TY - GEN
T1 - Exponential Speedup over Locality in MPC with Optimal Memory.
AU - Balliu, Alkida
AU - Brandt, Sebastian
AU - Fischer, Manuela
AU - Latypov, Rustam
AU - Maus, Yannic
AU - Olivetti, Dennis
AU - Uitto, Jara
N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2022/10/1
Y1 - 2022/10/1
N2 - Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal independent set, and coloring problems. A successful line of research has been studying the complexities of LCL problems on paths/cycles, trees, and general graphs, providing many interesting results for the LOCAL model of distributed computing. In this work, we initiate the study of LCL problems in the low-space Massively Parallel Computation (MPC) model. In particular, on forests, we provide a method that, given the complexity of an LCL problem in the LOCAL model, automatically provides an exponentially faster algorithm for the low-space MPC setting that uses optimal global memory, that is, truly linear. While restricting to forests may seem to weaken the result, we emphasize that all known (conditional) lower bounds for the MPC setting are obtained by lifting lower bounds obtained in the distributed setting in tree-like networks (either forests or high girth graphs), and hence the problems that we study are challenging already on forests. Moreover, the most important technical feature of our algorithms is that they use optimal global memory, that is, memory linear in the number of edges of the graph. In contrast, most of the state-of-the-art algorithms use more than linear global memory. Further, they typically start with a dense graph, sparsify it, and then solve the problem on the residual graph, exploiting the relative increase in global memory. On forests, this is not possible, because the given graph is already as sparse as it can be, and using optimal memory requires new solutions.
AB - Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal independent set, and coloring problems. A successful line of research has been studying the complexities of LCL problems on paths/cycles, trees, and general graphs, providing many interesting results for the LOCAL model of distributed computing. In this work, we initiate the study of LCL problems in the low-space Massively Parallel Computation (MPC) model. In particular, on forests, we provide a method that, given the complexity of an LCL problem in the LOCAL model, automatically provides an exponentially faster algorithm for the low-space MPC setting that uses optimal global memory, that is, truly linear. While restricting to forests may seem to weaken the result, we emphasize that all known (conditional) lower bounds for the MPC setting are obtained by lifting lower bounds obtained in the distributed setting in tree-like networks (either forests or high girth graphs), and hence the problems that we study are challenging already on forests. Moreover, the most important technical feature of our algorithms is that they use optimal global memory, that is, memory linear in the number of edges of the graph. In contrast, most of the state-of-the-art algorithms use more than linear global memory. Further, they typically start with a dense graph, sparsify it, and then solve the problem on the residual graph, exploiting the relative increase in global memory. On forests, this is not possible, because the given graph is already as sparse as it can be, and using optimal memory requires new solutions.
KW - Distributed computing
KW - Locally checkable labeling problems
KW - Massively Parallel Computation
KW - Sublinear memory
KW - Trees
UR - http://www.scopus.com/inward/record.url?scp=85140911020&partnerID=8YFLogxK
U2 - 10.4230/LIPICS.DISC.2022.9
DO - 10.4230/LIPICS.DISC.2022.9
M3 - Conference paper
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 9:1-9:21
BT - 36th International Symposium on Distributed Computing (DISC 2022)
A2 - Scheideler, Christian
PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik
T2 - 36th International Symposium on Distributed Computing
Y2 - 25 October 2022 through 27 October 2022
ER -