Isomorphic factorization, the Kronecker product and the line digraph

In this paper, we investigate isomorphic factorizations of the Kronecker product graphs. Using these relations, it is shown that (1) the Kronecker product of the d-out-regular digraph and the complete symmetric digraph is factorized into the line digraph, (2) the Kronecker product of the Kautz digraph and the de Bruijn digraph is factorized into the Kautz digraph, (3) the Kronecker product of binary generalized de Bruijn digraphs is factorized into the binary generalized de Bruijn digraph.     

A parallel algorithm to construct a dominance graph on nonoverlapping rectangles

A parallel algorithm to generate the dominance graph on a collection of nonoverlapping iso-oriented rectangles is presented. This graph arises from the constraint graph commonly used in compaction algorithms for VLSI circuits. The dominance graph expresses the notion of aboveness on a collection of nonoverlapping rectangles: it is the directed graph which contains an edge from a rectangleb to rectanglec iffc is immediately aboveb. The algorithm is based on the divide and conquer paradigm; in the EREW PRAM model, it has time complexityO(log² n), usingn/logn processors. Its processor-time product isO(nlogn), which is optimal.     

A graph isomorphism algorithm for object recognition

We present an algorithm to solve the graph isomorphism problem for the purpose of object recognition. Objects, such as those which exist in a robot workspace, may be represented by labelled graphs (graphs with attributes on their nodes and/or edges). Thereafter, object recognition is achieved by matching pairs of these graphs. Assuming that all objects are sufficiently different so that their corresponding representative graphs are distinct, then given a new graph, the algorthm efficiently finds the isomorphic stored graph (if it exists). The algorithm consists of three phases: preprocessing, link construction, and ambiguity resolution. Results from experiments on a wide variety and sizes of graphs are reported. Results are also reported for experiments on recognising graphs that represent protein molecules. The algorithm works for all types of graphs except for a class of highly ambiguous graphs which includes strongly regular graphs. However, members of this class are detected in polynomial time, which leaves the option of switching to a higher complexity algorithm if desired.     

A time-optimal distributed sorting algorithm on a line network

We have achieved a strict lower time bound of n−1 for distributed sorting on a line network, where n is the number of processes. The lower time bound has traditionally been considered to be n because it is proved based on the number of disjoint comparison-exchange operations in parallel sorting on a linear array. Our result has overthrown the traditional common belief.     

An efficient parallel graph edge matching algorithm and its applications

A fast and efficient parallel algorithm for finding a maximal edge matching in an undirected graphG(V,E) is proposed.It runs in O(log n)time with O(m,/log n n)processors on an EREW PRAM for a class of graph set П,where n=|V|,m=|E|and П includes at least (i)planar graphs;(ii) graphs of bounded genus;and (iii)graphs of bounded maximum degress and so on.Our algorithm improves the previously known best algorithms by a factor of logn in the time complexity with linear number of processors on EREW PRAMs when the input is limited to П.     

A practical approximation algorithm for the LMS line estimator

The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Robust estimators are widely used because of their lack of sensitivity to outlying data points. The least median-of-squares (LMS) regression line estimator is among the best known robust estimators. Given a set of n points in the plane, it is defined to be the line that minimizes the median squared residual or, more generally, the line that minimizes the residual of any given quantile q, where 0<q?1. This problem is equivalent to finding the strip defined by two parallel lines of minimum vertical separation that encloses at least half of the points.The best known exact algorithm for this problem runs in O(n²) time. We consider two types of approximations, a residual approximation, which approximates the vertical height of the strip to within a given error bound ε_r?0, and a quantile approximation, which approximates the fraction of points that lie within the strip to within a given error bound ε_q?0. We present two randomized approximation algorithms for the LMS line estimator. The first is a conceptually simple quantile approximation algorithm, which given fixed q and ε_q>0 runs in O(nlogn) time. The second is a practical algorithm, which can solve both types of approximation problems or be used as an exact algorithm. We prove that when used as a quantile approximation, this algorithm's expected running time is . We present empirical evidence that the latter algorithm is quite efficient for a wide variety of input distributions, even when used as an exact algorithm.     

