TR07-137 Authors: Yijia Chen, Jörg Flum, Moritz Müller

Publication: 29th December 2007 02:58

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Among others, refining the methods of [Fortnow and Santhanam, ECCC Report TR07-096] we improve a result of this paper and show for any parameterized problem with a ``linear weak OR'' and with NP-hard underlying classical problem that there is no polynomial reduction from the problem to itself that assigns to every instance $x$ with parameter $k$ an instance $y$ with $|y| = k^{O(1)} \cdot |x|^{1-\epsilon}$ unless the polynomial hierarchy collapses to its third level (here $\epsilon$ is any given real number greater than zero).