scholarly journals The subset sum game revisited

2021 ◽  
Author(s):  
Astrid Pieterse ◽  
Gerhard J. Woeginger
Keyword(s):  
Weak Sense ◽  
Constant Factor ◽  
The Other ◽  
Total Weight ◽  
Subset Sum ◽  
Common Resource ◽  
Game Theoretic ◽  
Np Complete ◽  
Polynomially Solvable ◽  
Solvable Problems

AbstractWe discuss a game theoretic variant of the subset sum problem, in which two players compete for a common resource represented by a knapsack. Each player owns a private set of items, players pack items alternately, and each player either wants to maximize the total weight of his own items packed into the knapsack or to minimize the total weight of the items of the other player. We show that finding the best packing strategy against a hostile or a selfish adversary is PSPACE-complete, and that against these adversaries the optimal reachable item weight for a player cannot be approximated within any constant factor (unless P=NP). The game becomes easier when the adversary is short-sighted and plays greedily: finding the best packing strategy against a greedy adversary is NP-complete in the weak sense. This variant forms one of the rare examples of pseudo-polynomially solvable problems that have a PTAS, but do not allow an FPTAS (unless P=NP).

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

scholarly journals Statistical mechanics of an NP-complete problem: subset sum

2001 ◽  
Vol 34 (44) ◽  
pp. 9555-9567 ◽  
Author(s):  
Tomohiro Sasamoto ◽  
Taro Toyoizumi ◽  
Hidetoshi Nishimori
Keyword(s):  
Statistical Mechanics ◽  
Complete Problem ◽  
Subset Sum ◽  
Np Complete

scholarly journals Variation of MODIS reflectance and vegetation indices with viewing geometry and soybean development

2012 ◽  
Vol 84 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Fábio M. Breunig ◽  
Lênio S. Galvão ◽  
Antônio R. Formaggio ◽  
José C.N. Epiphanio
Keyword(s):  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Vegetation Indices ◽  
Constant Factor ◽  
The Other ◽  
Large Field ◽  
Phenological Stages ◽  
Water Index ◽  
Growing Seasons ◽  
Moderate Resolution Imaging Spectroradiometer

Directional effects introduce a variability in reflectance and vegetation index determination, especially when large field-of-view sensors are used (e.g., Moderate Resolution Imaging Spectroradiometer - MODIS). In this study, we evaluated directional effects on MODIS reflectance and four vegetation indices (Normalized Difference Vegetation Index - NDVI; Enhanced Vegetation Index - EVI; Normalized Difference Water Index - NDWI1640 and NDWI2120) with the soybean development in two growing seasons (2004-2005 and 2005-2006). To keep the reproductive stage for a given cultivar as a constant factor while varying viewing geometry, pairs of images obtained in close dates and opposite view angles were analyzed. By using a non-parametric statistics with bootstrapping and by normalizing these indices for angular differences among viewing directions, their sensitivities to directional effects were studied. Results showed that the variation in MODIS reflectance between consecutive phenological stages was generally smaller than that resultant from viewing geometry for closed canopies. The contrary was observed for incomplete canopies. The reflectance of the first seven MODIS bands was higher in the backscattering. Except for the EVI, the other vegetation indices had larger values in the forward scattering direction. Directional effects decreased with canopy closure. The NDVI was lesser affected by directional effects than the other indices, presenting the smallest differences between viewing directions for fixed phenological stages.

scholarly journals The principal magnetic susceptibilities of neodymium sulphate octahydrate at low temperatures

1939 ◽  
Vol 170 (941) ◽  
pp. 266-271 ◽  
Keyword(s):  
Low Temperatures ◽  
Room Temperature ◽  
Energy Levels ◽  
Constant Factor ◽  
The Other ◽  
Crystalline Field ◽  
Cubic Symmetry ◽  
The Subject ◽  
The Difference ◽  
The One

The magnetic and other related properties of neodymium sulphate have been the subject of numerous investigations in recent years, but there is still a remarkable conflict of evidence on all the essential points. The two available determinations of the susceptibility of the powdered salt at low temperatures, those of Gorter and de Haas (1931) from 290 to 14° K and of Selwood (1933) from 343 to 83° K both fit the expression X ( T + 45) = constant over the range of temperature common to both, but the constants are not the same and the susceptibilities at room temperature differ by 11%. The fact that the two sets of results can be converted the one into the other by multiplying throughout by a constant factor suggested that the difference in the observed susceptibilities was due to some error of calibration. It could, however, also be due to the different purity of the samples examined though the explanation of the occurrence of the constant factor is then by no means obvious. From their analysis of the absorption spectrum of crystals of neodymium sulphate octahydrate Spedding and others (1937) conclude that the crystalline field around the Nd+++ ion is predominantly cubic in character since they find three energy levels at 0, 77 and 260 cm. -1 .* Calculations of the susceptibility from these levels reproduce Selwood’s value at room temperature but give no agreement with the observations-at other temperatures. On the other hand, Penney and Schlapp (1932) have shown that Gorter and de Haas’s results fit well on the curve calculated for a crystalline field of cubic symmetry and such a strength that the resultant three levels lie at 0, 238 and 834 cm. -1 , an overall spacing almost three times as great as Spedding’s.

