Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Approximability of the Minimum Test Collection Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Theoretical Computer Science
Journal of Computer and System Sciences
Solving MAX-r-SAT Above a Tight Lower Bound
Algorithmica
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Systems of linear equations over F2 and problems parameterized above average
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Parameterized Complexity
(Non-)existence of polynomial kernels for the Test Cover problem
Information Processing Letters
Hi-index | 0.00 |
In this paper we carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the Test Cover problem we are given a set [n]={1,…,n} of items together with a collection, $\cal T$, of distinct subsets of these items called tests. We assume that $\cal T$ is a test cover, i.e., for each pair of items there is a test in $\cal T$ containing exactly one of these items. The objective is to find a minimum size subcollection of $\cal T$, which is still a test cover. The generic parameterized version of Test Cover is denoted by $p(k,n,|{\cal T}|)$-Test Cover. Here, we are given $([n],\cal{T})$ and a positive integer parameter k as input and the objective is to decide whether there is a test cover of size at most $p(k,n,|{\cal T}|)$. We study four parameterizations for Test Cover and obtain the following: (a) k-Test Cover, and (n−k)-Test Cover are fixed-parameter tractable (FPT), i.e., these problems can be solved by algorithms of runtime $f(k)\cdot poly(n,|{\cal T}|)$, where f(k) is a function of k only. (b) $(|{\cal T}|-k)$-Test Cover and (logn+k)-Test Cover are W[1]-hard. Thus, it is unlikely that these problems are FPT.