Graphs Cannot Be Indexed in Polynomial Time for Sub-quadratic Time String Matching, Unless SETH Fails

The string matching problem on a node-labeled graph $$G=(V,E)$$ asks whether given pattern P has an occurrence in G, the form of path whose concatenation node labels equals P. This is basic primitive various problems bioinformatics, databases, or networks, but only recently proven to have O(|E||P|)-time lower bound, under Orthogonal Vectors Hypothesis (OVH). We consider here its indexed version, which we can index order support time-efficient queries. show that, OVH, no polynomial-time indexing scheme querying time $$O(|P|+|E|^\delta |P|^\beta )$$ , with either $$\delta < 1$$ $$\beta . As side-contribution, introduce notion linear independent-components (lic) reduction allowing for simple proof our result. another illustration that hardness follows as corollary lic reduction, also translate quadratic conditional bound Backurs and Indyk (STOC 2015) query inside text, edit distance. obtain analogous tight improving recent result Cohen-Addad, Feuilloley Starikovskaya (SODA 2019), slightly different boundary condition.