Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Polynomial Delay Algorithm for Listing Minimal Edge Dominating sets in Graphs

The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open problem, and up to now there are few examples of hypergraph classes where the problem is solved. A minimal dominating set in a graph is a subset of its vertex set that has a non empty intersection with the closed neighborhood of every vertex. It is proved in [M. M. Kant\'e, V. Limouzy, A. Mary, L. Nourine, On the Enumeration of Minimal Dominating Sets and Related Notions, In Revision 2014] that the enumeration of minimal dominating sets in graphs and the enumeration of minimal transversals in hypergraphs are two equivalent problems. Hoping this equivalence can help to get new insights in the Transversal problem, it is natural to look inside graph classes. It is proved independently and with different techniques in [Golovach et al. - ICALP 2013] and [Kant\'e et al. - ISAAC 2012] that minimal edge dominating sets in graphs (i.e, minimal dominating sets in line graphs) can be enumerated in incremental output-polynomial time. We provide the first polynomial delay and polynomial space algorithm that lists all the minimal edge dominating sets in graphs, answering an open problem of [Golovach et al. - ICALP 2013]. Besides the result, we hope the used techniques that are a mix of a modification of the well-known Berge's algorithm and a strong use of the structure of line graphs, are of great interest and could be used to get new output-polynomial time algorithms.Comment: proofs simplified from previous version, 12 pages, 2 figure

Beyond Hypergraph Dualization

International audienceThis problem concerns hypergraph dualization and generalization to poset dualization. A hypergraph H = (V, E) consists of a finite collection E of sets over a finite set V , i.e. E ⊆ P(V) (the powerset of V). The elements of E are called hyperedges, or simply edges. A hypergraph is said simple if none of its edges is contained within another. A transversal (or hitting set) of H is a set T ⊆ V that intersects every edge of E. A transversal is minimal if it does not contain any other transversal as a subset. The set of all minimal transversal of H is denoted by T r(H). The hypergraph (V, T r(H)) is called the transversal hypergraph of H. Given a simple hypergraph H, the hypergraph dualization problem (Trans-Enum for short) concerns the enumeration without repetitions of T r(H). The Trans-Enum problem can also be formulated as a dualization problem in posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric, and transitive relation on the set P). For A ⊆ P , ↓ A (resp. ↑ A) is the downward (resp. upward) closure of A under the relation ≤ (i.e. ↓ A is an ideal and ↑ A a filter of (P, ≤)). Two antichains (B + , B −) of P are said to be dual if ↓ B + ∪ ↑ B − = P and ↓ B + ∩ ↑ B − = ∅. Given an implicit description of a poset P and an antichain B + (resp. B −) of P , the poset dualization problem (Dual-Enum for short) enumerates the set B − (resp. B +), denoted by Dual(B +) = B − (resp. Dual(B −) = B +). Notice that the function dual is self-dual or idempotent, i.e. Dual(Dual(B)) = B

Экономическая целесообразность реализации проектов в ОАО «Новосибирскнефтегаз»

В процессе исследования проводилась оценка экономической целесообразности реализации инвестиционных проектов нефтесервисной компанией ОАО "Новосибирскнефтегаз". В результате написания магистерский диссертации проводилась оценка инвестиционных проектов, реализованных ОАО "ННГ" с использованием различных методов определения эффективности проектов, в результате выявления наиболее эффективного инвестиционного проекта.In the course of the research, the economic feasibility of implementing investment projects was evaluated by the oilfield services company Novosibirskneftegaz. As a result of writing the master's thesis, an evaluation of investment projects implemented by NNG was carried out using various methods of determining the effectiveness of projects, as a result of identifying the most effective investment project

