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- Christian Glaßer, Christian Reitwießner, Maximilian Witek
- FSTTCS
- 2011

We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1 /2-approximable on directed graphs and randomized 2 /3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiabilty problem is 1 /2-approximable. 1 Introduction We… (More)

We study the approximability and the hardness of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). Our contributions are: – We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions. – These solution notions induce corresponding NP-hardness notions for… (More)

- Christian Glaßer, Dung T. Nguyen, Christian Reitwießner, Alan L. Selman, Maximilian Witek
- Electronic Colloquium on Computational Complexity
- 2013

- Christian Glaßer, Christian Reitwießner, Maximilian Witek
- Electronic Colloquium on Computational Complexity
- 2009

We improve and derandomize the best known approximation algorithm for the two-criteria metric traveling salesman problem (2-TSP). More precisely, we construct a deter-ministic 2-approximation which answers an open question by Manthey. Moreover, we show that 2-TSP is randomized (3 /2 + ε, 2)-approximable, and we give the first randomized approximations for… (More)

- Christian Glaßer, Christian Reitwießner, Heinz Schmitz, Maximilian Witek
- Electronic Colloquium on Computational Complexity
- 2010

We systematically study the hardness and the approximability of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). We define solution notions that precisely capture the typical algorithmic tasks in multi-objective optimization. These notions inherit polynomial-time Turing reducibility from mul-tivalued functions,… (More)

- Christian Glaßer, Maximilian Witek
- Electronic Colloquium on Computational Complexity
- 2013

We study the autoreducibility and mitoticity of complete sets for NP and other complexity classes, where the main focus is on logspace reducibilities. In particular, we obtain:

For every list of integers x 1 ,. .. , x m there is some j such that x 1 + · · · + x j − x j+1 − · · · − x m ≈ 0. So the list can be nearly balanced and for this we only need one alternation between addition and subtraction. But what if the x i are k-dimensional integer vectors? Using results from topological degree theory we show that balancing is still… (More)

We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1 /2-approximable on directed graphs and randomized 2 /3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1 /2-approximable.

- Krzysztof Fleszar, Christian Glaßer, Fabian Lipp, Christian Reitwießner, Maximilian Witek
- Electronic Colloquium on Computational Complexity
- 2011

Instances of optimization problems with multiple objectives can have several optimal solutions whose cost vectors are incomparable. This ambiguity leads to several reasonable notions for solving multiobjective problems. Each such notion defines a class of multivalued functions. We systematically investigate the computational complexity of these classes.… (More)