An external-memory depth-first search algorithm for general grid graphs

Abstract

Graph data in modern scientific and engineering applications are often too large to fit in the computer’s main memory. Input/output (I/O) complexity is a major research issue in this context. Minimization of the number of I/O operations (in external memory graph algorithms) is the main focus of current research while classical (internal memory) graph algorithms were designed to minimize temporal complexity. In this paper, we propose an external memory depth first search algorithm for general grid graphs. The I/O-complexity of the algorithm is O ( sort ( N ) log 2 N M ) , where N = | V | + | E | , sort ( N ) = Θ ( N B log M / B N B ) is the sorting I/O-complexity, M is the memory size, and B is the block size. The best known algorithm for this class of graph is the standard (internal memory) DFS algorithm with appropriate block (sub-grid) I/O-access. Its I/O-complexity is O ( N / B ) . Recently, the authors proposed an O ( sort ( N ) ) algorithm for solid grid graphs.