Link scheduling in wireless sensor networks: Distributed edge-coloring revisited

We consider the problem of link scheduling in a sensor network employing a TDMA MAC protocol. Our algorithm consists of two phases. The first phase involves edge-coloring: an assignment of a color to each edge in the network such that no two edges incident on the same node are assigned the same color. Our main result for the first phase is a distributed edge-coloring algorithm that needs at most (Δ+1) colors, where Δ is the maximum degree of the network. To our knowledge, this is the first distributed algorithm that can edge-color a graph using at most (Δ+1) colors. The second phase uses the edge-coloring solution for link scheduling. We map each color to a unique timeslot and attempt to assign a direction of transmission along each edge such that the hidden terminal problem is avoided; an important result we obtain is a characterization of network topologies for which such an assignment exists. Next, we consider topologies for which a feasible transmission assignment does not exist for all edges, and obtain such an assignment using additional timeslots. Finally, we show that reversing the direction of transmission along every edge leads to another feasible direction of transmission. Using both the transmission assignments, we obtain a TDMA MAC schedule which enables two-way communication between every pair of adjacent sensor nodes. For acyclic topologies, we prove that at most 2(Δ+1) timeslots are required. Results for general topologies are demonstrated using simulations; for sparse graphs, we show that the number of timeslots required is around 2(Δ+1). We show that the message and time complexity of our algorithm is O(nΔ²+n²m), where n is the number of nodes and m is the number of edges in the network. Through simulations, we demonstrate that the energy consumption of our solution increases linearly with Δ. We also propose extensions to account for non-ideal radio characteristics.     

Distributed edge coloration for bipartite networks

This paper presents a self-stabilizing algorithm to color the edges of a bipartite network such that any two adjacent edges receive distinct colors. The algorithm has the self-stabilizing property; it works without initializing the system. It also works in a de-centralized way without a leader computing a proper coloring for the whole system. Moreover, it finds an optimal edge coloring and its time complexity is O(n ² k + m) moves, where k is the number of edges that are not properly colored in the initial configuration. This is a completely revised and extended version of [15]. This research was supported in part by the National Science Council of the Republic of China under the Contract NSC94-2213-E008-001.     

Images as Embedded Maps and Minimal Surfaces: Movies,Color, Texture,and Volumetric Medical Images

We extend the geometric framework introduced in Sochen et al. (IEEE Trans. on Image Processing, 7(3):310–318, 1998) for image enhancement. We analyze and propose enhancement techniques that selectively smooth images while preserving either the multi-channel edges or the orientation-dependent texture features in them. Images are treated as manifolds in a feature-space. This geometrical interpretation lead to a general way for grey level, color, movies, volumetric medical data, and color-texture image enhancement.We first review our framework in which the Polyakov action from high-energy physics is used to develop a minimization procedure through a geometric flow for images. Here we show that the geometric flow, based on manifold volume minimization, yields a novel enhancement procedure for color images. We apply the geometric framework and the general Beltrami flow to feature-preserving denoising of images in various spaces.Next, we introduce a new method for color and texture enhancement. Motivated by Gabor's geometric image sharpening method (Gabor, Laboratory Investigation, 14(6):801–807, 1965), we present a geometric sharpening procedure for color images with texture. It is based on inverse diffusion across the multi-channel edge, and diffusion along the edge.     

On-Line Edge-Coloring with a Fixed Number of Colors

Abstract. We investigate a variant of on-line edge-coloring in which there is a fixed number of colors available and the aim is to color as many edges as possible. We prove upper and lower bounds on the performance of different classes of algorithms for the problem. Moreover, we determine the performance of two specific algorithms, First-Fit and Next-Fit . Specifically, algorithms that never reject edges that they are able to color are called fair algorithms. We consider the four combinations of fair/ not fair and deterministic/ randomized. We show that the competitive ratio of deterministic fair algorithms can vary only between approximately 0.4641 and 1/2, and that Next-Fit is worst possible among fair algorithms. Moreover, we show that no algorithm is better than 4/7-competitive. If the graphs are all k -colorable, any fair algorithm is at least 1/2-competitive. Again, this performance is matched by Next-Fit while the competitive ratio for First-Fit is shown to be k/(2k-1) , which is significantly better, as long as k is not too large.     

