A well-known approach to intradomain traffic engineering consists in finding the set of link weights that minimizes a network-wide objective function for a given intradomain traffic matrix. This approach is inadequate because it ignores a potential impact on interdomain routing. Indeed, the resulting set of link weights may trigger BGP to change the BGP next hop for some destination prefixes, to enforce hot-potato routing policies. In turn, this results in changes in the intradomain traffic matrix that have not been anticipated by the link weights optimizer, possibly leading to degraded network performance. We propose a BGP-aware link weights optimization method that takes these effects into account, and even turns them into an advantage. This method uses the interdomain traffic matrix and other available BGP data, to extend the intradomain topology with external virtual nodes and links, on which all the well-tuned heuristics of a classical link weights optimizer can be applied. A key innovative asset of our method is its ability to also optimize the traffic on the interdomain peering links. We show, using an operational network as a case study, that our approach does so efficiently at almost no extra computational cost.
Cerav- have already shown in @cite_14 that the link weights found by a LWO may change the intradomain TM considered as input. In that paper they also show that applying LWO recursively on the resulting intradomain TM may not converge. They propose a method that keeps track of the series of resulting TMs and at each iteration they optimize the weights for the previous resulting intradomain TMs simultaneously. However, they do not consider the general problem with multiple exit points for each destination prefix, let alone taking advantage of it.
@cite_14
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Weight modifications in traditional neural nets are computed by hard-wired algorithms. Without exception, all previous weight change algorithms have many specific limitations. Is it (in principle) possible to overcome limitations of hard-wired algorithms by allowing neural nets to run and improve their own weight change algorithms? This paper constructively demonstrates that the answer (in principle) is ‘yes’. I derive an initial gradientbased sequence learning algorithm for a ‘self-referential’ recurrent network that can ‘speak’ about its own weight matrix in terms of activations. It uses some of its input and output units for observing its own errors and for explicitly analyzing and modifying its own weight matrix, including those parts of the weight matrix responsible for analyzing and modifying the weight matrix. The result is the first ‘introspective’ neural net with explicit potential control over all of its own adaptive parameters. A disadvantage of the algorithm is its high computational complexity per time step which is independent of the sequence length and equals O(nconnlognconn), where riconn is the number of connections. Another disadvantage is the high number of local minima of the unusually complex error surface. The purpose of this paper, however, is not to come up with the most efficient ‘introspective’ or ‘self-referential’ weight change algorithm, but to show that such algorithms are possible at all. Dynamic time warping (DTW), which finds the minimum path by providing non-linear alignments between two time series, has been widely used as a distance measure for time series classification and clustering. However, DTW does not account for the relative importance regarding the phase difference between a reference point and a testing point. This may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition. Therefore, we propose a novel distance measure, called a weighted DTW (WDTW), which is a penalty-based DTW. Our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers. The rationale underlying the proposed distance measure is demonstrated with some illustrative examples. A new weight function, called the modified logistic weight function (MLWF), is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point. By applying different weights to adjacent points, the proposed algorithm can enhance the detection of similarity between two time series. We show that some popular distance measures such as DTW and Euclidean distance are special cases of our proposed WDTW measure. We extend the proposed idea to other variants of DTW such as derivative dynamic time warping (DDTW) and propose the weighted version of DDTW. We have compared the performances of our proposed procedures with other popular approaches using public data sets available through the UCR Time Series Data Mining Archive for both time series classification and clustering problems. The experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems. In the Maximum Weight Independent Set of Rectangles (MWISR) problem we are given a set of n axis-parallel rectangles in the 2D-plane, and the goal is to select a maximum weight subset of pairwise non-overlapping rectangles. Due to many applications, e.g. in data mining, map labeling and admission control, the problem has received a lot of attention by various research communities. We present the first (1 + e)-approximation algorithm for the MWISR problem with quasipolynomial running time 2poly(log n e). In contrast, the best known polynomial time approximation algorithms for the problem achieve superconstant approximation ratios of O(log log n) (unweighted case) and O(log n log log n) (weighted case). Key to our results is a new geometric dynamic program which recursively subdivides the plane into polygons of bounded complexity. We provide the technical tools that are needed to analyze its performance. In particular, we present a method of partitioning the plane into small and simple areas such that the rectangles of an optimal solution are intersected in a very controlled manner. Together with a novel application of the weighted planar graph separator theorem due to [4] this allows us to upper bound our approximation ratio by 1 + e. Our dynamic program is very general and we believe that it will be useful for other settings. In particular, we show that, when parametrized properly, it provides a polynomial time (1 + e)-approximation for the special case of the MWISR problem when each rectangle is relatively large in at least one dimension. Key to this analysis is a method to tile the plane in order to approximately describe the topology of these rectangles in an optimal solution. This technique might be a useful insight to design better polynomial time approximation algorithms or even a PTAS for the MWISR problem. In particular, note that our results imply that the MWISR problem is not APX-hard, unless NP ⊆ DTIME(2polylog (n)). A common assumption in supervised learning is that the input points in the training set follow the same probability distribution as the input points that will be given in the future test phase. However, this assumption is not satisfied, for example, when the outside of the training region is extrapolated. The situation where the training input points and test input points follow different distributions while the conditional distribution of output values given input points is unchanged is called the covariate shift. Under the covariate shift, standard model selection techniques such as cross validation do not work as desired since its unbiasedness is no longer maintained. In this paper, we propose a new method called importance weighted cross validation (IWCV), for which we prove its unbiasedness even under the covariate shift. The IWCV procedure is the only one that can be applied for unbiased classification under covariate shift, whereas alternatives to IWCV exist for regression. The usefulness of our proposed method is illustrated by simulations, and furthermore demonstrated in the brain-computer interface, where strong non-stationarity effects can be seen between training and test sessions.