In this paper, we consider solving the all-pairs regular path problem on large graphs efficiently. Let G be a graph and r be a regular path query, and consider finding the answers of r on G. If G is so small that it fits in main memory, it suffices to load entire G into main memory and traverse G to find paths matching r. However, if G is too large and cannot fit in main memory, we need another approach. In this paper, we propose a novel approach based on external memory algorithm. Our algorithm finds the answers matching r by scanning the node list of G sequentially. We made a small experiment, which suggests that our algorithm can solve the problem efficiently.

Cascading Style Sheets (CSS) is a popular language for describing the styles of XML documents as well as HTML documents. To resolve conflicts among CSS rules, CSS has a mechanism called specificity. For a DTD D and a CSS code R, due to specificity R may contain “unsatisfiable” rules under D, e.g., rules that are not applied to any element of any document valid for D. In this paper, we consider the problem of detecting unsatisfiable CSS rules under DTDs. We focus on CSS fragments in which descendant, child, adjacent sibling, and general sibling combinators are allowed. We show that the problem is coNP-hard in most cases, even if only one of the four combinators is allowed and under very restricted DTDs. We also show that the problem is in coNP or PSPACE depending on restrictions on DTDs and CSS. Finally, we present four conditions under which the problem can be solved in polynomial time.