Multi‐view 3‐D display employing a flat‐panel display with slanted pixel arrangement

Abstract— A flat‐panel display with a slanted subpixel arrangement has been developed for a multi‐view three‐dimensional (3‐D) display. A set of 3M × N subpixels (M × N subpixels for each R, G, and B color) corresponds to one of the cylindrical lenses, which constitutes a lenticular lens, to construct each 3‐D pixel of a multi‐view display that offers M × N views. Subpixels of the same color in each 3‐D pixel have different horizontal positions, and the R, G, and B subpixels are repeated in the horizontal direction. In addition, the ray‐emitting areas of the subpixels within a 3‐D pixel are continuous in the horizontal direction for each color. One of the vertical edges of each subpixel has the same horizontal position as the opposite vertical edge of another subpixel of the same color. Cross‐talk among viewing zones is theoretically zero. This structure is suitable for providing a large number of views. A liquid‐crystal panel having this slanted subpixel arrangement was fabricated to construct a mobile 3‐D display with 16 views and a 3‐D resolution of 256 × 192. A 3‐D pixel is comprised of 12 × 4 subpixels (M = 4 and N = 4). The screen size was 2.57 in.     

CODON: On Orchestrating Cross-Domain Attentions for Depth Super-Resolution

The ready accessibility of high-resolution image sensors has stimulated interest in increasing depth resolution by leveraging paired color information as guidance. Nevertheless, how to effectively exploit the depth and color features to achieve a desired depth super-resolution effect remains challenging. In this paper, we propose a novel depth super-resolution method called CODON, which orchestrates cross-domain attentive features to address this problem. Specifically, we devise two essential modules: the recursive multi-scale convolutional module (RMC) and the cross-domain attention conciliation module (CAC). RMC discovers detailed color and depth features by sequentially stacking weight-shared multi-scale convolutional layers, in order to deepen and widen the network at low-complexity. CAC calculates conciliated attention from both domains and uses it as shared guidance to enhance the edges in depth feature while suppressing textures in color feature. Then, the jointly conciliated attentive features are combined and fed into a RMC prediction branch to reconstruct the high-resolution depth image. Extensive experiments on several popular benchmark datasets including Middlebury, New Tsukuba, Sintel, and NYU-V2, demonstrate the superiority of our proposed CODON over representative state-of-the-art methods.

     

On the Parameterized Complexity of Layered Graph Drawing

We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case either the total span or the maximum span of edges can be minimized. In contrast to the Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers. Research initiated at the International Workshop on Fixed Parameter Tractability in Graph Drawing, Bellairs Research Institute of McGill University, Holetown, Barbados, Feb. 9–16, 2001, organized by S. Whitesides. Research of Canada-based authors is supported by NSERC; research of Quebec-based authors is also supported by a grant from FCAR. Research of D.R. Wood completed while visiting McGill University. Research of G. Liotta supported by CNR and MURST.     

Algorithmic Aspects of Acyclic Edge Colorings

Abstract. A proper coloring of the edges of a graph G is called acyclic if there is no two-colored cycle in G . The acyclic edge chromatic number of G , denoted by a'(G) , is the least number of colors in an acyclic edge coloring of G . For certain graphs G , a'(G)\geq Δ(G)+2 where Δ(G) is the maximum degree in G . It is known that a'(G)≤ Δ + 2 for almost all Δ -regular graphs, including all Δ -regular graphs whose girth is at least cΔ log Δ . We prove that determining the acyclic edge chromatic number of an arbitrary graph is an NP-complete problem. For graphs G with sufficiently large girth in terms of Δ(G) , we present deterministic polynomial-time algorithms that color the edges of G acyclically using at most Δ(G)+2 colors.     

Finding Maximum Induced Matchings in Subclasses of Claw-Free and <Emphasis Type="Italic">P</Emphasis><Subscript>5</Subscript>-Free Graphs,and in Graphs with Matching and Induced Matching of Equal Maximum Size

In a graph G a matching is a set of edges in which no two edges have a common endpoint. An induced matching is a matching in which no two edges are linked by an edge of G. The maximum induced matching (abbreviated MIM) problem is to find the maximum size of an induced matching for a given graph G. This problem is known to be NP-hard even on bipartite graphs or on planar graphs. We present a polynomial time algorithm which given a graph G either finds a maximum induced matching in G, or claims that the size of a maximum induced matching in G is strictly less than the size of a maximum matching in G. We show that the MIM problem is NP-hard on line-graphs, claw-free graphs, chair-free graphs, Hamiltonian graphs and r-regular graphs for r \geq 5. On the other hand, we present polynomial time algorithms for the MIM problem on (P ₅,D _m )-free graphs, on (bull, chair)-free graphs and on line-graphs of Hamiltonian graphs.     

