We show that the parameterized problem Perfect Code belongs to W[1]. This result closes an old open question, because it was often conjectured that Perfect ...

Jul 20, 2000 · This paper solves the question of the precise degree of parameterized complexity of the PerFect Code problem : we show that it belongs to W[1], ...

We show that the parameterized problem PERFECT CODE belongs to W[1]. This result closes an old open question, because it was often conjectured that PERFECT ...

Oct 22, 2024 · The problem k-PERFECT CODE is that of deciding whether a given graph G has a perfect code of size exactly k. The problem k-PERFECT CODE is W[1]- ...

Jan 22, 2019 · First, [math]W-[/math]hierarchy problems are different from [math]NP-[/math]complete problems. They are different kind of 'problems'.

Jul 21, 2021 · If P=NP, then there is polynomial time algorithm for the W[1]-complete problem k-Clique, so FPT=W[1]. Taking the contrapositive, we get that FPT ...

Proof. We show that Condorcet-CC-AV is W[1]-hard by a FPT-reduction from W[1]-complete parameterized Perfect Code.

PERFECT CODE is hard for W[1]. Proof. We reduce from INDEPENDENT SET. Let G = (V,E) be a graph. We show how to produce a graph H = (V 0,E0) that has a ...

Mar 15, 1998 · The proof of W[1]-hardness is based on a parametric polynomial-time reduction from the Perfect Code problem for graphs. Such a proof estab-.

Nov 6, 2015 · Note that the distance of this code is 2e+1: two codewords belong to two different "balls", and each ball is of radius e (in Hamming distance).