TY - GEN
T1 - Simple Distributed Spanners in Dense Congest Networks
AU - Barenboim, Leonid
AU - Maimon, Tzalik
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - The problem of computing a sparse spanning subgraph is a well-studied problem in the distributed setting, and a lot of research was done in the direction of computing spanners or solving the more relaxed problem of connectivity. Still, efficiently constructing a linear-size spanner deterministically remains a challenging open problem even in specific topologies. In this paper we provide several simple spanner constructions of linear size, for various graph families. Our first result shows that the connectivity problem can be solved deterministically using a linear size spanner within constant running time on graphs with bounded neighborhood independence. This is a very wide family of graphs that includes unit-disk graphs, unit-ball graphs, line graphs, claw-free graphs and many others. Moreover, our algorithm works in the model. It also immediately leads to a constant time deterministic solution for the connectivity problem in the Congested-Clique. Our second result provides a linear size spanner in the model for graphs with bounded diversity. This is a subtype of graphs with bounded neighborhood independence that captures various types of networks, such as wireless networks and social networks. Here too our result has constant running time and is deterministic. Moreover, the latter result has an additional desired property of a small stretch.
AB - The problem of computing a sparse spanning subgraph is a well-studied problem in the distributed setting, and a lot of research was done in the direction of computing spanners or solving the more relaxed problem of connectivity. Still, efficiently constructing a linear-size spanner deterministically remains a challenging open problem even in specific topologies. In this paper we provide several simple spanner constructions of linear size, for various graph families. Our first result shows that the connectivity problem can be solved deterministically using a linear size spanner within constant running time on graphs with bounded neighborhood independence. This is a very wide family of graphs that includes unit-disk graphs, unit-ball graphs, line graphs, claw-free graphs and many others. Moreover, our algorithm works in the model. It also immediately leads to a constant time deterministic solution for the connectivity problem in the Congested-Clique. Our second result provides a linear size spanner in the model for graphs with bounded diversity. This is a subtype of graphs with bounded neighborhood independence that captures various types of networks, such as wireless networks and social networks. Here too our result has constant running time and is deterministic. Moreover, the latter result has an additional desired property of a small stretch.
KW - Distributed computing
KW - Diversity
KW - Spanners
UR - http://www.scopus.com/inward/record.url?scp=85079096350&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-38919-2_22
DO - 10.1007/978-3-030-38919-2_22
M3 - Conference contribution
AN - SCOPUS:85079096350
SN - 9783030389185
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 260
EP - 272
BT - SOFSEM 2020
A2 - Chatzigeorgiou, Alexander
A2 - Dondi, Riccardo
A2 - Herodotou, Herodotos
A2 - Kapoutsis, Christos
A2 - Manolopoulos, Yannis
A2 - Papadopoulos, George A.
A2 - Sikora, Florian
PB - Springer
T2 - 46th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2020
Y2 - 20 January 2020 through 24 January 2020
ER -