Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 01, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Torsten Mütze

Binary Decision Diagrams - A general-purpose toolkit for combinatorial problems

A binary decision diagram, BDD for short, is a data structure to represent a boolean function. In this talk I will discuss the amazing possibilities BDDs offer to solve the three most fundamental combinatorial problems:
- counting all objects from a family X
- generating uniformly random elements from X
- computing weighted maxima/minima over all elements in X
Here X is some family of combinatorial objects, e.g. all independent sets, matchings, colorings, spanning trees or Hamilton paths/cycles of a graph (choose your favourite). Based on material from [D. Knuth, The Art of Computer Programming, Vol. 4], I will introduce the main techniques to do combinatorics with BDDs and illustrate them with various examples.

Personal note: I got to know BDDs in the context of Boolean circuit verification, and when I learned about their applications in combinatorics from Knuth's book, I realized that this topic deserves to be much better known.

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