Recognizing Properties of Periodic Graphs

A periodic (dynamic) graph is an infinite graph with a repetitive structure and a compact representation. A periodic graph is represented by a finite directed graph, called the dependence or the static graph, with ddimensional integer vector weights associated with its edges. For every vertex in the dependence graph there corresponds a d-dimensional lattice in the periodic graph. For every edge (u , u) in the dependence graph with vector weight a , there are infinitely many edges in the periodic graph, namely, from every point on the lattice corresponding to u to the point shifted by a on the lattice corresponding to u . Periodic graphs are used, for example, to model VLSI circuits and systems of uniform recurrence relations. In this paper we give algorithms to compute weakly connected components, to test bipartiteness, and to compute a minimum average cost spanning tree for d-dimensional periodic graphs.