The optima of solution of initial-value problems in ODES is well studied for smooth right-hand Side functions. Much less is known about the optimality, of algorithms for singular problems. In this paper. We Study the ...
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The optima of solution of initial-value problems in ODES is well studied for smooth right-hand Side functions. Much less is known about the optimality, of algorithms for singular problems. In this paper. We Study the (worst case) solution of scalar problems with a right-hand side function having r continuous hounded derivatives in R, except for an unknown Singular point. We establish the minimal worst case error for such problems (which depends on r similarly as in the smooth case), and define optimal adaptive algorithms. The Crucial point is locating an unknown Singularity of the solution by properly adapting the grid. We also Study lower bounds on the error of an algorithm for classes of singular problems. In the case of a single singularity with nonadaptive information, or in the case of two or more singularities, the error of any algorithm is shown to be independent of r. (C) 2008 Elsevier Inc. All rights reserved.
In high-level synthesis for real-time systems, it typically employs heterogeneous functional-unit types to achieve high-performance and low-cost designs. In the design phase, it is critical to determine which function...
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In high-level synthesis for real-time systems, it typically employs heterogeneous functional-unit types to achieve high-performance and low-cost designs. In the design phase, it is critical to determine which functional-unit type to be mapped for each operation in a given application such that the total cost is minimized while the deadline can be met. For a path or tree structured application, existing approaches can obtain the minimum-cost assignment, called "optimal assignment", under which the resultant system satisfies a given timing constraint. However, it is still an open question whether there exist efficient algorithms to obtain the optimal assignment for the directed acyclic graph (DAG), or more generally, the data-flow graph with cycles (cyclic DFG). For DAGs, by analyzing the property of the problem, this paper designs an efficient algorithm to obtain the optimal assignments. For cyclic DFGs, we approach this problem with the combination of retiming technique to thoroughly explore the design space. We formulate a Mixed Integer Linear Programming (MILP) model to give the optimal solution. But because of the high degree of its time complexity, we devise a practical algorithm to obtain near-optimal solutions within a minute. Experimental results show the effectiveness of our algorithms. Specifically, compared with existing techniques, we can achieve 25.70 and 30.23 percent reductions in total cost on DAGs and cyclic DFGs, respectively.
Multi-objective optimization problem with Lipshitz objective functions is considered. It is shown that the worst-case optimal passive algorithm can be reduced to the computation of centers of balls producing the optim...
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Multi-objective optimization problem with Lipshitz objective functions is considered. It is shown that the worst-case optimal passive algorithm can be reduced to the computation of centers of balls producing the optimal cover of a feasible region, where the balls are of equal minimum radius. It is also shown, that in the worst-case, adaptivity does not improve the guaranteed accuracy achievable by the passive algorithm.
The bi-objective Lipschitz optimization with univariate objectives is considered. The concept of the tolerance of the lower Lipschitz bound over an interval is generalized to arbitrary subintervals of the search regio...
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The bi-objective Lipschitz optimization with univariate objectives is considered. The concept of the tolerance of the lower Lipschitz bound over an interval is generalized to arbitrary subintervals of the search region. The one-step worst-case optimality of trisecting an interval with respect to the resulting tolerance is established. The theoretical investigation supports the previous usage of trisection in other algorithms. The trisection-based algorithm is introduced. Some numerical examples illustrating the performance of the algorithm are provided. (C) 2015 Elsevier B.V. All rights reserved.
We propose two exhaustive search-type methods for the construction of Karatsuba-like algorithms for fast computation of certain bilinear forms in GF(2). The computation is done via an explicit construction of trilinea...
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We propose two exhaustive search-type methods for the construction of Karatsuba-like algorithms for fast computation of certain bilinear forms in GF(2). The computation is done via an explicit construction of trilinear decompositions using heuristica search algorithms. Using that approach several old and new algorithms for the fast computation of bilinear forms were obtained. (C) 2008 Elsevier Inc. All rights reserved.
An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if t...
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An implementation of the recently proposed semi-monotonic augmented Lagrangian algorithm for solving the large convex bound and equality constrained quadratic programming problems is considered. It is proved that if the algorithm is applied to the class of problems with uniformly bounded spectrum of the Hessian matrix, then the algorithm finds an approximate solution at O(1) matrix-vector multiplications. The optimality results are presented that do not depend on conditioning of the matrix which defines the equality constraints. Theory covers also the problems with dependent constraints. Theoretical results are illustrated by numerical experiments.
The general class of zero-order Global Optimization problems is split into subclasses according to a proposed "Complexity measure" and the computational complexity of each subclass is rigorously estimated. T...
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The general class of zero-order Global Optimization problems is split into subclasses according to a proposed "Complexity measure" and the computational complexity of each subclass is rigorously estimated. Then, the laboriousness (computational demand) of general Branch-and-Bound (BnB) methods is estimated for each subclass. For conventional "Cubic" BnB based on splitting an n-dimensional cube into sub-cubes, both upper and lower laboriousness estimates are obtained. The value of the Complexity measure for a problem subclass enters linearly into all complexity and laboriousness estimates for that subclass. A new BnB method based on the lattice is presented with upper laboriousness bound that is, though conservative, smaller by a factor of than the lower bound of the conventional method. The optimality of the new method is discussed. All results are extended to the class of Adaptive Covering problems-that is, covering of a large n-dimensional set by balls of different size, where the size of each ball is defined by a locally computed criterion.
作者:
HAN, YJDept. of Comput. Sci.
Kentucky Univ. Lexington KY USA Abstract Authors References Cited By Keywords Metrics Similar Download Citation Email Print Request Permissions n elements in time O(n/p+log n) on a local memory PRAM model ..." property="og:description">
We present a deterministic parallel algorithm for the linked list prefix problem. It computes linked list prefix for an input list of n elements in time O(n/p + log n) on a local memory PRAM model using p processors a...
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We present a deterministic parallel algorithm for the linked list prefix problem. It computes linked list prefix for an input list of n elements in time O(n/p + log n) on a local memory PRAM model using p processors and p shared memory cells.
We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously...
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We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs;a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.
In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better...
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In this paper we compare two new binary linear formulations to a standard quadratic binary program for the gray pattern problem and solved all three by the Gurobi solver. One formulation performed significantly better and obtained seven optimal solutions that were not proven optimal before. It is interesting that the formulation that performed best is based on significantly more variables and constraints.
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