In this paper, we analyse the single processor maximum completion time (makespan) minimization problem with distinct release dates of jobs and the sum-of-processing time-based learning effect. We prove that the consid...
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In this paper, we analyse the single processor maximum completion time (makespan) minimization problem with distinct release dates of jobs and the sum-of-processing time-based learning effect. We prove that the considered problem is strongly NP-hard, if, in addition to jobs with the same learning ratio, there are jobs with constant job processing times. Such jobs are not affected by learning and model, for instance, required system upgrades or training courses.
computational complexity results are obtained for decentralized discrete-event control problems. These results generalize the earlier work of Tsitsiklis, who showed that for a special class of centralized supervisory ...
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computational complexity results are obtained for decentralized discrete-event control problems. These results generalize the earlier work of Tsitsiklis, who showed that for a special class of centralized supervisory control problems under partial observation, there is an algorithm for determining in polynomial time whether or not a solution exists. The negative complexity results associated with Tsitsiklis' work also carry over to the decentralized case, so that solution existence for the more general class is not decidable in polynomial time, nor does there exist a polynomial-time algorithm for producing supervisor solutions when such solutions exist.
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through...
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Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn-Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn-Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn-Sham potential with controllable error bounds.
This paper presents a comparison study of the computational complexity of the general job shop protocol and the more structured flow line protocol in a flexible manufacturing system. Tt is shown that the representativ...
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This paper presents a comparison study of the computational complexity of the general job shop protocol and the more structured flow line protocol in a flexible manufacturing system. Tt is shown that the representative problem of finding resource invariants is NP-complete in the case of the job shop, while in the flow line case it admits a closed form solution. The importance of correctly selecting part flow and job routing protocols in flexible! manufacturing systems to reduce complexity is thereby conclusively demonstrated.
We explore the computational complexity of certain issues regarding parametric linear and integer linear programming. For example, we demonstrate that: (1) The equality of optimal value of two integer programs for all...
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We explore the computational complexity of certain issues regarding parametric linear and integer linear programming. For example, we demonstrate that: (1) The equality of optimal value of two integer programs for all right-hand sides (r.h.s) is NP-complete either when the problem is stated in matrix or in functional form; (2) The equality of optimal value of two linear programs for all r.h.s. in matrix form is polynomial, but it becomes NP-complete when one desires equality for all r.h.s. in a polyhedral cone described by generators; (3) The equality of a general polyhedral function (allowing nested "maxes") to the value of a linear program in matrix form, or to another polyhedral function, is NP-complete; (4) The shortest expression, for the optimum to the subadditive dual of an integer program in matrix form, can require exponential space.
Temporal reasoning problems arise in many areas of Al, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reas...
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Temporal reasoning problems arise in many areas of Al, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reasoning is fairly well understood. There are, however, many different cases where discrete time must be considered;various scheduling problems and reasoning about sampled physical systems are two examples. Here, the complexity of temporal reasoning is not as well-studied nor as well-understood. In order to get a better understanding, we consider the powerful Horn disjunctive linear relations (Horn DLR) formalism adapted for discrete time and study its computational complexity. We show that the full formalism is NP-hard and identify several maximal tractable subclasses. We also 'lift' the maximality results to obtain hardness results for other families of constraints. Finally, we discuss how the results and techniques presented in this paper can be used for studying even more expressive classes of temporal constraints. (C) 2012 Elsevier B.V. All rights reserved.
The computational complexity evaluation is necessary for software defined Forward Error Correction (FEC) decoders. However, currently there are a limited number of literatures concerning on the FEC complexity evaluati...
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The computational complexity evaluation is necessary for software defined Forward Error Correction (FEC) decoders. However, currently there are a limited number of literatures concerning on the FEC complexity evaluation using analytical methods. In this paper, three high efficient coding schemes including Turbo, QC-LDPC and Convolutional code (CC) are investigated. The hardware-friendly decoding pseudo-codes are provided with explicit parallel execution and memory access procedure. For each step of the pseudo-codes, the parallelism and the operations in each processing element are given. Based on it the total amount of operations is derived. The comparison of the decoding complexity among these FEC algorithms is presented, and the percentage of each computation step is illustrated. The requirements for attaining the evaluated results and reference hardware platforms are provided. The benchmarks of state-of-the-art SDR platforms are compared with the proposed evaluations. The analytical FEC complexity results are beneficial for the design and optimization of high throughput software defined FEC decoding platforms.
We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show...
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We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for a given bipartite graph, such a scheme can be found that eliminates every vertex is NP-complete. Moreover, we show that, for all fixed positive integers k >= 2, the problem of whether a given bipartite graph admits a scheme in which all vertices are eliminated in at most (exactly) k rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time. We also show that r-regular graphs with r >= 1, factor-critical graphs and 1-tough graphs admit a scheme in which all vertices are eliminated in one round. (C) 2007 Elsevier B.V. All rights reserved.
The authors analyze the computational complexity of sparse rational interpolation, and give the first deterministic algorithm for this problem with singly exponential bounds on the number of arithmetic operations.
The authors analyze the computational complexity of sparse rational interpolation, and give the first deterministic algorithm for this problem with singly exponential bounds on the number of arithmetic operations.
Chemical reaction network has been a model of interest to both theoretical and applied computer scientists, and there has been concern about its physical-realisticity which calls for study on the atomic property of ch...
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Chemical reaction network has been a model of interest to both theoretical and applied computer scientists, and there has been concern about its physical-realisticity which calls for study on the atomic property of chemical reaction networks. Informally, a chemical reaction network is atomic if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Primitive atomic, which requires each reaction to preserve the total number of atoms, is shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving (Mayr and Weihmann, in: International conference on applications and theory of petri nets and concurrency, Springer, New York, 2014), the equivalence we show gives an efficient algorithm to decide primitive atomicity. Subset atomic further requires all atoms be species, so intuitively this type of network is endowed with a better property than primitive atomic (i.e. mass conserving) ones in the sense that the atoms are not just abstract indivisible units, but also actual participants of reactions. We show that deciding if a network is subset atomic is in Reachably atomic, studied by Adleman et al.(On the mathematics of the law of mass action, Springer, Dordrecht, 2014. 10.1007/978-94-017-9041-3_1), and Gopalkrishnan (2016), further requires that each species has a sequence of reactions splitting it into its constituent atoms. Using a combinatorial argument, we show that there is a polynomial-time algorithm to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is decidable. We show that the reachability problem for reachably atomic networks is . Finally, we demonstrate equivalence relationsh
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