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Plan Introduction to multilevel heuristics Rich partitioning problems

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Presentation on theme: "Plan Introduction to multilevel heuristics Rich partitioning problems"— Presentation transcript:

1

2 Plan Introduction to multilevel heuristics Rich partitioning problems
New coarsening algorithm and applications Minipart partitioner Partitioning with general-purpose solvers

3 Graph partitioning

4 Graph partitioning Allocate nodes to bins Minimize # edges cut
Capacity constraints Model in High Performance Computing Electronic design …

5 Multilevel algorithms
Uncoarsening + local search Local search + coarsening

6 Coarsening Heavy-edge matching

7 Coarsening Heavy-edge matching

8 Coarsening Avoid huge nodes Handle "stars"

9 Local search Move one node at a time Steepest descent
Incremental gain computation  Fiduccia-Mattheyses algorithm

10 A rich problem: task allocation
Bins Graph Task1 CPU Mem Task2 Communication Task3 CPU Mem Task4 … …

11 A rich problem: task allocation
Bins Graph Task1 CPU Mem Task2 Multiple resources Task3 CPU Mem Task4 … …

12 A rich problem: task allocation
Bins Graph Require Task1 CPU Dynlib1 Mem Task2 Task3 Dynlib2 CPU Mem Task4 … … Facility opening effect

13 A rich problem: task allocation
Bins Graph Task1 Communication Resource usage CPU Mem Task2 Task3 CPU Mem Task4 … …

14 A rich problem: task allocation
Mem CPU Mem CPU Distance matters 2 links Mem CPU

15 A rich problem: task allocation
Mem CPU Latency Vs Throughput) Mem CPU Mem CPU

16 A rich problem: task allocation
Mem CPU Mem CPU Direction matters Mem CPU

17 Limitations of the coarsening approach
Assumes a well connected landscape Trivial feasibility Simple moves from solution to solution Assumes the graph structure is known Not possible for general-purpose solvers Misses other problem-specific structures

18 But general-purpose solvers are stuck

19 Search-driven coarsening
Coarsen without looking at the problem at all! Not specific to a problem type No need to know the graph  Perfect for general-purpose solvers

20 Search-driven coarsening
n solutions Node Solution #1 Solution #2 Solution #3 #1 2 #2 1 #3 #4 #5 #6 Merged

21 Application: Minipart
Open-source partitioning tool Uses search-driven coarsening Quality similar to best Hmetis results

22 Challenge: partitioning with a solver
No information on the problem type No special datastructure

23 Application: partitioning with LocalSolver
Python script using LocalSolver 7.5 Multiple runs of LocalSolver  generate solutions + Search-driven coarsening  add new constraints

24 Not stuck anymore!

25 Beyond benchmarks Partitioning with node replication
Typical problem in electronics Ad-hoc algorithms  labor-intensive 100 lines model + script

26 Conclusion New method  Simple to implement  Any solver
 Any partitioning problem Future work  Computing overhead  Local search could be faster

27 Questions

28 Links Minipart: Partitioning script: Minipart posts:

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