Christoph Lenzen
ABSTRACT
Consider a clique of n nodes, where in each synchronous round each pair of nodes can exchange O(log n) bits. We provide deterministic constant-time solutions for two problems in this model. The first is a routing problem where each node is source and destination of n messages of size O(log n). The second is a sorting problem where each node i is given n keys of size O(log n) and needs to receive the ith batch of n keys according to the global order of the keys. The latter result also implies deterministic constant-round solutions for related problems such as selection or determining modes.
- R. Cole, K. Ost, and S. Schirra. Edge-Coloring Bipartite Multigraphs in O(|E| log Δ) Time. Combinatorica, 21:5--12, 2001.Google Scholar
Cross Ref
- D. Dolev, C. Lenzen, and S. Peled. "Tri, Tri again": Finding Triangles and Small Subgraphs in a Distributed Setting. In Proc. 26th Symposium on Distributed Computing (DISC), pages 195--209, 2012. Google ScholarDigital Library
- M. Elkin. An Unconditional Lower Bound on the Time-Approximation Tradeoff for the Minimum Spanning Tree Problem. SIAM Journal on Computing, 36(2):463--501, 2006. Google ScholarDigital Library
- S. Frischknecht, S. Holzer, and R. Wattenhofer. Networks Cannot Compute Their Diameter in Sublinear Time. In Proc. 23rd Symposium on Discrete Algorithms (SODA), pages 1150--1162, 2012. Google ScholarDigital Library
- M. T. Goodrich. Communication-Efficient Parallel Sorting. SIAM Journal on Computing, 29(2):416--432, Oct. 1999. Google ScholarDigital Library
- F. Kuhn, T. Moscibroda, and R. Wattenhofer. Local Computation: Lower and Upper Bounds. Computing Research Repository, abs/1011.5470, 2010.Google Scholar
- C. Lenzen and R. Wattenhofer. Tight Bounds for Parallel Randomized Load Balancing. In Proc. 43rd Symposium on Theory of Computing (STOC), pages 11--20, 2011. Google ScholarDigital Library
- N. Linial. Locality in Distributed Graph Algorithms. SIAM Journal on Computing, 21(1):193--201, 1992. Google ScholarDigital Library
- Z. Lotker, B. Patt-Shamir, and D. Peleg. Distributed MST for Constant Diameter Graphs. Distributed Computing, 18(6):453--460, 2006.Google ScholarDigital Library
- L. Lovász and M. D. Plummer. Matching Theory. American Mathematical Society, 2009. Reprint with corrections.Google ScholarCross Ref
- M. Naor. A Lower Bound on Probabilistic Algorithms for Distributive Ring Coloring. SIAM Journal on Discrete Mathematics, 4(3):409--412, 1991.Google ScholarCross Ref
- B. Patt-Shamir and M. Teplitsky. The Round Complexity of Distributed Sorting: Extended Abstract. In Proc. 30th Symposium on Principles of Distributed Computing (PODC), pages 249--256, 2011. Google ScholarDigital Library
- D. Peleg. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, 2000. Google ScholarDigital Library
- D. Peleg and V. Rubinovich. Near-tight Lower Bound on the Time Complexity of Distributed MST Construction. SIAM Journal on Computing, 30:1427--1442, 2000. Google ScholarDigital Library
- A. D. Sarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai, G. Pandurangan, D. Peleg, and R. Wattenhofer. Distributed Verification and Hardness of Distributed Approximation. SIAM Journal on Computation, 41(5):1235--1265, 2012.Google Scholar
Index Terms
- Optimal deterministic routing and sorting on the congested clique
Recommendations
Toward Optimal Bounds in the Congested Clique: Graph Connectivity and MST
PODC '15: Proceedings of the 2015 ACM Symposium on Principles of Distributed ComputingWe study two fundamental graph problems, Graph Connectivity (GC) and Minimum Spanning Tree (MST), in the well-studied Congested Clique model, and present several new bounds on the time and message complexities of randomized algorithms for these ...
Brief Announcement: Symmetry Breaking in the CONGEST Model: Time- and Message-Efficient Algorithms for Ruling Sets
PODC '17: Proceedings of the ACM Symposium on Principles of Distributed ComputingWe study local symmetry breaking problems in the Congest model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem. Our work is motivated by the following central question: can we break the long-...
Optimal Time-Space Trade-Offs for Sorting
FOCS '98: Proceedings of the 39th Annual Symposium on Foundations of Computer ScienceWe study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.Beame has shown a lower bound of $\Omega(n^2)$ for this product leaving a ...
Comments