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A self-stabilizing algorithm for constructing a minimal reachable directed acyclic graph with two senders and two targets.
- Source :
-
Theoretical Computer Science . Jun2021, Vol. 874, p1-14. 14p. - Publication Year :
- 2021
-
Abstract
- In this paper, we introduce a new graph structure named an ST -reachable directed acyclic graph which is a directed acyclic graph (DAG) that guarantees reachability (i.e., a directed path exists) from every sender to every target. When an arbitrarily connected undirected graph G = (V , E) and two sets of the vertices, senders S (⊂ V) and targets T (⊂ V), are given, we consider the construction of a minimal ST -reachable DAG by changing some undirected edges to arcs and removing the remaining edges. In this paper, we present the necessary and sufficient condition under which a minimal ST -reachable DAG can be constructed when | S | ≤ 2 and | T | ≤ 2 , and propose a self-stabilizing algorithm for constructing a minimal ST -reachable DAG (if it exists) when an arbitrarily connected undirected graph, S (| S | ≤ 2) and T (| T | ≤ 2) are given. Moreover, our proposed algorithm can detect the non-existence of any ST -reachable DAG if the ST -reachable DAG of the given graph and two sets of vertices, S and T , do not exist. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DIRECTED acyclic graphs
*ALGORITHMS
*UNDIRECTED graphs
*DIRECTED graphs
Subjects
Details
- Language :
- English
- ISSN :
- 03043975
- Volume :
- 874
- Database :
- Academic Search Index
- Journal :
- Theoretical Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- 150411640
- Full Text :
- https://doi.org/10.1016/j.tcs.2021.05.005