We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme (1984) [1]. The game takes place on an undirected graph where n simultaneously moving cops attempt to captur...
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We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme (1984) [1]. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at the same speed. The players are allowed to pick their starting positions at the first move. The question of the computational complexity of deciding this game was raised by Goldstein and Reingold (1995)[9]. We prove that the game is hard for PSPACE. (c) 2012 Elsevier B.V. All rights reserved.
The computational complexity of finding a Nash equilibrium in a nonzero sum bimatrix game is an important open question. We put forward the notion of (0, 1)-bimatrix games, and show that some associated computational ...
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The computational complexity of finding a Nash equilibrium in a nonzero sum bimatrix game is an important open question. We put forward the notion of (0, 1)-bimatrix games, and show that some associated computational problems are as hard as in the general case. (c) 2005 Elsevier B.V. All rights reserved.
Permanents and determinants are special cases of immanants. The latter are polynomial matrix functions defined in terms of characters of symmetric groups and corresponding to Young diagrams. Valiant has proved that th...
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Permanents and determinants are special cases of immanants. The latter are polynomial matrix functions defined in terms of characters of symmetric groups and corresponding to Young diagrams. Valiant has proved that the evaluation of permanents is a complete problem in both the Turing machine model (#P-completeness) as well as in his algebraic model (VNP-completeness). We show that the evaluation of immanants corresponding to hook diagrams or rectangular diagrams of polynomially growing width is both #P-complete and VNP-complete.
Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications fo...
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Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications for maritime border protection and surveillance operations. The objective of the PBSPCC is to find a minimum size patrol boat fleet to provide ongoing continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. We introduce the PBSPCC via an example, discuss its relationship to related but dissimilar problems in the literature and proffer a mathematical description of the problem. We then show that the PBSPCC is NP-hard by a transformation of the Hamiltonian graph decision problem into the problem of finding a minimum cyclic covering of a patrol network. We conclude that the associated decision problem of whether a patrol network has a continuous cover is NP-complete, subject to the requirement that patrol covering solutions are cyclic of a bounded polynomial order.
As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are...
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As a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookings-namely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems.
Newly developed resampling algorithms for particle filters suitable for real-time implementation are described and their analysis is presented. The new algorithms reduce the complexity of both hardware and DSP realiza...
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Newly developed resampling algorithms for particle filters suitable for real-time implementation are described and their analysis is presented. The new algorithms reduce the complexity of both hardware and DSP realization through addressing common issues such as decreasing the number of operations and memory access. Moreover, the algorithms allow for use of higher sampling frequencies by overlapping in time the resampling step with the other particle filtering steps. Since resampling is not dependent on any particular application, the analysis is appropriate for all types of particle filters that use resampling. The performance of the algorithms is evaluated on particle filters applied to bearings-only tracking and joint detection and estimation in wireless communications. We have demonstrated that the proposed algorithms reduce the complexity without performance degradation.
We consider Stackelberg games and corresponding bilevel and trilevel programming models based on facility location and pricing processes. At the upper level of the bilevel models, the company decides on the location o...
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We consider Stackelberg games and corresponding bilevel and trilevel programming models based on facility location and pricing processes. At the upper level of the bilevel models, the company decides on the location of its uncapacitated facilities and the assignment of optimal prices for homogeneous products. In the trilevel models, two companies compete for client demand by making decisions sequentially. We have established the dependence of the computational complexity of the problems under study on the choice of pricing policy and the concept of facility allocation. We have divided the problems into three classes: polynomially solvable, NP-hard, and Sigma(P)(2)-hard. Moreover, the problems of stability analysis are discussed in conclusion.
We propose a method for characterizing the complexity of satisfiability and tautologicity of equational theories of varieties of algebras by relying on their representability in the theory of the ordered additive grou...
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We propose a method for characterizing the complexity of satisfiability and tautologicity of equational theories of varieties of algebras by relying on their representability in the theory of the ordered additive group of reals R(Q) with rational constants. We call semilinear those varieties which are generated by a subclass of algebras in which the operations are representable as semilinear functions with rational coefficients. Those functions are definable in the theory of R(Q) which admits quantifier elimination and whose existential theory is NP-complete. We prove that there is a polynomial time translation of the equational theories of semilinear varieties into the existential theory of R(Q). Then, if the variety is generated (up to isomorphism) by one semilinear algebra, the satisfiability problem is in NP, while the tautologicity problem is in co-NP. We apply this method in order to provide a comprehensive study of complexity of several varieties related to logics based on left-continuous conjunctive uninorms and left-continuous t-norms.
In this paper, a threshold bounded antenna selection scheduler (TBS) and a computational complexity bounded antenna selection scheduler (CCBS) are proposed to reduce computational complexity in multiple input multiple...
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In this paper, a threshold bounded antenna selection scheduler (TBS) and a computational complexity bounded antenna selection scheduler (CCBS) are proposed to reduce computational complexity in multiple input multiple output (MIMO) uplink. In contrast to previous works, a spatially correlated MIMO channel model is considered and a transmitter correlation value (TCV) is newly introduced to assist the antenna selection in addition to the channel gain. For the TBS or CCBS, with predetermined threshold of TCV or ratio of successful antennas (RSAs), full searching (FS) and sub searching (SS) are applied more efficiently to user equipments (UEs) compared with previous schedulers. As a result, the number of candidate antennas in the scheduling set can be reduced, which translates into a lower computational complexity in terms of number of evaluated antenna combinations. Additionally, compared with the TBS, the peak computational complexity can be further reduced by the CCBS. Simulation results show that with proposed schedulers the computational complexity can be reduced by at least 50% with an acceptable compromise of capacity. Copyright (C) 2010 John Wiley & Sons, Ltd.
The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input...
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The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input-mapping data-driven technique, which effectively improves the convergence rate through historical data compensation. However, this approach increases computational complexity in multi-input and multi-output (MIMO) systems due to the dependency of the number of online optimization variables on system dimensions. To improve applicability, this paper introduces a novel input-mapping-based online learning SMC strategy with low computational complexity. First, a new sliding mode surface is established through online convex combination of pre-designed offline surfaces. Then, an input-mapping-based online learning sliding mode control (IML-SMC) strategy is designed, utilizing a reaching law with adaptively adjusted convergence and switching coefficients to minimize chattering. The input-mapping technique employs the mapping relationship between historical input and output data for predicting future system dynamics. Accordingly, an optimization problem is formulated to learn from the past dynamics of the uncertain system online, thereby enhancing system performance. The optimization problem in this paper features fewer variables and is independent of system dimension. Additionally, the stability of the proposed method is theoretically validated, and the advantages are demonstrated through a MIMO system. Note to Practitioners-The design of control strategies that reduce the impact of mismatches between practical systems and models on system performance, while also ensuring applicability, is crucial. To address this issue, this paper proposes a low-complexity IML-SMC strategy. This strategy uses historical real input-output information and the mapping relationship with future dynamics to compensate for the impact of unknown dynamics and improve the system's conv
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