Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Monday, February 29, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Torsten Mütze (TU Berlin)

A new combinatorial Gray code for balanced combinations

Efficiently generating all objects in a particular combinatorial class (e.g. subsets, permutations, partitions, strings, trees, triangulations etc.) in such a way that each object is generated exactly once is one of the oldest and most fundamental problems in the area of combinatorial algorithms, and such generation algorithms are used as core building blocks in a wide range of practical applications. In this talk I present a new combinatorial Gray code and a corresponding time- and space-optimal algorithm for generating balanced combinations, i.e., all k-element subsets of {1,2,...,2k}, strengthening the classical Chung-Feller theorem. On a computer, balanced combinations are naturally represented by bitstrings of length 2k with exactly k many 1-bits, and thus encode a vast collection of Catalan-type objects such as Dyck paths, ordered trees, binary trees, triangulations etc. As an application of our results we construct cycle-factors in the odd graph and the middle levels graph --- two intensively studied families of highly symmetric graphs --- that consist of cycles of the same length.

This is joint work with Christoph Standke and Veit Wiechert.

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