A polynomial time approximation scheme (PTAS) for an optimization problem A is an algorithm that given in input an instance of A and epsilon > 0 finds a (1 + epsilon)-approximate solution in time that is polynomial...
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A polynomial time approximation scheme (PTAS) for an optimization problem A is an algorithm that given in input an instance of A and epsilon > 0 finds a (1 + epsilon)-approximate solution in time that is polynomial for each fixed epsilon. Typical running times are n(0(1/epsilon)) or 2(1/epsilon 0(1))n. While algorithms of the former kind tend to be impractical, the latter ones are more interesting. In several cases, the development of algorithms of the second type required considerably new, and sometimes harder, techniques. For some interesting problems, only n(0(1/epsilon)) approximation schemes are known. Under likely assumptions, we prove that for some problems (including natural ones) there cannot be approximation schemes running in time f(1/epsilon)n(0(1)), no matter how fast function f grows. Our result relies on a connection with Parameterized complexity Theory, and we show that this connection is necessary, (C) 1997 Published by Elsevier Science B.V.
Enhancing, modifying or adapting the software to new requirements increases the internal software complexity. Software with high level of internal complexity is difficult to maintain. Software refactoring reduces soft...
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Enhancing, modifying or adapting the software to new requirements increases the internal software complexity. Software with high level of internal complexity is difficult to maintain. Software refactoring reduces software complexity and hence decreases the maintenance effort. However, software refactoring becomes quite challenging task as the software evolves. The authors use clustering as a pattern recognition technique to assist in software refactoring activities at the package level. The approach presents a computer aided support for identifying ill-structured packages and provides suggestions for software designer to balance between intra-package cohesion and inter-package coupling. A comparative study is conducted applying three different clustering techniques on different software systems. In addition, the application of refactoring at the package level using an adaptive k-nearest neighbour (A-KNN) algorithm is introduced. The authors compared A-KNN technique with the other clustering techniques (viz. single linkage algorithm, complete linkage algorithm and weighted pair-group method using arithmetic averages). The new technique shows competitive performance with lower computational complexity.
A graph is an efficient open (resp. closed) domination graph if there exists a subset of vertices whose open (resp. closed) neighborhoods partition. its vertex set. Graphs that are efficient open as well as efficient ...
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A graph is an efficient open (resp. closed) domination graph if there exists a subset of vertices whose open (resp. closed) neighborhoods partition. its vertex set. Graphs that are efficient open as well as efficient closed (shortly EOCD graphs) are investigated. The structure of EOCD graphs with respect to their efficient open and efficient closed dominating sets is explained. It is shown that the decision problem regarding whether a graph is an EOCD graph is an NP-complete problem. A recursive description, that constructs all EOCD trees is given and EOCD graphs are characterized among the Sierpinski graphs. (C) 2016 Published by Elsevier B.V.
The state-assignment problem of finite-state machines (FSMs) is addressed. State assignment is a mapping from the set of states (symbolic names) of an FSM to the set of binary codes with the objective of minimising th...
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The state-assignment problem of finite-state machines (FSMs) is addressed. State assignment is a mapping from the set of states (symbolic names) of an FSM to the set of binary codes with the objective of minimising the area of the combinational circuit required to realise the FSM. It is one of the most important optimisation problems in the automatic synthesis of sequential circuits since it has a major impact on the area, speed, power and testability of the circuits. The problem of finding an optimal state assignment is NP-hard. A new scheme is presented based on mean-field annealing (MFA) to solve the graph-embedding problem which is the main step in the state-assignment process. The MFA algorithm combines the characteristics of the simulated annealing and the Hopfield neural network. To solve the problem by MFA, the graph-embedding problem is mapped into a neural network and an energy function is formulated. Experiments over the MCNC FSM benchmarks demonstrate that the proposed MFA algorithm can produce superior results compared with the specialised methods such as the MUSTANG, NOVA and genetic algorithm.
Approximate computing exploits the fact that many applications do not require the results to be exact but not to exceed a threshold in a given error metric. Algorithms in approximate computing require to compute the e...
