Parallel Algorithms for Graph Optimization Using Tree Decompositions

Technical Report · Sat Sep 01 00:00:00 EDT 2012

DOI:https://doi.org/10.2172/1042920· OSTI ID:1042920

Sullivan, Blair D. ^[1]; Weerapurage, Dinesh P. ^[1]; Groer, Christopher S. ^[1]

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1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Although many $$\cal{NP}$$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1042920
• Report Number(s): ORNL/TM--2012/194; KJ0401000; ERKJU04
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DYNAMIC PROGRAMMING
EXACT SOLUTIONS
HPC
IMPLEMENTATION
MADNESS
OPTIMIZATION
POLYNOMIALS
dynamic programming
graph
graph theory
parallel
tree decomposition
weighted independent set