Finding Small OBDDs for Incompletely Specified Truth Tables Is Hard

We present an efficient reduction mapping undirected graphs G with n = 2k vertices for integers k to tables of partially specified Boolean functions g : {0, 1}4k+1 {0, 1, } so that for any integer m, G has a vertex colouring using m colours if and only if g has a consistent ordered binary decision diagram with at most (2m+2)n2 +4n decision nodes. From this it follows that the problem of finding a minimum-sized consistent OBDD for an incompletely specified truth table is NP-hard and also hard to approximate.

• Type: Conference
• Year: 2006
• Where: COCOON
• Authors: Jesper Torp Kristensen, Peter Bro Miltersen
• Keywords: COCOON 2006, Combinatorics, Minimum-sized Consistent Obdd, Ordered Binary Decision Diagram, Undirected Graphs