结合四元数与最小核值相似区的边缘检测

目的 针对传统彩色图像边缘检测方法中未充分利用图像色度信息、颜色模型间非线性转换过程中时间和空间的大量耗费、算法实现复杂等问题,将四元数引入最小核值相似区（SUSAN）算法中,提出一种RGB空间下的结合四元数与最小核值相似区的边缘检测算法。方法 该算法首先对彩色图像进行四元数描述,然后用改进的SUSAN算子进行边缘检测。针对其中单一几何阈值g的限制,以及检测出的边缘较粗等问题,本文采用Otsu算法自适应获取双几何阈值,再对弱边缘点集进行边缘生长,最后根据USAN重心及其对称最长轴来确定边缘局部方向,实现对边缘点的局部非极大值抑制,得到最终细化后的边缘图像。结果 实验选取1幅合成彩色图像及3幅标准图像库图像,与彩色Canny算法、SUSAN算法,及采用单阈值的本文算法进行对比,并采用Pratt品质因数衡量边缘定位精度。本文算法能够检测出亮度相近的不同颜色区域之间的边缘,且提取的边缘比较连续、细致,漏检边缘较少。与公认边缘检测效果较好的彩色Canny算法相比,本文算法的品质因数提高了0.012 0,耗时缩短了2.527 9 s。结论 本文提出了一种结合四元数与最小核值相似区的边缘检测算法,实现了四元数与SUSAN算子的有效融合。实验结果表明,该算法能够提高边缘定位精度,对弱噪声具有较好的抑制能力,适用于对实时性要求不高的低层次彩色图像处理。     

纹理边缘引导的深度图像超分辨率重建

目的 深度图像作为一种普遍的3维场景信息表达方式在立体视觉领域有着广泛的应用。Kinect深度相机能够实时获取场景的深度图像,但由于内部硬件的限制和外界因素的干扰,获取的深度图像存在分辨率低、边缘不准确的问题,无法满足实际应用的需要。为此提出了一种基于彩色图像边缘引导的Kinect深度图像超分辨率重建算法。方法 首先对深度图像进行初始化上采样,并提取初始化深度图像的边缘;进一步利用高分辨率彩色图像和深度图像的相似性,采用基于结构化学习的边缘检测方法提取深度图的正确边缘;最后找出初始化深度图的错误边缘和深度图正确边缘之间的不可靠区域,采用边缘对齐的策略对不可靠区域进行插值填充。结果 在NYU2数据集上进行实验,与8种最新的深度图像超分辨率重建算法作比较,用重建之后的深度图像和3维重建的点云效果进行验证。实验结果表明本文算法在提高深度图像的分辨率的同时,能有效修正上采样后深度图像的边缘,使深度边缘与纹理边缘对齐,也能抑制上采样算法带来的边缘模糊现象;3维点云效果显示,本文算法能准确区分场景中的前景和背景,应用于3维重建等应用能取得较其他算法更好的效果。结论 本文算法普遍适用于Kinect深度图像的超分辨率重建问题,该算法结合同场景彩色图像与深度图像的相似性,利用纹理边缘引导深度图像的超分辨率重建,可以得到较好的重建结果。     

A scheme for edge-based multi-focus Color image fusion

In this paper, a novel region-based multi-focus color image fusion method is proposed, which employs the focused edges extracted from the source images to obtain a fused image with better focus. At first, the edges are obtained from the source images, using two suitable edge operators (Zero-cross and Canny). Then, a block-wise region comparison is performed to extract out the focused edges which have been morphologically dilated, followed by the selection of the largest component to remove isolated points. Any discontinuity in the detected edges is removed by consulting with the edge detection output from the Canny edge operator. The best reconstructed edge image is chosen, which is later converted into a focused region. Finally, the fused image is constructed by selecting pixels from the source images with the help of a prescribed color decision map. The proposed method has been implemented and tested on a set of real 2-D multi-focus image pairs (both gray-scale and color). The algorithm has a competitive performance with respect to the recent fusion methods in terms of subjective and objective evaluation.

     

Optimal fault-tolerant Hamiltonicity of star graphs with conditional edge faults

The star graph is viewed as an attractive alternative to the hypercube. In this paper, we investigate the Hamiltonicity of an n-dimensional star graph. We show that for any n-dimensional star graph (n≥4) with at most 3n−10 faulty edges in which each node is incident with at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves on the previously best known result for the case where the number of tolerable faulty edges is bounded by 2n−7. We also demonstrate that our result is optimal with respect to the worst case scenario, where every other node of a cycle of length 6 is incident with exactly n−3 faulty noncycle edges.     

