In this paper we prove, that the problem ”kdim(G) ≤ 3” is polynomially solvable for chordal graphs, thus partially solving the problem of P. Hlineny and J. Kratochvil. We show, that the problem of finding m-krausz dimension is NP-hard for every m ≥ 1, even if restricted to (1,2)-colorable graphs, but the problem ”kdimm(G) ≤ k” is polynomially solvable for (∞, 1)-polar graphs for every fixed k,m...

In this note, we point out two major errors in the paper “Minimizing total tardiness on parallel machines with preemptions” by Kravchenko and Werner [2010]. More precisely, they proved that both problems P |pmtn| ∑ Tj and P |rj , pj = p, pmtn| ∑ Tj are NP-Hard. We give a counterexample to their proofs, letting the complexity of these two problems open.

Remark 1. One may wonder why Impagliazzo’s hard core lemma (see the previous lecture for the lemma statement) is not enough to get a 12 −2 −δn-hard function starting with a 2−δn-hard function. The difficulty lies in the fact that the hard core lemma only tells about the existence of a hard core set such that on that set f is 1 2 − 2 −δn -hard. We do not know how to sample from that hard core se...

From 07/02/10 to 12/02/10, the Dagstuhl Seminar 10061 Circuits, Logic, and Games was held in Schloss Dagstuhl Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in thi...

Zimand [24] presented simple constructions of locally computable strong extractors whose analysis relies on the direct product theorem for one-way functions and on the Blum-Micali-Yao generator. For N -bit sources of entropy γN , his extractor has seed O(logN) and extracts N random bits. We show that his construction can be analyzed based solely on the direct product theorem for general functio...

Recent work has demonstrated that it is possible to boost the efficiency of combinatorial search procedures via the use of principled restart policies. We present a coupling of machine learning and dynamic programming that extends prior efforts by endowing restart policies with knowledge of the hardness of the specific instance being solved. This ability allows a restart policy to take into con...

This article accompanies the talk given by the author at the International Congress of Mathematicians, 2014. The article sketches some connections between approximability of NP-complete problems, analysis and geometry, and the role played by the Unique Games Conjecture in facilitating these connections. For a more extensive introduction to the topic, the reader is referred to survey articles [3...

statement of problem: there are controversial reports regarding physical and mechanical properties of resin composites and glass ionomer cements. some revealed higher strength and hardness for resin composites while others showed a comparable value for glass ionomer cements. evaluation of mechanical properties of different types of resin composites in comparison with resin modified glass ionome...