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Approximate computing exploits the fact that many applications do not require the results to be exact but not to exceed a threshold in a given error metric. Algorithms in approximate computing require to compute the error of the approximation in order to measure its quality. In this paper, the computational complexity of several of such error metrics commonly used in approximate computing is investigated. We show that these metrics lie within the complexity classes FPNP and #P and, therefore, are hard to compute. We further classify the error metrics into two classes. The framework used in this generalization is then used to exemplary develop specialized error metrics. (C) 2018 Elsevier B.V. All rights reserved.
We consider two types of graph domination-{k}-domination and k-tuple domination, for a fixed positive integer k and provide new NP-complete as well as polynomial time solvable instances for their related decision prob...
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We consider two types of graph domination-{k}-domination and k-tuple domination, for a fixed positive integer k and provide new NP-complete as well as polynomial time solvable instances for their related decision problems. Regarding NP-completeness results, we solve the complexity of the {k}-domination problem on split graphs, chordal bipartite graphs and planar graphs, left open in 2008. On the other hand, by exploiting Courcelle's results on Monadic Second Order Logic, we obtain that both problems are polynomial time solvable for graphs with clique-width bounded by a constant. In addition, we give an alternative proof for the linearity of these problems on strongly chordal graphs. (C) 2015 Elsevier B.V. All rights reserved.
A novel concatenated physical-layer encryption (CPLE) scheme is proposed in this study, where better security can be achieved as well as reliability advantage. In CPLE scheme, the encryption is embedded in rateless en...
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A novel concatenated physical-layer encryption (CPLE) scheme is proposed in this study, where better security can be achieved as well as reliability advantage. In CPLE scheme, the encryption is embedded in rateless encoding. The secret key, which is generated from wireless channel, controls the random degree and random linear combination. The rateless codes are also concatenated with other conventional channel codes, which can achieve better reliability. Different from security codes, both the security and reliability in the proposed scheme can be improved. Furthermore, there is no extra computation requirement on decoding process. Security analysis is presented including time complexity comparison and attacks resistance in practical application. Compared to other PLE schemes, the proposed scheme achieves lower complexity, and higher channel adaptation and performance advantage. On the basis of National Institute of Standards and Technology statistical test suite, CPLE scheme can achieve randomness as the traditional cipher system such as advanced encryption standard. Furthermore, simulation results show that the CPLE scheme outperforms the conventional concatenated codes at the same coderate.
We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the prob...
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We study a variant of the multi-agent path finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topological graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.
We investigate first-order separation logic with one record field restricted to a unique quantified variable (1SL1). Undecidability is known when the number of quantified variables is unbounded and the satisfiability ...
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We investigate first-order separation logic with one record field restricted to a unique quantified variable (1SL1). Undecidability is known when the number of quantified variables is unbounded and the satisfiability problem is PSPACE-complete for the propositional fragment. We show that the satisfiability problem for 1SL1 is PSPACE-complete and we characterize its expressive power by showing that every formula is equivalent to a Boolean combination of atomic properties. This contributes to our understanding of fragments of first-order separation logic that can specify properties about the memory heap of programs with singly-linked lists. All the fragments we consider contain the magic wand operator and first-order quantification over a single variable.
Due to the high-dimensional data space generated by hyperspectral sensors together with the real-time requirements of several remote sensing applications, it is important to accelerate hyperspectral data analysis. For...
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Due to the high-dimensional data space generated by hyperspectral sensors together with the real-time requirements of several remote sensing applications, it is important to accelerate hyperspectral data analysis. For this purpose, we aim to improve the performance of an existing classification algorithm and reduce its execution time. The proposed algorithm is based on sparse representation and using extended multiattribute profiles as spectral-spatial features, and sparse unmixing by variable splitting and augmented Lagrangian as the optimization method. The speeding up is mainly achieved by exploiting the interdependencies among iterative calls and providing an appropriate memorization technique to reduce the extra cost by factorizing the algebraic computations. The experimental results on two HSI data sets prove that the optimized algorithm is really faster than the original one while retaining the same classification accuracy. This study shows how useful it is to adapt the implementation of the generic module in order to become more appropriate to the application and to minimize the extra costs as much as possible. (C) 2018 SPIE and IS&T
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