A note on the size of OBDDs for the graph of integer multiplication

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are the most common dynamic data structure for Boolean functions. Among the many areas of application are verification, model checking, computer-aided design, relational algebra, and symbolic graph algorithms. Analyzing the limits of symbolic graph algorithms for the all-pairs-shortest paths problem which work on OBDD-represented graph instances the so-called graph of integer multiplication has been investigated by Sawitzki D. Sawitzki, Lower bounds on the OBDD size of graphs of some popular functions, in: Proc. of SOFSEM, LNCS, vol. 3381, 2005, pp. 298-309]. Using simple arguments his lower bound of ²n/768−1 on the size of OBDDs representing the graph of integer multiplication is improved up to ²n/24.