Jochen Alber, Henning Fernau, Rolf Niedermeier

A parameterized problem is called fixed parameter tractable

if it admits a solving algorithm whose running time on

input instance $(I,k)$ is $f(k) \cdot |I|^\alpha$, where $f$

is an arbitrary function depending only on~$k$. Typically,

$f$ is some exponential function, e.g., $f(k)=c^k$ for ...
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Oliver Kullmann

We consider the next step from boolean conjunctive normal forms to

arbitrary constraint satisfaction problems (with arbitrary constraints), namely "generalised clause-sets" (or "sets of no-goods"), which allow negative literals "v <> e" for variables v and values e --- this level of generality appears to be the right level for ...
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Vikraman Arvind, Bireswar Das, Johannes Köbler, Seinosuke Toda

We describe a fixed parameter tractable (fpt) algorithm for Colored Hypergraph Isomorphism} which has running time $b!2^{O(b)}N^{O(1)}$, where the parameter $b$ is the maximum size of the color classes of the given hypergraphs and $N$ is the input size. We also describe fpt algorithms for certain permutation group problems that ... more >>>

Subhash Khot, Igor Shinkar

In the $Gap-clique(k, \frac{k}{2})$ problem, the input is an $n$-vertex graph $G$, and the goal is to decide whether $G$ contains a clique of size $k$ or contains no clique of size $\frac{k}{2}$. It is an open question in the study of fixed parameterized tractability whether the $Gap-clique(k, \frac{k}{2})$ problem ... more >>>

Thomas O'Neil

A symmetric representation for a set of objects requires the same amount of space for the set as for its complement. Complexity classifications that are based on the length of the input can depend on whether the representation is symmetric. In this article we describe a symmetric representation scheme for ... more >>>

Vikraman Arvind, Venkatesan Guruswami

We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the Union-of-Subspace Avoidance (USA) problem), and finding a common zero of a system of ... more >>>