Polyhedral Techniques

Polyhedral techniques are powerful mathematical approaches used to analyze the structure of linear programs and constraint satisfaction problems. These techniques can be used to identify feasible solutions, develop solution strategies, and optimize existing solutions. They involve a combination of algebraic analysis, graph theory, and combinatorial optimization. Polyhedral approaches are particularly useful for applications that deal with large datasets as they can provide efficient solutions without requiring exhaustive search methods. Polyhedral approaches have been used in various fields such as computer architecture, compilers, operating systems, and databases. These techniques are particularly useful when targeting complex hardware architectures or parallel computing platforms.  Additionally, these techniques can be used to detect potential bottlenecks in an application’s code that may compromise overall performance. Thanks to its versatility and accuracy, the polyhedral technique is becoming increasingly popular among software developers and engineers who are looking for ways to improve the performance of their applications. 

Furthermore, polyhedral techniques are not just confined to basic linear programming models. In recent years, they have been extended to non-linear and integer programming as well as to problems such as scheduling and network optimization. This has enabled businesses to solve complex problems more efficiently and effectively than ever before. By leveraging the power of these sophisticated mathematical approaches, companies can optimize their resources and maximize productivity without compromising on quality or customer satisfaction.  

Cerebras Systems has developed a high-level polyhedral compiler that takes a high-level algorithm description that can be written manually or extracted from a TensorFlow computation graph and generates input to the low-level C-based compiler. Cerebras Systems has demonstrated that effective combination of two relatively well-known polyhedral operations, variable compression and fixed-size box hull, can be used to expose rectangular sets of operations that can be mapped to the advanced SIMD operations of the Cerebras CS-1 architecture.