REPORTS > KEYWORD > POLYNOMIAL TIME:
Stephen A. Bloch, Jonathan F. Buss, Judy Goldsmith
Sharply Bounded Alternation within P
We define the sharply bounded hierarchy, SBHQL, a hierarchy of
classes within P, using quasilinear-time computation and
quantification over values of length log n. It generalizes the
limited nondeterminism hierarchy introduced by Buss and Goldsmith,
while retaining the invariance properties. The new hierarchy has
several alternative characterizations.
We define ... more >>>
Richard Beigel
Gaps in Bounded Query Hierarchies
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Prior results show that most bounded query hierarchies cannot
contain finite gaps. For example, it is known that
<center>
P<sub>(<i>m</i>+1)-tt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup> implies P<sub>btt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup>
</center>
and for all sets <i>A</i>
<ul>
<li> FP<sub>(<i>m</i>+1)-tt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup> implies FP<sub>btt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup>
</li>
<li> P<sub>(<i>m</i>+1)-T</sub><sup><i>A</i></sup> = P<sub><i>m</i>-T</sub><sup><i>A</i></sup> implies P<sub>bT</sub><sup><i>A</i></sup> = ...
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Oliver Kullmann
Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs
Revisions: 2A relativized hierarchy of conjunctive normal forms
is introduced, recognizable and SAT decidable in polynomial
time. The corresponding hardness parameter, the first level
of inclusion in the hierarchy, is studied in detail, admitting
several characterizations, e.g., using pebble games, the space
complexity of (relativized) tree-like ...
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Oliver Kullmann
An application of matroid theory to the SAT problem
A basic property of minimally unsatisfiable clause-sets F is that
c(F) >= n(F) + 1 holds, where c(F) is the number of clauses, and
n(F) the number of variables. Let MUSAT(k) be the class of minimally
unsatisfiable clause-sets F with c(F) <= n(F) + k.
Poly-time decision algorithms are known ... more >>>
Piotr Berman, Marek Karpinski
Improved Approximations for General Minimum Cost Scheduling
We give improved trade-off results on approximating general
minimum cost scheduling problems.
Paul Spirakis, haralampos tsaknakis
Computing 1/3-approximate Nash equilibria of bimatrix games in polynomial time.
Revisions: 2In this paper we propose a methodology for determining approximate Nash equilibria of non-cooperative bimatrix games and, based on that, we provide a polynomial time algorithm that computes $\frac{1}{3} + \frac{1}{p(n)} $ -approximate equilibria, where $p(n)$ is a polynomial controlled by our algorithm and proportional to its running time. The ... more >>>
Vikraman Arvind, Partha Mukhopadhyay
The Ideal Membership Problem and Polynomial Identity Testing
Revisions: 2\begin{abstract}
Given a monomial ideal $I=\angle{m_1,m_2,\cdots,m_k}$ where $m_i$
are monomials and a polynomial $f$ as an arithmetic circuit the
\emph{Ideal Membership Problem } is to test if $f\in I$. We study
this problem and show the following results.
\begin{itemize}
\item[(a)] If the ideal $I=\angle{m_1,m_2,\cdots,m_k}$ for a
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