Abstract
Pattern matching in directed graphs is a natural extension of pattern matching in trees and has many applications to different areas. In this paper, we study several pattern matching problems in ordered labeled directed graphs. For the rooted directed graph pattern matching problem, we present an efficient algorithm which runs in time and space O(¦E(P)¦×¦V(T)¦+¦E(T)¦), where ¦E(P)¦, ¦V(T)¦ and ¦E(T)¦ are the number of edges in the pattern graph P, the number of nodes in the target graph T and the number of edges in the pattern graph T, respectively. It is by far the fastest algorithm for this problem. This algorithm can also solve the directed graph pattern matching problem without increasing time or space complexity. Our solution to this problem outperforms the best existing method by Katzenelson, Pinter and Schenfeld by a factor of at least ¦V(P)¦. We also present an algorithm for the directed graph topological embedding problem which runs in time O(¦V(P)¦×¦E(T)¦+¦E(P)¦) and space O(¦V(P)¦×¦V(T)¦+¦E(P)¦+¦E(T)¦), where ¦V(P)¦ is the number of nodes in the pattern graph P. To our knowledge, this algorithm is the first one for this problem.
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