面向图分割问题的确定性退火控制算法

图分割问题是一种典型的NP-hard 问题, 如何对其进行高效求解一直都是学界和工业界的一个难题. 本文构建了一种新型的确定性退火控制算法, 提供了图分割问题的一种高质量近似解法. 算法主要由两部分构成: 全局收敛的迭代过程以及屏障函数最小点组成的收敛路径. 我们证明了,当屏障因子从足够大的实数降为0, 沿着一系列由屏障问题最小点组成的收敛路径可以得到图分割问题的一种高质量的近似解. 仿真计算结果表明本文所构建算法相比已有方法的优越性     

A parallel implementation of the douglas-peucker line simplification algorithm

As parallel machines become more widely available, many existing algorithms are being converted to take advantage of the improved speed offered by such computers. However, the method by which the algorithm is distributed is crucial towards obtaining the speed-ups required for many real-time tasks. This paper presents three parallel implementations of the Douglas—Peucker line simplification algorithm on a Sequent Symmetry computer and compares the performance of each with the original sequential algorithm.     

Bipartite output consensus in networked multi-agent systems of high-order power integrators with signed digraph and input noises

In this paper, we concentrate on investigating bipartite output consensus in networked multi-agent systems of high-order power integrators. Systems with power integrator are ubiquitous among weakly coupled, unstable and underactuated mechanical systems. In the presence of input noises, an adaptive disturbance compensator and a technique of adding power integrator are introduced to the complex nonlinear multi-agent systems to reduce the deterioration of system performance. Additionally, due to the existence of negative communication weights among agents, whether bipartite output consensus of high-order power integrators can be achieved remains unknown. Therefore, it is of great importance to study this issue. The underlying idea of designing the distributed controller is to combine the output information of each agent itself and its neighbours, the state feedback within its internal system and input adaptive noise compensator all together. When the signed digraph is structurally balanced, bipartite output consensus can be reached. Finally, numerical simulations are provided to verify the validity of the developed criteria.     

A genetic algorithm for a single hoist scheduling in the printed-circuit-board electroplating line

In this paper, the problem of determining cyclic schedules for a material handling hoist in the printed-circuit-board(PCB) electroplating line is considered. The objective of this research is to determine an optimal simple-cycle schedule of the hoist which in turn maximizes the line throughput rate. Previous approaches to the cyclic hoist scheduling problem are all mathematical programming-based approaches to develop cyclic schedules(Mixed Integer Programming, Linear Programming based Branch and Bound, Branch and Bound Search Method and so on). In this paper, a genetic algorithm-based approach for a single hoist scheduling in the PCB electroplating line is described. Through an experiment for the well known example data, the proposed algorithm is shown to be more efficient than the previous mathematical programming-based algorithm.     

A Hough transform based line recognition method utilizing both parameter space and image space

Hough Transform (HT) is recognized as a powerful tool for graphic element extraction from images due to its global vision and robustness in noisy or degraded environment. However, the application of HT has been limited to small-size images for a long time. Besides the well-known heavy computation in the accumulation, the peak detection and the line verification become much more time-consuming for large-size images. Another limitation is that most existing HT-based line recognition methods are not able to detect line thickness, which is essential to large-size images, usually engineering drawings. We believe these limitations arise from that these methods only work on the HT parameter space. This paper therefore proposes a new HT-based line recognition method, which utilizes both the HT parameter space and the image space. The proposed method devises an image-based gradient prediction to accelerate the accumulation, introduces a boundary recorder to eliminate redundant analyses in the line verification, and develops an image-based line verification algorithm to detect line thickness and reduce false detections as well. It also proposes to use pixel removal to avoid overlapping lines instead of rigidly suppressing the N×N neighborhood. We perform experiments on real images with different sizes in terms of speed and detection accuracy. The experimental results demonstrate the significant performance improvement, especially for large-size images.     

