Solving String Problems on Graphs Using the Labeled Direct Product

Abstract Suffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching , longest common substring statistics and repeated . Recent lines research focused on extending some these problems vertex-labeled graphs, either by using efficient ad-hoc approaches which do not generalize all input or indexing difficult graphs having worst-case exponential complexities. In absence ubiquitous polynomial tool like suffix tree for labeled we introduce direct product two a general obtaining algorithms in worst case: obtain conceptually simpler quadratic () graphs. Our run time linear size graph, may be smaller than inputs, their run-time is predictable, because graph can precomputed efficiently. We also solve containing cycles, was left open problem Shimohira et al. 2011. To show power apply it Moreover, that our (worst-case quadratic) optimal, conditioned Orthogonal Vectors Hypothesis. Finally, complete complexity picture around studying undirected