Semi-dynamic algorithms for strongly chordal graphs

Abstract

Within the broad ambit of algorithm design, the study of dynamic graph algorithms continues to be a thriving area of research. Commensurate with this interest is an extensive literature on the topic. Not surprisingly, dynamic algorithms for all varieties of shortest path problems, in view of their practical importance, occupy a preeminent position. Relevant to this paper are fully dynamic algorithms for chordal graphs. Surprisingly, to the best of our knowledge, there seems to be no reported results for the problem of dynamic algorithms for strongly chordal graphs. To redress 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, [Formula: see text]. The query complexity of an edge-deletion is [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] of the candidate edge [Formula: see text], while the query complexity of an edge-insertion is [Formula: see text], where [Formula: see text] is the number of vertices of [Formula: see text].