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Electronic Colloquium on Computational Complexity

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All reports by Author Christian Reitwießner:

TR13-047 | 27th March 2013
Christian Glaßer, Dung Nguyen, Christian Reitwießner, Alan Selman, Maximilian Witek

Autoreducibility of Complete Sets for Log-Space and Polynomial-Time Reductions

Comments: 1

We investigate the autoreducibility and mitoticity of complete sets for several classes with respect to different polynomial-time and logarithmic-space reducibility notions.

Previous work in this area focused on polynomial-time reducibility notions. Here we obtain new mitoticity and autoreducibility results for the classes EXP and NEXP with respect to some restricted ... more >>>

TR11-053 | 11th April 2011
Krzysztof Fleszar, Christian Glaßer, Fabian Lipp, Christian Reitwießner, Maximilian Witek

The Complexity of Solving Multiobjective Optimization Problems and its Relation to Multivalued Functions

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.

Some solution notions S ... more >>>

TR10-031 | 4th March 2010
Christian Glaßer, Christian Reitwießner, Heinz Schmitz, Maximilian Witek

Hardness and Approximability in Multi-Objective Optimization

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 multivalued functions, which allows us to compare the solution notions and ... more >>>

TR09-076 | 19th August 2009
Christian Glaßer, Christian Reitwießner, Maximilian Witek

Improved and Derandomized Approximations for Two-Criteria Metric Traveling Salesman

Revisions: 1

We improve and derandomize the best known approximation algorithm for the two-criteria metric traveling salesman problem (2-TSP). More precisely, we construct a deterministic 2-approximation which answers an open question by Manthey.

Moreover, we show that 2-TSP is randomized $(3/2+\epsilon ,2)$-approximable, and we give the first randomized approximations for the two-criteria ... more >>>

TR08-029 | 7th January 2008
Christian Glaßer, Christian Reitwießner, Victor Selivanov

The Shrinking Property for NP and coNP

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results.

1. NP ... more >>>

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