A new approximation algorithm for labeling points with circle pairs

We study the NP-hard problem of labeling points with maximum-radius circle pairs: given n point sites in the plane, find a placement for 2n interior-disjoint uniform circles, such that each site touches two circles and the circle radius is maximized. We present a new approximation algorithm for this problem that runs in time and O(n) space and achieves an approximation factor of (≈1.486+ε), which improves the previous best bound of 1.491+ε.     

A self-stabilizing algorithm for the maximum planarization problem in complete bipartite networks

The maximum planarization problem is to find a spanning planar subgraph having the largest number of edges for a given graph. In this paper, we propose a self-stabilizing algorithm to solve this problem for complete bipartite networks. The proposed algorithm finds the maximum planar subgraph of 2n−4 edges in O(n) rounds, where n is the number of nodes.     

An output sensitive algorithm for computing a maximum independent set of a circle graph

We present an output sensitive algorithm for computing a maximum independent set of an unweighted circle graph. Our algorithm requires O(nmin{d,α}) time at worst, for an n vertex circle graph where α is the independence number of the circle graph and d is its density. Previous algorithms for this problem required Θ(nd) time at worst.     

A simple factor-3 approximation for labeling points with circles

In this paper we present a simple factor-(3+ε), 0<ε<1, approximation algorithm, which runs in O(nlogn+n(1/ε)^O(1/ε2)log(D₃/εD₂)) time, for the problem of labeling a set P of n distinct points with uniform circles. (D₂ is the closest pair of P and D₃ is the minimum diameter of all subsets of P with size three.) This problem is known to be NP-hard. Our bound improves the previous factor of 3.6+ε.     

New Linear-Time Algorithms for Edge-Coloring Planar Graphs

We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree Δ with max {Δ,9} colors. Thus the coloring is optimal for graphs with maximum degree Δ≥9. Moreover for Δ=4,5,6 we give linear-time algorithms that use Δ+2 colors. These results improve over the algorithms of Chrobak and Yung (J. Algorithms 10:35–51, 1989) and of Chrobak and Nishizeki (J. Algorithms 11:102–116, 1990) which color planar graphs using max {Δ,19} colors in linear time or using max {Δ,9} colors in time. R. Cole supported in part by NSF grants CCR0105678 and CCF0515127 and IDM0414763. Ł. Kowalik supported in part by KBN grant 4T11C04425. Part of this work was done while Ł. Kowalik was staying at the Max Planck Institute in Saarbruecken, Germany.     

A fast heuristic for quay crane scheduling with interference constraints

This paper considers the problem of scheduling quay cranes which are used at sea port container terminals to load and unload containers. This problem is studied intensively in a recent stream of research but still lacks a correct treatment of crane interference constraints. We present a revised optimization model for the scheduling of quay cranes and propose a heuristic solution procedure. At its core a Branch-and-Bound algorithm is applied for searching a subset of above average quality schedules. The heuristic takes advantage from efficient criteria for branching and bounding the search with respect to the impact of crane interference. Although the used techniques are quite standard, the new heuristic produces much better solutions in considerably shorter run times than all algorithms known from the literature.     

A maximum independent set approach for collusion detection in voting pools

From agreement problems to replicated software execution, we frequently find scenarios with voting pools. Unfortunately, Byzantine adversaries can join and collude to distort the results of an election. We address the problem of detecting these colluders, in scenarios where they repeatedly participate in voting decisions. We investigate different malicious strategies, such as naïve or colluding attacks, with fixed identifiers or in whitewashing attacks. Using a graph-theoretic approach, we frame collusion detection as a problem of identifying maximum independent sets. We then propose several new graph-based methods and show, via analysis and simulations, their effectiveness and practical applicability for collusion detection.     

低度图的最大团求解算法

在图的最大团问题中,当图的顶点数不大于阈值m时,很容易求解其最大团问题,求解算法的时间复杂度为O(d)。给出一种求解低度图的最大团的确定性算法。该算法通过对图按顶点逐步分解实现分别计算,较好地解决低度图的最大团问题。算法时间复杂度为O(d&#8226;n3)。其中,n表示图的顶点数,图中顶点的最大度小于m或者图可以通过逐个删除度小于m的顶点而使所有顶点的度都小于m。     

基于Hopcroft-Tarjan判定算法的平面图嵌入算法

给出了一个基于Hopcroft-Tarjan平面图判定算法的平面图嵌入算法，并具体实现了该算法。与其它基于Hopcroft-Tarjian平面图判定算法的嵌入算法的实现方法相比，该方法更容易实现，并且判定和嵌入同时完成。     

基于三角环的顶点着色问题解法

图的着色问题是一个NP难问题,本文着重探讨无向图的顶点的三色问题,提出了用构造三角环的极大独立集方法判断并尝试给出顶点三色问题的可行解,解决了顶点三色的可满足性问题,克服了以前图遍历过程中的回溯问题,以及由此推论顶点四色和五色问题的极大独立集。     

基于双向标注融合的汉语最长短语识别方法

汉语最长短语（最长名词短语和介词短语）具有显著的语言学特点.采用基于分类器的确定性标注方法进行双向标注,其结果能够显示最长短语识别在汉语句子正（由左至右）反（由右至左）2个方向上的互补性.基于此,利用确定性的双向标注技术来识别汉语最长短语,并提出了一种基于“分歧点”的概率融合策略以融合该双向标注结果.实验表明,这一融合算法能够有效发掘这2个方向的互补特性,从而获得较好的短语识别效果.     

