| Full text | |
| Author(s): |
Ferreira, Carlos Eduardo
;
Pereira Franco, Alvaro Junio
Total Authors: 2
|
| Document type: | Journal article |
| Source: | DISCRETE APPLIED MATHEMATICS; v. 245, p. 12-pg., 2018-08-20. |
| Abstract | |
A flowgraph G = (V, A, s) is a digraph such that there is a dipath from s to u for every vertex u in G. A vertex w dominates a vertex u if and only if all dipaths in G from s to u pass through w. The vertex s dominates trivially any vertex in G. In this work, we define two sets called dominator cover and junction partition. A dominator cover in G is a set of vertices that includes s and non-trivial dominators for all vertices in G. A junction partition B = {B-1, . . . , B-k) is a partition of V which satisfies the following property: if vertex u belongs to B-j and vertex v belongs to B-j (i # j), then there are internally vertex-disjoint dipaths from s to u and from s to v, for short, s is a junction of u and v. The first part of this work shows that, in flowgraphs, the minimum size of a dominator cover is equal to the maximum size of a junction partition. The second part describes some applications for this relation, such as, a new correctness proof of an algorithm that finds a maximum junction partition in reducible flowgraphs; and good time and space complexity algorithms for problems related to junctions and nearest common ancestors in acyclic digraphs. (C) 2017 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |