Decision support systems play an important role in aiding decision-making processes by providing valuable insights and recommendations driven by data analysis. However, as decision support systems increasingly employ ...
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Decision support systems play an important role in aiding decision-making processes by providing valuable insights and recommendations driven by data analysis. However, as decision support systems increasingly employ complex Artificial Intelligence (AI) techniques, the need for explainability becomes essential to build trust and transparency with users. As a result, explainable AI (XAI) has emerged as a paradigm that seeks to make AI decision-making processes transparent and understandable to humans. While explainability enhances user comprehension, it introduces computational complexity challenges. In the evolving landscape of Explainable Decision Support Systems (XDSS), the quest for optimizing computational complexity without sacrificing explainability presents a challenge. This paper delves into the potential of bio-inspired algorithms as a novel approach to addressing this challenge. Through a comprehensive theoretical analysis, this paper explores various bio-inspired algorithms, such as Genetic Algorithms, Particle Swarm Optimization, and Ant Colony Optimization, to assess their applicability and effectiveness in enhancing the computational efficiency of XDSS. By establishing a set of selection criteria to identify the most promising bio-inspired algorithm for optimizing computational complexity in XDSS. The paper sets the groundwork for future research by highlighting theoretical foundations, potential applications, and a clear direction for empirical validation. This exploration not only contributes to the theoretical advancement in the field of XDSS but also opens new avenues for practical implementations that can significantly improve explainable decision support systems’ performance and usability.
We prove that determining the weak saturation number of a host graph F with respect to a pattern graph H is already a computationally hard problem when H is the triangle. As our main tool we establish a connection bet...
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In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is *** prove that...
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In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is *** prove that an absolute minimum core(AMC)model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane,has its computational complexity O(2mn).Any algorithms to make the model smaller(or simpler)than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original ***,the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2mn)by any algorithms,which is in subexponential time,superpolynomial.
A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agent...
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A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle form, the -additive form, and as straight-line programs. We study the computational complexity of social welfare optimization in multiagent resource allocation, where we consider utilitarian and egalitarian social welfare and social welfare by the Nash product. Solving some of the open problems raised by Chevaleyre et al. (2006) and confirming their conjectures, we prove that egalitarian social welfare optimization is -complete for the bundle form, and both exact utilitarian and exact egalitarian social welfare optimization are -complete, each for both the bundle and the -additive form, where is the second level of the boolean hierarchy over . In addition, we prove that social welfare optimization by the Nash product is -complete for both the bundle and the -additive form, and that the exact variants are -complete for the bundle and the -additive form. For utility functions represented as straight-line programs, we show -completeness for egalitarian social welfare optimization and social welfare optimization by the Nash product. Finally, we show that social welfare optimization by the Nash product in the -additive form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the -additive form with a fixed number of agents.
This paper introduces a new class of membrane systems called simple P systems, and studies their computational complexity. We start by presenting the knapsack problem and its time complexity. Then we study the computa...
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This paper introduces a new class of membrane systems called simple P systems, and studies their computational complexity. We start by presenting the knapsack problem and its time complexity. Then we study the computational complexity of simple P systems by considering the allocation of resources enabling the parallel application of the rules. We show that the decision version of the resource allocation problem for simple P systems is NP-complete, by using the knapsack problem.
The amount of work needed to generate the families of complete, maximal complete, independent, and maximal independent subsets of the interference graphs of mobile radio telephone networks is investigated. It is shown...
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The amount of work needed to generate the families of complete, maximal complete, independent, and maximal independent subsets of the interference graphs of mobile radio telephone networks is investigated. It is shown that the family of maximal complete subsets can always be computed, whereas, for complete sets, difficulties arise with larger reuse distances, and both the independent and maximal independent sets remain inaccessible except for networks with only little frequency reuse. It is shown that the size of the network is a limiting factor in the case of independent and maximal independent sets, since the number of members of these families always increases exponentially with the number of cells. On the other hand, the growth of the number of complete or maximal complete subsets with the size of the network is always linear.< >
Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of th...
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Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of the rule, over a finite input configuration. Here, we perform the study of the entire elementary cellular automata rule space, for the two possible decision cases of the problem, namely, changes in v from state 0 to 1 (0 -> 1), and the other way round (1 -> 0). Out of the 256 elementary cellular automata, we show that for all of them, at least one of the two decision problems is in the NC complexity class.
Petri net is a powerful modeling tool for concurrent systems. Liveness, which is a problem to verify there exists no local deadlock, is one of the most important properties of Petri net to analyze. computational compl...
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Petri net is a powerful modeling tool for concurrent systems. Liveness, which is a problem to verify there exists no local deadlock, is one of the most important properties of Petri net to analyze. computational complexity of liveness of a general Petri net is deterministic exponential space. Liveness is studied for subclasses of Petri nets to obtain necessary and sufficient conditions that need less computational cost. These are mainly done using a subset of places called siphons. CS-property, which denotes that every siphon has token(s) in every reachable marking, in one of key properties in liveness analysis. On the other hand, normal Petri net is a subclass of Petri net whose reachability set can be effectively calculated. This paper studies computational complexity of liveness problem of normal Petri nets. First, it is shown that liveness of a normal Petri net is equivalent to cs-property. Then we show this problem is co-NP complete by deriving a nondeterministic algorithm for non-liveness which is similar to the algorithm for liveness suggested by Howell et al. Lastly, we study structural feature of bounded Petri net where liveness and cs-property are equivalent. From this consideration, liveness problem of bounded normal Petri net is shown to be deterministic polynomial time complexity.
In this paper, we analyze the two-machine flowshop problem with the makespan minimization and the learning effect, which computational complexity was not determined yet. First, we show that an optimal solution of this...
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In this paper, we analyze the two-machine flowshop problem with the makespan minimization and the learning effect, which computational complexity was not determined yet. First, we show that an optimal solution of this problem does not have to be the 'permutation' schedule if the learning effect is taken into consideration. Furthermore, it is proved that the permutation and non-permutation versions of this problem are NP-hard even if the learning effect, in a form of a step learning curve, characterizes only one machine. However, if both machines have learning ability and the learning curves are stepwise then the permutation version of this problem is strongly NP-hard. Furthermore, we prove the makespan minimization problem in m-machine permutation proportional flowshop environment remains polynomially solvable with identical job processing times on each machine even if they are described by arbitrary functions (learning curves) dependent on a job position in a sequence. Finally, approximation algorithms for the general problem are proposed and analyzed. (C) 2011 Elsevier Ltd. All rights reserved.
This paper provides a comprehensive overview of research related to computational complexity of structured singular value (a.k.a. mu) problems. A survey of computational complexity results in mu problems is followed b...
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This paper provides a comprehensive overview of research related to computational complexity of structured singular value (a.k.a. mu) problems. A survey of computational complexity results in mu problems is followed by a concise introduction to computational complexity theory that is useful to characterize the inherent difficulty of solving an optimization. Results on the study for NP-hardness of epsilon-approximation of mu problems are discussed and conservatism of convex mu upper-bounds including ones obtained from absolute stability theory is studied. NP-hardness of mu computation and conservatism of convex upper-bounds open new research trends. In particular, we give an overview of polynomial-time model reduction methods and probabilistic randomized algorithms that have been active research topics since the mid-1990s. (C) 2013 Elsevier Ltd. All rights reserved.
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