Approximating minimum coloring and maximum independent set in dotted interval graphs

Dotted interval graphs are introduced by Aumann et al. as a generalization of interval graphs. We study two optimization problems in dotted interval graphs that find application in high-throughput genotyping. We present improved approximations for minimum coloring and the first approximation for maximum independent set in dotted interval graphs.     

A linear algorithm to find a rectangular dual of a planar triangulated graph

We develop anO(n) algorithm to construct a rectangular dual of ann-vertex planar triangulated graph.This research was supported in part by the National Science Foundation under Grant MCS-83-05567.     

A strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs

In recent years growing interest in local distributed algorithms has widely been observed. This results from their high resistance to errors and damage, as well as from their good performance, which is independent of the size of the network. A local deterministic distributed algorithm finding an approximation of a Minimum Dominating Set in planar graphs has been presented by Lenzen et al., and they proved that the algorithm returns a 130-approximation of the Minimum Dominating Set. In this article we will show that the algorithm is two times more effective than was previously assumed, and we prove that the algorithm by Lenzen et al. outputs a 52-approximation to a Minimum Dominating Set. Therefore the gap between the lower bound and the approximation ratio of the best yet local deterministic distributed algorithm is reduced by half.     

Elliptic Gabriel graph for finding neighbors in a point set and its application to normal vector estimation

Point-based shape representation has received increased attention in recent years, mainly due to its simplicity. One of the most fundamental operations for point set processing is to find the neighbors of each point. Mesh structures and neighborhood graphs are commonly used for this purpose. However, though meshes are very popular in the field of computer graphics, neighbor relations encoded in a mesh are often distorted. Likewise, neighborhood graphs, such as the minimum spanning tree (MST), relative neighborhood graph (RNG), and Gabriel graph (GG), are also imperfect as they usually give too few neighbors for a given point. In this paper, we introduce a generalization of Gabriel graph, named elliptic Gabriel graph (EGG), which takes an elliptic influence region instead of the circular region in GG. In order to determine the appropriate aspect ratio of the elliptic influence region of EGG, this paper also presents the analysis between the aspect ratio of the elliptic influence region and the average valence of the resulting neighborhood. Analytic and empirical test results are included.     

A spectral clustering algorithm for manufacturing cell formation

A graph clustering algorithm constructs groups of closely related parts and machines separately. After they are matched for the least intercell moves, a refining process runs on the initial cell formation to decrease the number of intercell moves. A simple modification of this main approach can deal with some practical constraints, such as the popular constraint of bounding the maximum number of machines in a cell. Our approach makes a big improvement in the computational time. More importantly, improvement is seen in the number of intercell moves when the computational results were compared with best known solutions from the literature.     

A refined search tree technique for Dominating Set on planar graphs

We establish a refined search tree technique for the parameterized DOMINATING SET problem on planar graphs. Here, we are given an undirected graph and we ask for a set of at most k vertices such that every other vertex has at least one neighbor in this set. We describe algorithms with running times O(8^kn) and O(8^kk+n³), where n is the number of vertices in the graph, based on bounded search trees. We describe a set of polynomial time data-reduction rules for a more general “annotated” problem on black/white graphs that asks for a set of k vertices (black or white) that dominate all the black vertices. An intricate argument based on the Euler formula then establishes an efficient branching strategy for reduced inputs to this problem. In addition, we give a family examples showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final search tree algorithm is easy to implement; its analysis, however, is involved.     

A fast algorithm for one-unit ICA-R

Independent component analysis (ICA) aims to recover a set of unknown mutually independent source signals from their observed mixtures without knowledge of the mixing coefficients. In some applications, it is preferable to extract only one desired source signal instead of all source signals, and this can be achieved by a one-unit ICA technique. ICA with reference (ICA-R) is a one-unit ICA algorithm capable of extracting an expected signal by using prior information. However, a drawback of ICA-R is that it is computationally expensive. In this paper, a fast one-unit ICA-R algorithm is derived. The reduction of the computational complexity for the ICA-R algorithm is achieved through (1) pre-whitening the observed signals; and (2) normalizing the weight vector. Computer simulations were performed on synthesized signals, a speech signal, and electrocardiograms (ECG). Results of these analyses demonstrate the efficiency and accuracy of the proposed algorithm.