Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th International Conference on Theory and Applications of Satisfiability Testin

The parameterized complexity of positional games

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows’ influential list of open problems from 1999. Previously, the problem was thought of as a natural candidate for AW[*]-completeness. Our main tool is a new fragment of first-order logic where universally quantified variables only occur in inequalities. We show that model-checking on arbitrary relational structures for a formula in this fragment is W[1]-complete when parameterized by formula size. We also consider a general framework where a positional game is represented as a hypergraph and two players alternately pick vertices. In a Maker-Maker game, the first player to have picked all the vertices of some hyperedge wins the game. In a Maker-Breaker game, the first player wins if she picks all the vertices of some hyperedge, and the second player wins otherwise. In an Enforcer-Avoider game, the first player wins if the second player picks all the vertices of some hyperedge, and the second player wins otherwise. Short Maker-Maker, Short Maker-Breaker, and Short Enforcer-Avoider are respectively AW[*]-, W[1]-, and co-W[1]-complete parameterized by the number of moves. This suggests a rough parameterized complexity categorization into positional games that are complete for the first level of the W-hierarchy when the winning condition only depends on which vertices one player has been able to pick, but AW[*]-complete when it depends on which vertices both players have picked. However, some positional games with highly structured board and winning configurations are fixed-parameter tractable. We give another example of such a game, Short k-Connect, which is fixed-parameter tractable when parameterized by the number of moves

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

Backdoors to q-Horn

The class q-Horn, introduced by Boros, Crama and Hammer in 1990, is one of the largest known classes of propositional CNF formulas for which satisfiability can be decided in polynomial time. This class properly contains the fundamental classes of Horn and Krom formulas as well as the class of renamable (or disguised) Horn formulas. In this paper we extend this class so that its favorable algorithmic properties can be made accessible to formulas that are outside but "close"\u27 to this class. We show that deciding satisfiability is fixed-parameter tractable parameterized by the distance of the given formula from q-Horn. The distance is measured by the smallest number of variables that we need to delete from the formula in order to get a q-Horn formula, i.e., the size of a smallest deletion backdoor set into the class q-Horn. This result generalizes known fixed-parameter tractability results for satisfiability decision with respect to the parameters distance from Horn, Krom, and renamable Horn

On the Two q-Analogue Logarithmic Functions

There is a simple, multi-sheet Riemann surface associated with e_q(z)'s inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be defined. However, the topology of the Riemann surface for ln_q(w) changes each time "q" increases above the collision point of a pair of the turning points of e_q(x). There is also a power series representation for ln_q(1+w). An infinite-product representation for e_q(z) is used to obtain the ordinary natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power series in terms of values of these sum rules. The values of the sum rules for the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General. Some explict formulas added, and to update the reference

MODEL PENGGUNAAN LAHAN DAN PERUBAHAN PENGGUNAAN LAHAN UNTUK BAHAN BAKU BIODISEL KELAPA SAWIT: STUDI KASUS DI KABUPATEN ROKAN HILIR

Land use and land use change for palm oil plantation is having both positive and negative influence to the increase of CO2 emission. This research was intended to (1) Analyze land use change in such case of Rokan Hilir district between the year of 2009 and 2011; (2) Measure CO2 emission that produced by land use change for palm oil plantation, and (3) Designing a model of land use and land use change in order to minimize CO2 emission. Land use change was identified using GIS based analysis, while CO2 emission was measured by using IPCC 2006 method. The model of land use change was established through the method of Genetic Algorithm. The result of the research shows that net CO2 emission that produced during the year of 2009 to 2011 in Rokan Hilir district was 0.89 Mt/year. The additional area of 676 Ha for biodiesel feedsctock of palm oil was came from 169 gens of 13x13 matrix where produced negative emission value (carbon sequestration) of 0.067 Mt CO2e/year. This emission can be reduced significantly by changing land use as calculated using the model of land use change that developed is this research, where as the number of emission then will be 0.82 Mt CO2e/year.Keywords: carbon stock, CO2 emission, land use and land use change, palm oil, genetic algorith

Archaeological memory and urban morphology: the republican model in the imperial E42

The idea that the modern city should rise on a tabula rasa of the ancient city has been promoted since the Plan Voisin (Lecorbusier, 1925), and was essentially conceived on the ideology of the destruction of the ancienne regime, or to better say the destruction of its space, as a base to build a new world. Nowadays we recognize that demolitions of urban fabric inside historical cities are not conceivable, they were accomplished mostly by absolutist regimes or war bombings, upholding in substance the very same effect. Therefore we should reconsider critically the foundation of the E42 in Rome (1941), shown by fascist propaganda as a modern foundation, but planned outside the city centre. Even though meaningful demolitions were accomplished inside the monumental area of the Roman forums in the ‘30, in a very subtle manner, the archaeological topography of the ancient republican Rome became part of the new E42. The foundation was based on analogous orientations, in relationship with the foundation day of ancient Rome. Form and meaning of architectures, recalling the memory urban parts of ancient Rome, were used as archetypes to symbolize the past glory of Rome. This study presents the comparative analysis of the Palace of Receptions and Congresses (Adalberto Libera, 1938) and of the Temple of Venus and Rome (Hadrian, 121 ad), analyzing the city through models, proposing a new interpretation of the E42 as an analogous city. This comparative analysis recognizes in the plan elements of non-immediate perception, tracing a key to understand the meaning of the spaces of the city.Publisher versio

Separate, measure and conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, such as Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for an improved running time analysis. We illustrate the method with improved algorithms for Max (r,2) -CSP and #Dominating Set. For Max (r,2) -CSP instances with domain size r and m constraints, the running time improves from r m/6 to r m/7.5 for cubic instances and from r 0.19⋅m to r 0.18⋅m for general instances, omitting subexponential factors. For #Dominating Set instances with n vertices, the running time improves from 1.4143 n to 1.2458 n for cubic instances and from 1.5673 n to 1.5183 n for general instances. It is likely that other algorithms relying on local transformations can be improved using our method, which exploits a non-local property of graphs