The Parameterised Complexity of Counting Connected Subgraphs and Graph Motifs [article]

Mark Jerrum, Kitty Meeks
2014 arXiv   pre-print
We introduce a class of parameterised counting problems on graphs, p-#Induced Subgraph With Property(\Phi), which generalises a number of problems which have previously been studied. This paper focusses on the case in which \Phi defines a family of graphs whose edge-minimal elements all have bounded treewidth; this includes the special case in which \Phi describes the property of being connected. We show that exactly counting the number of connected induced k-vertex subgraphs in an n-vertex
more » ... h is #W[1]-hard, but on the other hand there exists an FPTRAS for the problem; more generally, we show that there exists an FPTRAS for p-#Induced Subgraph With Property(\Phi) whenever \Phi is monotone and all the minimal graphs satisfying \Phi have bounded treewidth. We then apply these results to a counting version of the Graph Motif problem.
arXiv:1308.1575v3 fatcat:fryb77k3gze65clacn6kgap4pq