Encoding CSPs with Zero-Suppressed Decision Diagrams

A well established technology in the knowledge compilation community is the encoding of constraint satisfaction problems (CSPs) by binary decision diagrams (BDDs). A technology that among other things has found its use interactive configuration and other kinds of decision support. The main contribution of this paper is the observation that zero-suppressed binary decision diagrams (ZBDDs)that originally was intended for set-manipulation are very well suited to represent CSPs efficiently. As ZBDDs are already efficiently supported by the popular decision diagram package Cudd [17], no extra implementation is needed in order to use ZBDDs instead of BDDs. Using the real-world CSP instances from CLib [5], we empirically demonstrate that using ZBDDs instead of BDDs often result in significantly smaller representations. We also show that this trend holds as well during the compilation of the decision diagrams, which can make the difference between whether or not a CSP can be compiled, given the amount of RAM available.