Semi-dynamic Algorithms for Strongly Chordal Graphs

Abstract: There is an extensive literature on dynamic algorithms for a large number of graph theoretic problems, particularly for all varieties of shortest path problems. Germane to this paper are a number fully dynamic algorithms that are known for chordal graphs. However, to the best of our knowledge no study has been done for the problem of dynamic algorithms for strongly chordal graphs. To address this gap, in this paper, we propose a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in a strongly chordal graph, $G = (V, E)$, on $n$ vertices and $m$ edges. The query complexity of an edge-deletion is $O(d_u^2d_v^2 (n + m))$, where $d_u$ and $d_v$ are the degrees of the vertices $u$ and $v$ of the candidate edge ${u, v}$, while the query-complexity of an edge-insertion is $O(n^2)$.