基于图染色问题的混合优化算法

为了提高图染色算法的寻优能力和收敛速度,结合禁忌搜索算法和遗传算法的优缺点,提出了一种混合优化算法（GA-HM）。该算法利用遗传算法生成初始解,将染色元素分到不同的色集中,然后通过禁忌算法进行变领域搜索来更新顶点染色。实验结果表明,GA-HM对求解相同的目标解具有更好的全局最优性和收敛性。     

A parallel algorithm for graph matching and its MasParimplementation

Search of discrete spaces is important in combinatorial optimization. Such problems arise in artificial intelligence, computer vision, operations research, and other areas. For realistic problems, the search spaces to be processed are usually huge, necessitating long computation times, pruning heuristics, or massively parallel processing. We present an algorithm that reduces the computation time for graph matching by employing both branch-and-bound pruning of the search tree and massively-parallel search of the as-yet-unpruned portions of the space. Most research on parallel search has assumed that a multiple-instruction-stream/multiple-data-stream (MIMD) parallel computer is available. Since massively parallel stream (SIMD) computers are much less expensive than MIMD systems with equal numbers of processors, the question arises as to whether SIMD systems can efficiently handle state-space search problems. We demonstrate that the answer is yes, and in particular, that graph matching has a natural and efficient implementation on SIMD machines     

A parametric filtering algorithm for the graph isomorphism problem

We introduce a new filtering algorithm, called IDL(d)-filtering, for a global constraint dedicated to the graph isomorphism problem—the goal of which is to decide if two given graphs have an identical structure. The basic idea of IDL(d)-filtering is to label every vertex with respect to its relationships with other vertices around it in the graph, and to use these labels to filter domains by removing values that have different labels. IDL(d)-filtering is parameterized by a positive integer value d which gives a limit on the distance between a vertex to be labelled and the set of vertices considered to build its label. We experimentally compare different instantiations of IDL(d)-filtering with state-of-the-art dedicated algorithms and show that IDL(d)-filtering is more efficient on regular sparse graphs and competitive on other kinds of graphs.     

A Line Extraction Algorithm for Hand Drawings

This paper presents an algorithm for extracting lines from hand drawings.It starts from contour pixel tracing,fits them into contour segments,and then extracts skeleton lines from the contour segments.The algorithm finds all contours in one scan of the input matrix without detecting and marking multiple pixels.In line extraction,the method Elastic Contour Segment Tracing is proposed which extracts lines by referring to the contour segments at both sides,overcoming noise and passing through blotted areas by fitting and extrapolation. Experiments on free hand mechanical drawings,sketches,letter/numerals,as well as Chinese characters are carried out and satisfactory results are achieved.     

Finding the closed partition of a planar graph

In this paper we consider the problem of finding aclosed partition in a directed graph. This problem has applications in concurrent probabilistic program verification. The best sequential algorithm known for this problem runs inO(mn) time wherem is the number of directed edges andn is the number of vertices in the given digraph. In this paper we present a linear-time sequential algorithm to solve the closed partition problem for planar digraphs that arecompact. We then build on this algorithm to obtain an O(n^1.5)-time sequential algorithm to solve the closed partition problem for a general planar digraph.This work was supported in part by NSF Grant CCR 89-10707.     

A line clipping algorithm and its analysis

One of the classical problems of Computer Graphics: line clipping against a rectangle is revisited. Coordinate raster refinement and some unusual forms of the parametric equation of the line are used to develop formulae for a line clipping algorithm. The algorithm is first presented in a form, where clarity of presentation is the prime concern. It is then transformed into one big nested branch, which after optimisation is assumed to be the most efficient form with a heavy cost on size. It is assumed that any mathematical consideration of the clipping problem would after a similar optimisation lead to a branching structure of equal complexity and speed. Line clipping thus belongs to the class of problems for which after a proper mathematical and logical analysis automatic program transformations may do the rest. This work has been supported by a grant from the Hungarian Academy of Sciences, Project No. OTKA 2572/1991