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Pratik Agarwal and Edwin Olson University of Freiburg and University of Michigan Variable reordering strategies for SLAM
Graph based SLAM Good ordering Bad ordering 24 times more zeros
Graph based SLAM Reorder
Reordering = =
Reordering is essential for SLAM Bad ordering 10s Good ordering 0.1s Good ordering 100 times faster
Exact minimum degree (EMD) Remove node with min edges Connect neighbors
Our method: bucket heap AMD Advantage over EMD: Single query - multiple vertex elimination How? Lists of vertices with similar #edges
BHAMD in action
Multiple vertices eliminated
BHAMD on a 10,000 node graph EMD - 10,000 steps BHAMD - 107 steps Max heap size in BHAMD 42
State-of-the-art techniques AMD Approximate Minimum Degree COLAMD Column Approximate Minimum Degree NESDIS Nested Dissection METIS Serial Graph Partition
Evaluation – reordering time EMD is slowest
Evaluation – solve time
Further room for improvement? maximum improvement of 0.5% (with 1 week compute time)
Conclusion 1.All methods comparable EMD & COLAMD on A 2.BHAMD - simple yet competitive 3.Negligible improvement with small changes
Reordering matrix - P
Toy example Good ordering Bad ordering
Multiple Min Degree (MMD) vs BHAMD Similarity multiple elimination Difference MMD computes and eliminates independent nodes MMD is still exact unlike BHAMD
But I use CSparse with COLAMD It calls AMD if the matrix is PSD Be careful when opening the box
Graph based SLAM Good ordering Bad ordering 24 times sparser
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