26 research outputs found
On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems
We show improved NP-hardness of approximating Ordering Constraint
Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum
Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of
and .
An OCSP is said to be approximation resistant if it is hard to approximate
better than taking a uniformly random ordering. We prove that the Maximum
Non-Betweenness Problem is approximation resistant and that there are width-
approximation-resistant OCSPs accepting only a fraction of
assignments. These results provide the first examples of
approximation-resistant OCSPs subject only to P \NP
On Solving the Maximum Betweenness Problem Using Genetic Algorithms
In this paper a genetic algorithm (GA) is applied on Maximum
Betweennes Problem (MBP). The maximum of the objective function is
obtained by finding a permutation which satisfies a maximal number of
betweenness constraints. Every permutation considered is genetically coded
with an integer representation. Standard operators are used in the GA.
Instances in the experimental results are randomly generated. For smaller
dimensions, optimal solutions of MBP are obtained by total enumeration.
For those instances, the GA reached all optimal solutions except one. The
GA also obtained results for larger instances of up to 50 elements and 1000
triples. The running time of execution and finding optimal results is quite
short
Variations on an ordering theme with constraints
We investigate the problem of nding a total order of a nite set that satis es various local ordering constraints. Depending on the admitted constraints, we provide an e cient algorithm or prove NP-completeness. We discuss several generalisations and systematically classify the problems4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI
Learning Lines with Ordinal Constraints
We study the problem of finding a mapping f from a set of points into the real line, under ordinal triple constraints. An ordinal constraint for a triple of points (u,v,w) asserts that |f(u)-f(v)| < |f(u)-f(w)|. We present an approximation algorithm for the dense case of this problem. Given an instance that admits a solution that satisfies (1-?)-fraction of all constraints, our algorithm computes a solution that satisfies (1-O(?^{1/8}))-fraction of all constraints, in time O(n?) + (1/?)^{O(1/?^{1/8})} n