Exact k-way sparse matrix partitioning

To minimize the communication in parallel sparse matrix-vector multiplication while maintaining load balance, we need to partition the sparse matrix optimally into k disjoint parts, which is an NP-complete problem. We present an exact algorithm based on the branch and bound (BB) method which partitions a matrix for any k, and we explore exact sparse matrix partitioning beyond bipartitioning. The algorithm has been implemented in a software package General Matrix Partitioner (GMP). We also present an integer linear programming (ILP) model for the same problem, based on a hypergraph formulation. We used both methods to determine optimal 2,3,4-way partitionings for a subset of small matrices from the SuiteSparse Matrix Collection. For k=2, BB outperforms ILP, whereas for larger k, ILP is superior. We used the results found by these exact methods for k=4 to analyse the performance of recursive bipartitioning (RB) with exact bipartitioning. For 46 matrices of the 89 matrices in our test set of matrices with less than 250 nonzeros, the communication volume determined by RB was optimal. For the other matrices, RB is able to find 4-way partitionings with communication volume close to the optimal volume

Exact k-way sparse matrix partitioning

To minimize the communication in parallel sparse matrix-vector multiplication while maintaining load balance, we need to partition the sparse matrix optimally into k disjoint parts, which is an NP-complete problem. We present an exact algorithm based on the branch and bound (BB) method which partitions a matrix for any k, and we explore exact sparse matrix partitioning beyond bipartitioning. The algorithm has been implemented in a software package General Matrix Partitioner (GMP). We also present an integer linear programming (ILP) model for the same problem, based on a hypergraph formulation. We used both methods to determine optimal 2,3,4-way partitionings for a subset of small matrices from the SuiteSparse Matrix Collection. For k=2, BB outperforms ILP, whereas for larger k, ILP is superior. We used the results found by these exact methods for k=4 to analyse the performance of recursive bipartitioning (RB) with exact bipartitioning. For 46 matrices of the 89 matrices in our test set of matrices with less than 250 nonzeros, the communication volume determined by RB was optimal. For the other matrices, RB is able to find 4-way partitionings with communication volume close to the optimal volume

A Shear-Wave Seismic System to Look Ahead of a Tunnel Boring Machine

The Earth’s properties, composition and structure ahead of a tunnel boring machine (TBM) should be mapped for hazard assessment during excavation. We study the use of seismic-exploration techniques for this purpose. We focus on a seismic system for soft soils, where shear waves are better and easier to interpret than compressional waves, as has been shown over the last decade. The system is intended to be deployed on the machine’s cutter head, with a few seismic sources and sufficiently many seismic sensors to tackle spatial variability and noise characteristics. An important property of the newly developed system is its ability to process data with very little human interaction. Images need to be available in near real time, without human interactions slowing down the imaging process. This can be achieved by employing Full Waveform Inversion, which minimizes the difference between modeled and observed data. Because this method may suffer from local minima in the cost function if the data lack low-frequency information, we employ a dedicated seismic source that can generate sufficiently low frequencies for the relevant length scales. With data acquired in a number of field settings that mimic realistic TBM configurations, we show that the designed seismic system can successfully look ahead of the TBM and offers a valuable capability to support decision-making during tunnel excavation.Applied Geophysics and Petrophysic