Query-Number Preserving Reductions and Linear Lower Bounds for Testing

Yuichi YOSHIDA, Hiro ITO
<span title="">2010</span> <i title="Institute of Electronics, Information and Communications Engineers (IEICE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xosmgvetnbf4zpplikelekmdqe" style="color: black;">IEICE transactions on information and systems</a> </i> &nbsp;
In this paper, we study lower bounds on the query complexity of testing algorithms for various problems. Given an oracle that returns information of an input object, a testing algorithm distinguishes the case that the object has a given property P from the case that it has a large distance to having P with probability at least 2 3 . The query complexity of an algorithm is measured by the number of accesses to the oracle. We introduce two reductions that preserve the query complexity. One is
more &raquo; ... ved from the gap-preserving local reduction and the other is from the L-reduction. By using the former reduction, we show linear lower bounds on the query complexity for testing basic NP-complete properties, i.e., 3edge-colorability, directed Hamiltonian path/cycle, undirected Hamiltonian path/cycle, 3-dimensional matching and NP-complete generalized satisfiability problems. Also, using the second reduction, we show a linear lower bound on the query complexity of approximating the size of the maximum 3-dimensional matching.
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