Arc graphs and their possible application to sparse matrix problems

In continuation of earlier work on the graph algorithmic language GRAAL, a new type of graph representation is introduced involving solely the arcs and their incidence relations. In line with the set theoretical foundation of GRAAL, the are graph structure is defined in terms of four Boolean mappings over the power set of the ares. A simple data structure is available for are graphs requiring only storage of the order of the cardinality of the are set. As an application, the LU decomposition of large sparse matrices and the solution of the corresponding linear systems are formulated in terms of are graphs and their operators, and experimental results involving these algorithms are presented.