GRS 1915+105 : High-energy Insights with SPI/INTEGRAL

We report on results of two years of INTEGRAL/SPI monitoring of the Galactic microquasar GRS 1915+105. From September 2004 to May 2006, the source has been observed twenty times with long (approx 100 ks) exposures. We present an analysis of the SPI data and focus on the description of the high-energy (> 20 keV) output of the source. We found that the 20 - 500 keV spectral emission of GRS 1915+105 was bound between two states. It seems that these high-energy states are not correlated with the temporal behavior of the source, suggesting that there is no direct link between the macroscopic characteristics of the coronal plasma and the the variability of the accretion flow. All spectra are well fitted by a thermal comptonization component plus an extra high-energy powerlaw. This confirms the presence of thermal and non-thermal electrons around the black hole.Comment: 7 pages, 8 figures, 2 tables; accepted (09/11/2008) for publication in A&

An Efficient Implementation of a Quasi-polynomial Algorithm for Generating Hypergraph Transversals

Given a finite set V, and a hypergraph , the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for . This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan (1996) gave an incremental quasi-polynomial time algorithm for solving the hypergraph transversal problem [9]. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same bound on the running time as in [9], practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the algorithm in [9] can be used to give a stronger bound on the running time

Comparing energy system optimization models and integrated assessment models: Relevance for energy policy advice

Background: The transition to a climate neutral society such as that envisaged in the European Union Green Deal requires careful and comprehensive planning. Integrated assessment models (IAMs) and energy system optimisation models (ESOMs) are both commonly used for policy advice and in the process of policy design. In Europe, a vast landscape of these models has emerged and both kinds of models have been part of numerous model comparison and model linking exercises. However, IAMs and ESOMs have rarely been compared or linked with one another. Methods: This study conducts an explorative comparison and identifies possible flows of information between 11 of the integrated assessment and energy system models in the European Climate and Energy Modelling Forum. The study identifies and compares regional aggregations and commonly reported variables. We define harmonised regions and a subset of shared result variables that enable the comparison of scenario results across the models. Results: The results highlight how power generation and demand development are related and driven by regional and sectoral drivers. They also show that demand developments like for hydrogen can be linked with power generation potentials such as onshore wind power. Lastly, the results show that the role of nuclear power is related to the availability of wind resources. Conclusions: This comparison and analysis of modelling results across model type boundaries provides modellers and policymakers with a better understanding of how to interpret both IAM and ESOM results. It also highlights the need for community standards for region definitions and information about reported variables to facilitate future comparisons of this kind. The comparison shows that regional aggregations might conceal differences within regions that are potentially of interest for national policy makers thereby indicating a need for national-level analysis

Increasing the Operation Efficiency of Air Conditioning System for Integrated Power Plant on the Base of Its Monitoring

Increasing the Operation Efficiency of Air Conditioning System for Integrated Power Plant on the Base of Its Monitoring / E. Trushliakov, A. Radchenko, S. Forduy, A. Zubarev, A. Hrych // Advances in intelligent systems and computing. – 2020. – Т. 1113 AISC . – P. 351–360Abstract. The efficiency of reciprocating gas engines of integrated energy systems (IES) for combined electricity, heat and refrigeration generation is strictly influenced by their cyclic air temperatures. To evaluate the effect of gas engine cyclic air deep cooling, compared with conventional its cooling, the data on dependence of fuel consumption and power output of gas engine JMS 420 GS-N.L on its inlet air temperature at varying ambient air temperatures at the entrance of the radiator for scavenge air cooling were received. The results of treatment of gas engine efficiency monitoring proved non-effective operation of conventional chilling all the ambient air, coming into the engine room, because of increased air temperature at the inlet of turbocharger (TC), caused by heat influx from surroundings in the engine room. A new method of gas engine inlet air two-stage cooling at increased ambient air temperatures and advanced cyclic air cooling system with absorption lithium-bromide chiller and refrigerant ejector chiller was proposed. With this chilled water from absorption lithiumbromide chiller is used as a coolant in the first high-temperature stage of engine inlet air cooler and boiling refrigerant of ejector chiller in the second lowtemperature stage