TY - GEN
T1 - Proof Labeling Schemes for Reachability-Related Problems in Directed Graphs
AU - Ben Shimon, Yoav
AU - Fischer, Orr
AU - Oshman, Rotem
N1 - Publisher Copyright: © 2022, Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - We study proof labeling schemes in directed networks, and ask what assumptions are necessary to be able to certify reachability-related problems such as strong connectivity, or the existence of a node from which all nodes are reachable. In contrast to undirected networks, in directed networks, having unique identifiers alone does not suffice to be able to certify all graph properties; thus, we study the effect of knowing the size of the graph, and of each node knowing its out-degree. We formalize the notion of giving the nodes initial knowledge about the network, and give tight characterizations of the types of knowledge that are necessary and sufficient to certify several reachability-related properties, or to be able to certify any graph property. For example, we show that in order to certify that the network contains a node that is reachable from all nodes, it is necessary and sufficient to have any two of the assumptions we study (unique identifiers, knowing the size, or knowing the out-degree); and to certify strong connectivity, it is necessary and sufficient to have any single assumption.
AB - We study proof labeling schemes in directed networks, and ask what assumptions are necessary to be able to certify reachability-related problems such as strong connectivity, or the existence of a node from which all nodes are reachable. In contrast to undirected networks, in directed networks, having unique identifiers alone does not suffice to be able to certify all graph properties; thus, we study the effect of knowing the size of the graph, and of each node knowing its out-degree. We formalize the notion of giving the nodes initial knowledge about the network, and give tight characterizations of the types of knowledge that are necessary and sufficient to certify several reachability-related properties, or to be able to certify any graph property. For example, we show that in order to certify that the network contains a node that is reachable from all nodes, it is necessary and sufficient to have any two of the assumptions we study (unique identifiers, knowing the size, or knowing the out-degree); and to certify strong connectivity, it is necessary and sufficient to have any single assumption.
UR - http://www.scopus.com/inward/record.url?scp=85134304127&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-09993-9_2
DO - 10.1007/978-3-031-09993-9_2
M3 - منشور من مؤتمر
SN - 9783031099922
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 21
EP - 41
BT - Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
A2 - Parter, Merav
PB - Springer Science and Business Media Deutschland GmbH
T2 - 29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022
Y2 - 27 June 2022 through 29 June 2022
ER -