EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

Computational methods for airspace sectorisation

A problem of combining elementary sectors of an airspace region is considered, in which a minimum number of combined sectors must be obtained with restrictions on their load and feasibility of combinations such as the requirement of the space connectivity or the membership of a given set of permissible combinations. Computational methods are proposed and tested to be used for solution of general problems of airspace sectorization. In particular, two types of combinatorial algorithms are proposed for constructing partitions of a finite set with specified element weights and graph-theoretical relationships between the elements. Partitions are constructed by use of a branch and bound method to minimize the number of subsets in the final partition, while limiting the total weight of elements in the subset. In the first type algorithm, ready-made components of the final partition are formed in each node of the branch and bound tree. The remaining part of the original set is further divided at the lower nodes. In the second type algorithm, the entire current partition is formed in each node, the components of which are supplemented at the lower nodes. When comparing algorithms performance, the problems are divided into two groups, one of which contains a connectivity requirement, and the other does not. Several integer programming formulations are also presented. Computational complexity of two problem variants is established: a bin packing type problem with restrictions on feasible combinations, and covering type problem.