This paper presents a polynomial time algorithm for the construction and training of a class of multilayer perceptrons for classification. It uses linear programming models to incrementally generate the hidden layer i...
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This paper presents a polynomial time algorithm for the construction and training of a class of multilayer perceptrons for classification. It uses linear programming models to incrementally generate the hidden layer in a restricted higher-order perceptron. polynomialtime complexity of the method is proven. Computational results are provided for several well-known applications in the areas of speech recognition, medical diagnosis, and target detection. In all cases, very small nets were created that had error rates similar to those reported so far.
Let G be a connected interval graph with n vertices and m edges. For any positive integer k and any subset S of E(G), we design an O(k|S| + m) timealgorithm to find a minimum k-vertex-edge dominating set of G with re...
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Let G be a connected interval graph with n vertices and m edges. For any positive integer k and any subset S of E(G), we design an O(k|S| + m) timealgorithm to find a minimum k-vertex-edge dominating set of G with respect to S. This shows that the vertex-edge domination problem and the double vertex-edge domination problem can be solved in linear time. Furthermore, the k-vertex-edge domination problem can also be solved in O(km) timealgorithm in interval graphs. Finally, we present a linear timealgorithm to solve the independent vertex-edge domination problem for unit interval graphs.
This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, and minimum order quantity (CLSP-MOQ). In this problem, a demand must be satisfied at each period t over ...
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This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, and minimum order quantity (CLSP-MOQ). In this problem, a demand must be satisfied at each period t over a planning horizon of T periods. This demand can be satisfied from the stock or by a production at the same period. When a production is made at period t, the produced quantity must be greater to than a minimum order quantity (L) and lesser than the production capacity (U). To solve this problem optimally, a polynomial time algorithm in O(T-5) is proposed and it is computationally tested on various instances. (C) 2012 Elsevier B.V. All rights reserved.
Following Golubitsky, Stewart, and others, we give definitions of networks and input trees. In order to make our work as general as possible, we work with a somewhat extended notion of multiplicity, and introduce the ...
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Following Golubitsky, Stewart, and others, we give definitions of networks and input trees. In order to make our work as general as possible, we work with a somewhat extended notion of multiplicity, and introduce the concept of "bunching" of trees. We then de. ne balanced equivalence relations on networks, and a partial ordering on these relations. Previous work has shown that there is a maximal balanced equivalence relation on networks of certain classes: we provide a different style of proof which gives this result for any network. We de. ne two algorithms to determine this relation in practice on a given finite network-one for use with networks with all multiplicities equal, and a second for the more general case. We then provide illustrative examples of each algorithm in use. We show both of these algorithms to be quartic in the size of the given network.
Aiming at the inefficiency of polynomial time algorithm of linear network coding (NC) for multicast applications, the authors propose an improved algorithm which combines polynomial time algorithm with subtree decompo...
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Aiming at the inefficiency of polynomial time algorithm of linear network coding (NC) for multicast applications, the authors propose an improved algorithm which combines polynomial time algorithm with subtree decomposition. The algorithm is composed of five steps, including line graph transforming, subtree decomposition, static subtree set generating, assigning of global coding vector, and calculation of local coding vector. Subtree decomposition decreases network scale and coding complexity steeply, so it is an efficient algorithm of linear NC for multicast. An example is given to illustrate the implementation of the algorithm. Detailed analysis to algorithm complexity and a group of numerical experiments are made to show the efficiency of the algorithm.
The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chor...
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The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomialtime for unit interval graphs. For this reason, it is a well-known open problem to prove whether there exists a polynomial time algorithm solving the TPP on interval graphs. In this paper, we give an answer to the problem.(c) 2023 Elsevier B.V. All rights reserved.
This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, considering minimum order quantity and dynamic time windows. The frequency constraints on the production ...
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This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, considering minimum order quantity and dynamic time windows. The frequency constraints on the production lots are modeled by dynamic time windows. Between two consecutive production lots, there are at least Q periods and at most R periods. This paper presents an optimal algorithm in 0((T -Q)(2) (R-Q)T-4/Q(3)), which is bounded by O(T-7). (C) 2014 Elsevier B.V. All rights reserved.
We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order autonomous ODE F = 0, we give an exact degree bound for its rational solutions, based on th...
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We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For a first order autonomous ODE F = 0, we give an exact degree bound for its rational solutions, based on the connection between rational solutions of F = 0 and rational parametrizations of the plane algebraic curve defined by F = 0. For a first order autonomous ODE, we further give a polynomial time algorithm for computing a rational general solution if it exists based on the computation of Laurent series solutions and Pade approximants. Experimental results show that the algorithm is quite efficient. (c) 2006 Elsevier Ltd. All rights reserved.
This paper gives an O( n √ n log 3 n ) timealgorithm for the chance-constrained sequencing problem on a single machine, where n is the number of jobs and the objective is to minimize the number of jobs which are ear...
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This paper gives an O( n √ n log 3 n ) timealgorithm for the chance-constrained sequencing problem on a single machine, where n is the number of jobs and the objective is to minimize the number of jobs which are early with probability not smaller than α (a given constant) against the common due time d .
In some important application areas of hard real-time systems, e.g., avionics, automotive, industrial controls, and robotics, preemptive sporadic tasks with harmonic periods and constrained deadlines running on a uni-...
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ISBN:
(纸本)9783031066788;9783031066771
In some important application areas of hard real-time systems, e.g., avionics, automotive, industrial controls, and robotics, preemptive sporadic tasks with harmonic periods and constrained deadlines running on a uni-processor platform play an important role. For such applications we have to check the system task set for guaranteed compliance with deadlines. For this purpose, we present a new algorithm that has a lower computational complexity than known algorithms for the same system class. For this we determine the worst-case response time for each task with a linear computational complexity in the number of tasks, if the task priorities are defined according to their periodic request rates. Otherwise we have to add the time for task ordering.
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