Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

Reza, Tahsin; Steil, Trevor; Sanders, Geoffrey; Pearce, Roger

doi:10.1016/j.jpdc.2023.104717

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

Journal Article · Tue Jun 20 00:00:00 EDT 2023 · Journal of Parallel and Distributed Computing

DOI:https://doi.org/10.1016/j.jpdc.2023.104717· OSTI ID:2007614

Reza, Tahsin ^[1]; Steil, Trevor ^[1]; Sanders, Geoffrey ^[1]; Pearce, Roger ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

In this report, we present a parallel 2-approximation Steiner minimal tree algorithm and its MPI-based distributed implementation. In place of expensive distance computations between all pairs of seed vertices, the solution we employ exploits a cheaper Voronoi cell computation. Our design leverages asynchronous processing and message prioritization to accelerate convergence of distance computations, and harnesses vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance using real-world graphs with up to 128 billion edges and 512 compute nodes, and show the ability to find Steiner trees with up to one million seed vertices. Using 12 data instances, we present comparison with the state-of-the-art exact solver, SCIP-Jack, and two sequential 2-approximate algorithms. We empirically show that, on average, the total distance of the Steiner tree identified by our solution is 1.1290 times greater than the Steiner minimal tree – well within the theoretical approximation bound of 2.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2007614

Alternate ID(s):: OSTI ID: 1999952

Report Number(s):: LLNL-JRNL--850367; 1075552

Journal Information:: Journal of Parallel and Distributed Computing, Journal Name: Journal of Parallel and Distributed Computing Journal Issue: N/A Vol. 181; ISSN 0743-7315

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (18)

A distributed dual ascent algorithm for Steiner problems in multicast routing Drummond, Lúcia M. A.; Santos, Marcelo; Uchoa, Eduardo Networks, Vol. 53, Issue 2 https://doi.org/10.1002/net.20276	journal	October 2008
Steiner's problem in graphs and its implications Hakimi, S. L. Networks, Vol. 1, Issue 2 https://doi.org/10.1002/net.3230010203	journal	January 1971
A fast algorithm for Steiner trees Kou, L.; Markowsky, G.; Berman, L. Acta Informatica, Vol. 15, Issue 2 https://doi.org/10.1007/BF00288961	journal	January 1981
A faster approximation algorithm for the Steiner problem in graphs Wu, Y. F.; Widmayer, P.; Wong, C. K. Acta Informatica, Vol. 23, Issue 2 https://doi.org/10.1007/BF00289500	journal	May 1986
Path-distance heuristics for the Steiner problem in undirected networks Winter, Pawel; MacGregor Smith, J. Algorithmica, Vol. 7, Issue 1-6 https://doi.org/10.1007/BF01758765	journal	June 1992
Thinning out Steiner trees: a node-based model for uniform edge costs Fischetti, Matteo; Leitner, Markus; Ljubić, Ivana Mathematical Programming Computation, Vol. 9, Issue 2 https://doi.org/10.1007/s12532-016-0111-0	journal	September 2016
A robust and scalable algorithm for the Steiner problem in graphs Pajor, Thomas; Uchoa, Eduardo; Werneck, Renato F. Mathematical Programming Computation, Vol. 10, Issue 1 https://doi.org/10.1007/s12532-017-0123-4	journal	September 2017
A faster approximation algorithm for the Steiner problem in graphs Mehlhorn, Kurt Information Processing Letters, Vol. 27, Issue 3 https://doi.org/10.1016/0020-0190(88)90066-X	journal	March 1988
Class Steiner trees and VLSI-design Ihler, Edmund; Reich, Gabriele; Widmayer, Peter Discrete Applied Mathematics, Vol. 90, Issue 1-3 https://doi.org/10.1016/S0166-218X(98)00090-0	journal	January 1999
Searching Steiner trees for web graph query Lee, Wookey; Loh, Woong-Kee; Sohn, Mye M. Computers & Industrial Engineering, Vol. 62, Issue 3 https://doi.org/10.1016/j.cie.2011.11.013	journal	April 2012
Solving the Graphical Steiner Tree Problem Using Genetic Algorithms Kapsalis, A.; Raywad-Smith, V. J.; Smith, G. D. Journal of the Operational Research Society, Vol. 44, Issue 4 https://doi.org/10.1057/jors.1993.69	journal	April 1993
On wirelength estimations for row-based placement Caldwell, A. E.; Kahng, A. B.; Mantik, S. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 18, Issue 9 https://doi.org/10.1109/43.784119	journal	January 1999
The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks Sun, Yahui; Brazil, Marcus; Thomas, Doreen IEEE/ACM Transactions on Networking, Vol. 27, Issue 1 https://doi.org/10.1109/TNET.2018.2888864	journal	February 2019
Steiner Minimal Trees Gilbert, E. N.; Pollak, H. O. SIAM Journal on Applied Mathematics, Vol. 16, Issue 1 https://doi.org/10.1137/0116001	journal	January 1968
Distributed Approximation Algorithms for Steiner Tree in the CONGESTED CLIQUE Saikia, Parikshit; Karmakar, Sushanta International Journal of Foundations of Computer Science, Vol. 31, Issue 07 https://doi.org/10.1142/S0129054120500367	journal	November 2020
SYNC or ASYNC: time to fuse for distributed graph-parallel computation Xie, Chenning; Chen, Rong; Guan, Haibing ACM SIGPLAN Notices, Vol. 50, Issue 8 https://doi.org/10.1145/2858788.2688508	journal	December 2015
The node-weighted Steiner tree approach to identify elements of cancer-related signaling pathways Sun, Yahui; Ma, Chenkai; Halgamuge, Saman BMC Bioinformatics, Vol. 18, Issue S16 https://doi.org/10.1186/s12859-017-1958-4	journal	December 2017
Gpu-Accelerated vlsi Routing Using Group Steiner Trees Maringanti, Venkata Suhas; Imana, Basileal; Yoon, Peter The Journal of Computational Science Education, Vol. 8, Issue 1 https://doi.org/10.22369/issn.2153-4136/8/1/4	journal	January 2017

Similar Records

Improving Steiner trees of a network under multiple constraints

Conference · Mon Jul 01 00:00:00 EDT 1996 · OSTI ID:251414

Parallel computation of Steiner Minimal Trees

Conference · Thu Nov 30 23:00:00 EST 1995 · OSTI ID:125514

Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds

Journal Article · Sat Jul 01 00:00:00 EDT 2017 · Sbornik. Mathematics · OSTI ID:22875751

Related Subjects

97 MATHEMATICS AND COMPUTING

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

Citation Formats

References (18)

Similar Records

Related Subjects