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Parameterized Complexity
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This paper deals with the Max-Rep and Min-Rep problems, both of which are related to the famous Label Cover problem. These are of notable theoretical interest, since they are often used to prove hardness results for other problems. In many cases new complexity results for these problems may be preserved by the reductions, and so new results for Max-Rep and Min-Rep could be applicable to a wide range of other problems as well. Both Max-and Min-Rep are strongly inapproximable, and the best approximation algorithms have a ratio of O(n1/3) and O(n1/3 log2/3 n) respectively. Thus, other approaches are desperately needed to tackle these hard problems. In our paper we use the very successful parameterized complexity paradigm and obtain new complexity results for various parameterizations of the problems.