345,022 research outputs found
Complexity results and exact algorithms for robust knapsack problems.
This paper studies the robust knapsack problem, for which solutions are, up to a certain point, immune to data uncertainty. We complement the works found in the literature where uncertainty affects only the profits or only the weights of the items by studying the complexity and approximation of the general setting with uncertainty regarding both the profits and the weights, for three different objective functions. Furthermore, we develop a scenario-relaxation algorithm for solving the general problem and present computational results.Knapsack problem; Robustness; Scenario-relaxation algorithm; NP-hard; Approximation;
On the Computation of the Kullback-Leibler Measure for Spectral Distances
Efficient algorithms for the exact and approximate computation of the symmetrical Kullback-Leibler (1998) measure for spectral distances are presented for linear predictive coding (LPC) spectra. A interpretation of this measure is given in terms of the poles of the spectra. The performances of the algorithms in terms of accuracy and computational complexity are assessed for the application of computing concatenation costs in unit-selection-based speech synthesis. With the same complexity and storage requirements, the exact method is superior in terms of accuracy
Exact Algorithms for 0-1 Integer Programs with Linear Equality Constraints
In this paper, we show -time and -space exact
algorithms for 0-1 integer programs where constraints are linear equalities and
coefficients are arbitrary real numbers. Our algorithms are quadratically
faster than exhaustive search and almost quadratically faster than an algorithm
for an inequality version of the problem by Impagliazzo, Lovett, Paturi and
Schneider (arXiv:1401.5512), which motivated our work. Rather than improving
the time and space complexity, we advance to a simple direction as inclusion of
many NP-hard problems in terms of exact exponential algorithms. Specifically,
we extend our algorithms to linear optimization problems
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A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs
Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs
Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms
The local minimum degree of a graph is the minimum degree that can be reached
by means of local complementation. For any n, there exist graphs of order n
which have a local minimum degree at least 0.189n, or at least 0.110n when
restricted to bipartite graphs. Regarding the upper bound, we show that for any
graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n)
for bipartite graphs, improving the known n/2 upper bound. We also prove that
the local minimum degree is smaller than half of the vertex cover number (up to
a logarithmic term). The local minimum degree problem is NP-Complete and hard
to approximate. We show that this problem, even when restricted to bipartite
graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which
W[1]-hardness is a long standing open question. Finally, we show that the local
minimum degree is computed by a O*(1.938^n)-algorithm, and a
O*(1.466^n)-algorithm for the bipartite graphs
On the Construction of Polar Codes
We consider the problem of efficiently constructing polar codes over binary
memoryless symmetric (BMS) channels. The complexity of designing polar codes
via an exact evaluation of the polarized channels to find which ones are "good"
appears to be exponential in the block length. In \cite{TV11}, Tal and Vardy
show that if instead the evaluation if performed approximately, the
construction has only linear complexity. In this paper, we follow this approach
and present a framework where the algorithms of \cite{TV11} and new related
algorithms can be analyzed for complexity and accuracy. We provide numerical
and analytical results on the efficiency of such algorithms, in particular we
show that one can find all the "good" channels (except a vanishing fraction)
with almost linear complexity in block-length (except a polylogarithmic
factor).Comment: In ISIT 201
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