paths problem (APSP), which consists of maintaining a directed graph with real-valued edge weights under an intermixed sequence of the following operations:

delete(u, v)::

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