A Uniform Approach to Semi-Dynamic Problems on Digraphs

In this paper we propose a uniform approach to deal with incremental problems on digraphs and with decremental problems on dags generalizing a technique used by La Poutr´e and van Leeuwen in [17] for updating the transitive closure and the transitive reduction of a dag. We define a propagation property on a binary relationship over the vertices of a digraph as a simple sufficient condition to apply this approach. The proposed technique is suitable for a very simple implementation which does not depend on the particular problem; in other words, the same procedures can be used to deal with different problems by simply setting appropriate boundary conditions. In particular, we provide semi-dynamic algorithms and data structures for maintaining a binary relationship over the vertices of a digraph (dag) with n vertices and m edges, requiring O(n · max{q, m}) total time for any sequence of q edge insertions (deletions). This gives O(n) amortized time per operation over a sequence of Ω...

• Type: Journal
• Year: 1998
• Where: TCS
• Authors: Serafino Cicerone, Daniele Frigioni, Umberto Nanni, Francesco Pugliese
• Keywords: Binary Relationship, Edge Insertions, Problems, TCS 1998, Theoretical Computer Science