16722943
The Euclidean Orienteering Problem Revisited
We consider the rooted orienteering problem: Given a set $P$ of $n$ points in the plane, a starting point $r \in P$, and a length constraint $B$, one needs to find a path starting from $r$ that visits as many points of $P$ as possible and of length not exceeding $B$. We present a $(1-\varepsilon)$-approximation algorithm for this problem that runs in $n^{O(1/\varepsilon)}$ time; the computed path visits at least $ (1-\varepsilon)k_{\mathrm{opt}}$ points of $P$, where $k_{\mathrm{opt}}$ is the number of points visited by an optimal solution. This is the first polynomial time approximation scheme for this problem. The algorithm also works in higher dimensions.
618005
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use O(log n) colors, with high probability.
 We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using O(log3n) colors. This is the first efficient (i.e, using polylog(n) colors) deterministic online CF coloring algorithm for this problem.
1262399
Efficient Holistic Twig Join Algorithm on XML Documents with Optimization Rules and Index
Efficiently finding all occurrences of a twig pattern is a core operation of XML query processing. In this paper, we first propose a generic twig join algorithm TJFGeneric which only scans the leaf query nodes using a cursor interface to return elements. And then we present TJFGeneric+ algorithm incorporating two optimization rules into TJFGeneric to explore potential benefit of disk read and CPU cost. In particular, available indices (such as B+-tree) are applied to skip the elements that do not participate in final results. Experimental results on various datasets indicate that our algorithms outperform previous approaches significantly.
5747087
Efficient Processing of Warping Time Series Join of Motion Capture Data
Discovering non-trivial matching subsequences from two time series is very useful in synthesizing novel time series. This can be applied to applications such as motion synthesis where smooth and natural motion sequences are often required to be generated from existing motion sequences. We first address this problem by defining it as a problem of l-e-join over two time series. Given two time series, the goal of l-e-join is to find those non-trivial matching subsequences by detecting maximal l-connections from the e-matching matrix of the two time series. Given a querying motion sequence, the l-e-join can be applied to retrieve all connectable motion sequences from a database of motion sequences. To support efficient l-e-join of time series, we propose a two-step filter-and-refine algorithm, called Warping Time Series Join (WTSJ) algorithm. The filtering step serves to prune those sparse regions of the e-matching matrix where there are no maximal l-connections without incurring costly computation. The refinement step serves to detect closed l-connections within regions that cannot be pruned by the filtering step. To speed up the computation of e-matching matrix, we propose a block-based time series summarization method, based on which the block-wise e-matching matrix is first computed. Lots of pairwise distance computation of elements can then be avoided by applying the filtering algorithm on the block-wise e-matching matrix.Extensive experiments on l-e-join of motion capture sequences are conducted. The results confirm the efficiency and effectiveness of our proposed algorithm in processing l-e-join of motion capture time series.
17434449
On Two Multigrid Algorithms for Modeling Variational Multiphase Image Segmentation
In this paper, we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan. We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smoother which leads to a new and more effective smoother. Although MG1 is found many magnitudes faster than the fast method of additive operator splitting (AOS), both algorithms are not robust with regard to the initial guess. To overcome this dependence on the initial guess, we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the Chan-Vese two-phase model; our algorithm II solves this model by a multigrid algorithm (MG2). Numerical experiments show that both algorithms are efficient and in particular MG2 is more robust than MG1 with respect to initial guesses. AMS subject classifications: 68U10, 65F10, 65K10.
16909772
On the use of nearest feature line for speaker identification
As a new pattern classification method, nearest feature line (NFL) provides an effective way to tackle the sort of pattern recognition problems where only limited data are available for training. In this paper, we explore the use of NFL for speaker identification in terms of limited data and examine how the NFL performs in such a vexing problem of various mismatches between training and test. In order to speed up NFL in decision-making, we propose an alternative method for similarity measure. We have applied the improved NFL to speaker identification of different operating modes. Its text-dependent performance is better than the dynamic time warping (DTW) on the Ti46 corpus, while its computational load is much lower than that of DTW. Moreover, we propose an utterance partitioning strategy used in the NFL for better performance. For the text-independent mode, we employ the NFL to be a new similarity measure in vector quantization (VQ), which causes the VQ to perform better on the KING corpus. Some computational issues on the NFL are also discussed in this paper.
3106142
MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Online Solution of Linear Time-Varying Matrix Equation AXB-C=0
Different from gradient neural networks (GNN), a special kind ofrecurrent neural networks has been proposed recently by Zhanget alfor solving online linear matrix equations withtime-varying coefficients. Such recurrent neural networks, designedbased on a matrix-valued error-function, could achieve globalexponential convergence when solving online time-varying problemsin comparison with gradient neural networks. This paperinvestigates the MATLAB simulation of Zhang neural networks (ZNN)for real-time solution of linear time-varying matrix equationAXB- C= 0. Gradient neural networks aresimulated and compared as well. Simulation results substantiate thetheoretical analysis and efficacy of ZNN on linear time-varyingmatrix equation solving.