Improved Parameterized Algorithms for Network Query Problems

In the Partial Information Network Query (PINQ) problem, we are given a host graph H, and a pattern P whose topology is partially known. We seek a connected subgraph of H that resemblesP. PINQ is a generalization of Subgraph Isomorphism, where the topology of P is known, and Graph Motif, where the topology of P is unknown. This generalization addresses the major challenge of analyzing biological networks in the absence of certain topological data. In this paper, we use a non-standard hybridization of algebraic and combinatorial tools to develop an exact parameterized algorithm as well as an FPT-approximation scheme for PINQ.