Computation Of Optimization Problems Research Articles

Revisiting Decomposition by Clique Separators

We study the complexity of decomposing a graph by means of clique separators. This common algorithmic tool, first introduced by Tarjan, allows one to cut a graph into smaller pieces, and so it can be applied to preprocess the graph in the computation of optimization problems. However, the best-known algorithms for computing a decomposition have respective ${\cal O}(nm)$-time and ${\cal O}(n^{(3+\alpha)/2}) = o(n^{2.69})$-time complexity with $\alpha < 2.3729$ being the exponent for matrix multiplication. Such running times are prohibitive for large graphs. Here we prove that for every graph $G$, a decomposition can be computed in ${\cal O}(T(G) + \min\{n^{\alpha},\omega^2 n\})$-time with $T(G)$ and $\omega$ being, respectively, the time needed to compute a minimal triangulation of $G$ and the clique-number of $G$. In particular, it implies that every graph can be decomposed by clique separators in ${\cal O}(n^{\alpha}\log n)$-time. Based on prior work from Kratsch et al., we prove in addition that decompo...

PARAMETRIC OPTIMIZING ANALYSIS OF UNSTEADY STRUCTURES AND VISUALIZATION OF MULTIDIMENSIONAL DATA

The paper presents an approach to fast approximate estimation of conditions for space-time structures appearing in the flows. The approach is based on combination of optimization problem computation with methods of data visual presentation. The visual presentation methods are applied for analysis of multidimensional array containing discrete result data. Optimization problem solution is implemented by parallel computation in a multitask form. For some cases, the approach allows to obtain for control parameter of considered problem the sought-for approximate dependence on characteristic parameters in a quasi-analytical form.

Specification and computation of optimization problems

In [JOM95] we introduced a specification language, that we call partialorder programming, where we showed that partial-order clauses help render clear and concise formulations to a different kind of problems, in particular optimization problems. We also presented a formal semantics to this language as well as a top-down-procedure to compute the semantics of a large class of programs that we call monotonic. In ∗[OJ97∗] we gave a definition of a semantics for partial-order programs that do not have to be monotonic, and we showed that this semantics is well-behaved [Dix95]. In this paper we discuss some more typical problems that have a simple specification in our language. We briefly compare both approaches.