Linear Functions for Interactive Configuration Using Join Matching and CSP Tree Decomposition

Quick responses are required for interactive configuration. For this an ideal interactive configurator needs to provide the functionalities required for interactive configuration with at most linear time complexity. In this paper, we present such a data structure called Join Matched CSP (JMCSP). When a JMCSP is used to represent a configuration problem, the functionalities required for interactive configuration can be obtained with linear time complexity. Unlike the tree-of-BDDs [Subbarayan, 2005], the JMCSPs while taking advantage of treedecomposition also provide linear configuration functions. Although obtaining a JMCSP is exponential in the tree-width of the input configuration problem, due to tree-like hierarchical nature of configuration problems, this is typically feasible. We present the JMCSP compilation process along with the linear interactive configuration functions on it. The linear functionalities provided by the JMCSPs include computation of all minimum explanations.