Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey

Details Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey

2011-08-24

arxiv.org/abs/1108.4803v1

Computer Science

Data Structures and Algorithms

Scientific paper

We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above $m/2$: given a CNF formula $F$ with $m$ clauses, decide whether there is a truth assignment that satisfies at least $m/2+k$ clauses, where $k$ is the parameter. Among other problems we deal with are MaxLin2-AA (given a system of linear equations over $\mathbb{F}_2$ in which each equation has a positive integral weight, decide whether there is an assignment to the variables that satisfies equations of total weight at least $W/2+k$, where $W$ is the total weight of all equations), Max-$r$-Lin2-AA (the same as MaxLin2-AA, but each equation has at most $r$ variables, where $r$ is a constant) and Max-$r$-Sat-AA (given a CNF formula $F$ with $m$ clauses in which each clause has at most $r$ literals, decide whether there is a truth assignment satisfying at least $\sum_{i=1}^m(1-2^{r_i})+k$ clauses, where $k$ is the parameter, $r_i$ is the number of literals in Clause $i$, and $r$ is a constant). We also consider Max-$r$-CSP-AA, a natural generalization of both Max-$r$-Lin2-AA and Max-$r$-Sat-AA, order (or, permutation) constraint satisfaction problems of arities 2 and 3 parameterized above the average value and some other problems related to MaxSat. We discuss results, both polynomial kernels and parameterized algorithms, obtained for the problems mainly in the last few years as well as some open questions.

Affiliated with

Also associated with

No associations

Rating

Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377495