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Electronic Colloquium on Computational Complexity

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Reports tagged with polynomial time:
TR96-011 | 29th January 1996
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 >>>

TR98-026 | 5th May 1998
Richard Beigel

Gaps in Bounded Query Hierarchies

Prior results show that most bounded query hierarchies cannot
contain finite gaps. For example, it is known that
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>
and for all sets <i>A</i>
<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> 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> = ... more >>>

TR99-041 | 22nd August 1999
Oliver Kullmann

Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs

Revisions: 2

A 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 ... more >>>

TR00-018 | 16th February 2000
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 >>>

TR01-097 | 11th December 2001
Piotr Berman, Marek Karpinski

Improved Approximations for General Minimum Cost Scheduling

We give improved trade-off results on approximating general
minimum cost scheduling problems.

more >>>

TR07-067 | 22nd May 2007
Paul Spirakis, haralampos tsaknakis

Computing 1/3-approximate Nash equilibria of bimatrix games in polynomial time.

Revisions: 2

In 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 >>>

TR07-095 | 13th July 2007
Vikraman Arvind, Partha Mukhopadhyay

The Ideal Membership Problem and Polynomial Identity Testing

Revisions: 2

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.
\item[(a)] If the ideal $I=\angle{m_1,m_2,\cdots,m_k}$ for a
more >>>

TR12-176 | 14th December 2012
Marek Karpinski, Andrzej Lingas, Dzmitry Sledneu

Optimal Cuts and Partitions in Tree Metrics in Polynomial Time

We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one dimensional geometric metric settings. Our method of solution could be also of independent interest ... more >>>

TR17-016 | 31st January 2017
Vishwas Bhargava, Gábor Ivanyos, Rajat Mittal, Nitin Saxena

Irreducibility and deterministic r-th root finding over finite fields

Constructing $r$-th nonresidue over a finite field is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree $r^e$ (where $r$ is a prime) over a given finite field $\F_q$ of characteristic $p$ (equivalently, constructing the bigger field $\F_{q^{r^e}}$). Both these problems have famous randomized ... more >>>

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