Multigrid solver for axisymmetrical 2D fluid equations

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of the multigrid method with respect to the number of grid points allowed us to use $256\times 256$ grid, where we could achieve solutions in several minutes. Time limitations due to nonlinearity of the system are partially avoided by using multi level grids(the initial solution on $256\times 256$ grid was extrapolated steady solution from $128\times 128$ grid which allowed using "long" integration time steps). The fluid solver may be used as the basis for hybrid codes for DC discharges.Comment: preliminary version; presented at 28 ICPIG, July 15-20, 2007, Prague, Czech Republi

Branching and treewidth based exact algorithms

Abstract. Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of exact (exponential time) algorithms for NP hard problems. In this paper we discuss the eÆciency of simple algorithms based on combinations of these techniques. We give several examples of possible combinations of branching and programming which provide the fastest known algorithms for a number of NP hard problems: M�Ò�ÑÙÑ M�Ü�Ñ�Ð M�Ø ��Ò � and some variations, counting the number of maximum weighted independent sets. We also briefly discuss how similar techniques can be used to design parameterized algorithms. As an example, we give fastest known algorithm solving k-W����Ø� � V�ÖØ�Ü CÓÚ�Ö problem.

On the Parameterized Complexity Of Exact Satisfiability Problems

For many problems, the investigation of their parameterized complexity provides an interesting and useful point of view. The most obvious natural parameterization for the maximum satisfiability problem---the number of satisfiable clauses---makes little sense, because at least half of the clauses can be satisfied in any formula. We look at two optimization variants of the exact satisfiability problem, where a clause is only said to be fulfilled iff exactly one of its literals is set to true. Interestingly, these variants behave quite di#erently. In the case of ResMaxExactSAT, where over-satisfied clauses are entirely forbidden, we show fixed parameter tractability. On the other hand, if we choose to ignore over-satisfied clauses, the MaxExactSAT problem is obtained. Surprisingly