scholarly journals Game Theoretic Approaches to Weight Assignments in Data Envelopment Analysis Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Satoru Sekine ◽  
Jing Fu ◽  
Shigeo Muto
Keyword(s):  
Data Envelopment Analysis ◽  
Total Weight ◽  
Data Envelopment ◽  
Alternative Scheme ◽  
Game Theoretic ◽  
Divisible Goods

This paper deals with the problem of fairly allocating a certain amount of divisible goods or burdens among individuals or organizations in the multicriteria environment. It is analyzed within the framework of data envelopment analysis (DEA). We improve the game proposed by Nakabayashi and Tone (2006) and develop an alternative scheme by reassigning the total weight or power for the coalition members. The solutions and equilibria of the new DEA game proposed in this paper are also studied.

Membership Problem for Two-Dimensional General Row Jumping Finite Automata

2020 ◽  
Vol 31 (04) ◽  
pp. 527-538
Author(s):  
Grzegorz Madejski ◽  
Andrzej Szepietowski
Keyword(s):  
Computational Model ◽  
Turing Machine ◽  
Finite Automaton ◽  
Finite Automata ◽  
The Other ◽  
Membership Problem ◽  
Two Dimensional ◽  
Np Complete ◽  
Nondeterministic Turing Machine ◽  
Membership Problems

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in which segments of the row are read. In this paper, we study the membership problem for these automata. We show that each general row jumping finite automaton can be simulated by a nondeterministic Turing machine with space bounded by the logarithm. This means that the fixed membership problems for such automata are in NL, and so in P. On the other hand, we show that the uniform membership problem is NP-complete.

scholarly journals A scalable photonic computer solving the subset sum problem

2020 ◽  
Vol 6 (5) ◽  
pp. eaay5853 ◽  
Author(s):  
Xiao-Yun Xu ◽  
Xuan-Lun Huang ◽  
Zhan-Ming Li ◽  
Jun Gao ◽  
Zhi-Qiang Jiao ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Propagation Speed ◽  
Direct Writing ◽  
Laser Direct Writing ◽  
Time Consumption ◽  
Subset Sum Problem ◽  
Complete Problem ◽  
Strong Robustness ◽  
Subset Sum ◽  
Np Complete

The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)–complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward “photonic supremacy.”

Game-theoretic semantics for non-distributive logics

2019 ◽  
Vol 27 (5) ◽  
pp. 718-742
Author(s):  
Chrysafis Hartonas
Keyword(s):  
The Other ◽  
Game Playing ◽  
Modal Operators ◽  
Game Theoretic ◽  
Game Theoretic Semantics

AbstractWe introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators (Modal Lattice Logic).

Power-collapsing games

2008 ◽  
Vol 73 (4) ◽  
pp. 1433-1457 ◽  
Author(s):  
Miloš S. Kurilić ◽  
Boris Šobot
Keyword(s):  
Boolean Algebra ◽  
Dense Subset ◽  
Winning Strategy ◽  
Zero Element ◽  
The Other ◽  
Complete Boolean Algebra ◽  
Infinite Cardinal ◽  
Other Hand ◽  
Game Theoretic

AbstractThe game is played on a complete Boolean algebra , by two players. White and Black, in κ-many moves (where κ is an infinite cardinal). At the beginning White chooses a non-zero element p ∈ . In the α-th move White chooses pα ∈ (0, p) and Black responds choosing iα ∈{0, 1}. White winsthe play iff . where and .The corresponding game theoretic properties of c.B.a.'s are investigated. So, Black has a winning strategy (w.s.) if κ ≥ π() or if contains a κ-closed dense subset. On the other hand, if White has a w.s., then κ ∈ . The existence of w.s. is characterized in a combinatorial way and in terms of forcing. In particular, if 2<κ = κ ∈ Reg and forcing by preserves the regularity of κ, then White has a w.s. iff the power 2κ is collapsed to κ in some extension. It is shown that, under the GCH, for each set S ⊆ Reg there is a c.B.a. such that White (respectively. Black) has a w.s. for each infinite cardinal κ ∈ S (resp. κ ∉ S). Also it is shown consistent that for each κ ∈ Reg there is a c.B.a. on which the game is undetermined.

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