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<item>
  <id>02245463</id>
  <dt>j</dt>
  <an>02245463</an>
  <augroup>
    <au>Stearns, Richard E.</au>
    <au>Hunt, Harry B.III</au>
  </augroup>
  <ti>Resource bounds and subproblem independence.</ti>
  <so>Theory Comput. Syst. 38, No. 6, 731-761 (2005).</so>
  <py>2005</py>
  <pu>Springer-Verlag, New York, NY</pu>
  <lagroup>
    <la>EN</la>
  </lagroup>
  <ccgroup>
  </ccgroup>
  <utgroup>
    <ut>$q$-linear functions</ut>
  </utgroup>
  <cigroup>
  </cigroup>
  <ligroup>
    <li>doi:10.1007/s00224-004-1160-8</li>
  </ligroup>
  <abgroup>
    <ab>Summary: There are several reasons why some NP-hard problems can be solved deterministically in $2^{O(n^a)}$ time for some $a$, $0<a<1$. One reason is that the problem can be solved with a nondeterministic procedure which uses only $O(n^a)$ space. A second reason is that each instance of the problem exhibits a high degree of ``subproblem independence" (specifically $O(n^a)$ line channelwidth or treewidth). A third is that each instance of the problem can be solved using nondeterministic straight-line programs where the number of variables is only $O(n^a)$. In this paper we show that, after imposing $q$-linear bounds on the computation time and obliviousness constraints on the nondeterminism, these three reasons are essentially equivalent. ($q$-linear functions are similar to functions of the form $n(\log n)^k$.) Specifically, the problem classes associated with these reasons are interchangeable using reductions which are simultaneously polynomial time and $q$-linear size-bounded. We call these PQ-reductions. The classes of problems solvable by these methods we call $\text{NQ}n^{a}$. Because these classes are defined in a very general way, they include a rich variety of problems. We take this as evidence that these classes have ``power index" $a$ (i.e., that $2^{O(n^a)}$ is also a lower time bound). On the other hand, the easiness of all these problems can be derived from ``subproblem independence" considerations, and thus the techniques associated with subproblem independence are seen to be more widely applicable than one might expect.</ab>
    <rv></rv>
  </abgroup>
</item>