Coloring inductive graphs on-line

In this paper we consider the problem of on-line graph coloring. In an instance of on-line graph coloring, the nodes are presented one at a time. As each node is presented, its edges to previously presented nodes are also given. Each node must be assigned a color, different from the colors of its neighbors, before the next node is given. LetA(G) be the number of colors used by algorithmA on a graphG and letx(G) be the chromatic number ofG. The performance ratio of an on-line graph coloring algorithm for a class of graphsC is max_{G C(A(G)/(G))}. We consider the class ofd-inductive graphs. A graphG isd-inductive if the nodes ofG can be numbered so that each node has at mostd edges to higher-numbered nodes. In particular, planar graphs are 5-inductive, and chordal graphs arex(G)-inductive. First Fit is the algorithm that assigns each node the lowest-numbered color possible. We show that ifG isd-inductive, then First Fit usesO(d logn) colors onG. This yields an upper bound ofo(logn) on the performance ratio of First Fit on chordal and planar graphs. First Fit does as well as any on-line algorithm ford-inductive graphs: we show that, for anyd and any on-line graph coloring algorithmA, there is ad-inductive graph that forcesA to use (d logn) colors to colorG. We also examine on-line graph coloring with lookahead. An algorithm is on-line with lookaheadl, if it must color nodei after examining only the firstl+i nodes. We show that, forl/logn, the lower bound ofd logn colors still holds.This research was supported by an IBM Graduate Fellowship.     

基于双模式联合三边滤波器的深度图像超分辨率方法

彩色图像引导的深度图像超分辨率方法通过利用高分辨率彩色图像的高频信息来重建深度图像,取得了不错的重建效果,但当深度图像和彩色图像边缘不(完全)一致或彩色区域纹理丰富时,重建图像普遍存在边缘模糊和纹理拷贝问题.针对这一问题,提出一种边缘图像引导的双模式联合三边滤波器(DMJTF)方法.该方法利用单幅低分辨率深度图像构建了一个边缘图像金字塔字典,然后利用MRF模型构建了一个高分辨率边缘图像,该图像确定了滤波器的两种模式,分别用于重构深度图像的边缘和平滑区域.实验结果表明DMJTF算法有效地避免了纹理拷贝异常,降低了边缘模糊现象,在定性和定量两个方面都优于其他算法,取得了较好的超分效果.     

Constrained delaunay triangulations

Given a set ofn vertices in the plane together with a set of noncrossing, straight-line edges, theconstrained Delaunay triangulation (CDT) is the triangulation of the vertices with the following properties: (1) the prespecified edges are included in the triangulation, and (2) it is as close as possible to the Delaunay triangulation. We show that the CDT can be built in optimalO(n logn) time using a divide-and-conquer technique. This matches the time required to build an arbitrary (unconstrained) Delaunay triangulation and the time required to build an arbitrary constrained (non-Delaunay) triagulation. CDTs, because of their relationship with Delaunay triangulations, have a number of properties that make them useful for the finite-element method. Applications also include motion planning in the presence of polygonal obstacles and constrained Euclidean minimum spanning trees, spanning trees subject to the restriction that some edges are prespecified.An earlier version of the results presented here appeared in theProceedings of the Third Annual Symposium on Computational Geometry (1987).     

An efficient algorithm for line and polygon clipping

We present an algorithm for clipping a polygon or a line against a convex polygonal window. The algorithm demonstrates the practicality of various ideas from computational geometry. It spendsO(logp) time on each edge of the clipped polygon, wherep is the number of window edges, while the Sutherland-Hodgman algorithm spendsO(p) time per edge. Theoretical and experimental analyses show that the constants involved are small enough to make the algorithm competitive even for windows with four edges. The algorithm enables image-space clipping against windows whose boundaries are convex spline curves. The paper contains detailed pseudo-code implementation of the algorithm and an adaptation of the simulation of simplicity method for handling degenerate cases.     

Max-Stretch Reduction for Tree Spanners

A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t−1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G=(V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we show that it is -hard to decide, for a given graph G and its spanning tree of max-stretch t, whether or not one-edge insertion can decrease the max-stretch to t−1. (iv) Finally, we show that the max-stretch of an arbitrary graph on n vertices can be reduced to s′≥2 by inserting O(n/s′) edges, which can be determined in linear time, and observe that this number of edges is optimal up to a constant.     

Why Almost All k-Colorable Graphs Are Easy to Color

Coloring a k-colorable graph using k colors (k≥3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the uniform distribution over k-colorable graphs with n vertices and exactly cn edges, c greater than some sufficiently large constant. We rigorously show that all proper k-colorings of most such graphs lie in a single “cluster”, and agree on all but a small, though constant, portion of the vertices. We also describe a polynomial time algorithm that whp finds a proper k-coloring of such a random k-colorable graph, thus asserting that most such graphs are easy to color. This should be contrasted with the setting of very sparse random graphs (which are k-colorable whp), where experimental results show some regime of edge density to be difficult for many coloring heuristics.