The Schorr-Waite graph marking algorithm

Summary An explanation is given of the Schorr-Waite algorithm for marking all nodes of a directed graph that are reachable from one given node, using the axiomatic method.This research was supported by the National Science Foundation under Grant MCS76-22360     

The derivation of graph marking algorithms from distributed termination detection protocols

We show that on-the-fly garbage collection algorithms can be obtained by transforming distributed termination detection protocols. Virtually all known on-the-fly garbage collecting algorithms are obtained by applying the transformation. The approach leads to a novel and insightful derivation of, e.g., the concurrent garbage collection algorithms of Dijkstra et al. and of Hudak and Keller. The approach also leads to several new, highly parallel algorithms for concurrent garbage collection. We also analyze a garbage collecting system due to Hughes from our current perspective.     

Derivation of algorithms for cutwidth and related graph layout parameters

In this paper, we investigate algorithms for some related graph parameters. Each of these asks for a linear ordering of the vertices of the graph (or can be formulated as such), and constructive linear time algorithms for the fixed parameter versions of the problems have been published for several of these. Examples are cutwidth, pathwidth, and directed or weighted variants of these. However, these algorithms have complicated technical details. This paper attempts to present ideas in these algorithms in a different more easily accessible manner, by showing that the algorithms can be obtained by a stepwise modification of a trivial hypothetical non-deterministic algorithm. The methodology is applied to rederive known results for the cutwidth and the pathwidth problem, and obtain new results for several variants of these problems, like directed and weighted variants of cutwidth and modified cutwidth.     

Complexity of algorithms that construct subsets of data from formal definitions

Polynomial-time algorithms that construct subsets of data from formal logical definition are considered.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 49–57, September–October, 1991.     

FLASc: a formal algebra for labeled property graph schema

Automated Software Engineering - Mailing lists are a major communication channel for supporting developer coordination in open-source software projects. In a recent study, researchers explored...     

A graph grammar-based formal validation of object-process diagrams

Two basic requirements from a system’s conceptual model are correctness and comprehensibility. Most modeling methodologies satisfy only one of these apparently contradicting requirements, usually comprehensibility, leaving aside problems of correctness and ambiguousness that are associated with expressiveness. Some formal modeling languages do exist, but in these languages a complete model of a complex system is fairly complicated to understand. Object-process methodology (OPM) is a holistic systems modeling methodology that combines the two major aspects of a system—structure and behavior—in one model, providing mechanisms to manage the complexity of the model using refinement-abstraction operations, which divide a complex system into many interconnected diagrams. Although the basic syntax and semantics of an OPM model are defined, they are incomplete and leave room for incorrect or ambiguous models. This work advances the formal definition of OPM by providing a graph grammar for creating and checking OPM diagrams. The grammar provides a validation methodology of the semantic and syntactic correctness of a single object-process diagram.     

Inexact graph matching by means of estimation of distribution algorithms

Estimation of distribution algorithms (EDAs) are a quite recent topic in optimization techniques. They combine two technical disciplines of soft computing methodologies: probabilistic reasoning and evolutionary computing. Several algorithms and approaches have already been proposed by different authors, but up to now there are very few papers showing their potential and comparing them to other evolutionary computational methods and algorithms such as genetic algorithms (GAs). This paper focuses on the problem of inexact graph matching which is NP-hard and requires techniques to find an approximate acceptable solution. This problem arises when a nonbijective correspondence is searched between two graphs. A typical instance of this problem corresponds to the case where graphs are used for structural pattern recognition in images. EDA algorithms are well suited for this type of problems.

This paper proposes to use EDA algorithms as a new approach for inexact graph matching. Also, two adaptations of the EDA approach to problems with constraints are described as two techniques to control the generation of individuals, and the performance of EDAs for inexact graph matching is compared with the one of GAs.     

Unfolding semantics of graph transformation

Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper, we fully extend Winskel’s approach to single-pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of (semi-weighted) graph grammars and the category of prime algebraic domains, which factorises through the category of occurrence grammars and the category of asymmetric event structures. For general, possibly nonsemi-weighted single-pushout grammars, we define an analogous functorial concurrent semantics, which, however, is not characterised as an adjunction. Similar results can be obtained for double-pushout graph grammars, under the assumptions that nodes are never deleted.     

A novel clustering algorithm based on data transformation approaches

Clustering provides a knowledge acquisition method for intelligent systems. This paper proposes a novel data-clustering algorithm, by combining a new initialization technique, K-means algorithm and a new gradual data transformation approach to provide more accurate clustering results than the K-means algorithm and its variants by increasing the clusters’ coherence. The proposed data transformation approach solves the problem of generating empty clusters, which frequently occurs for other clustering algorithms. An efficient method based on the principal component transformation and a modified silhouette algorithm is also proposed in this paper to determine the number of clusters. Several different data sets are used to evaluate the efficacy of the proposed method to deal with the empty cluster generation problem and its accuracy and computational performance in comparison with other K-means based initialization techniques and clustering methods. The developed estimation method for determining the number of clusters is also evaluated and compared with other estimation algorithms. Significances of the proposed method include addressing the limitations of the K-means based clustering and improving the accuracy of clustering as an important method in the field of data mining and expert systems. Application of the proposed method for the knowledge acquisition in time series data such as wind, solar, electric load and stock market provides a pre-processing tool to select the most appropriate data to feed in neural networks or other estimators in use for forecasting such time series. In addition, utilization of the knowledge discovered by the proposed K-means clustering to develop rule based expert systems is one of the main impacts of the proposed method.     

The correctness of the Schorr-Waite list marking algorithm

Summary This paper presents a relatively simple proof of a nontrivial algorithm for marking all the nodes of a list structure. The proof separates properties of the algorithm from properties of the data on which it operates and is a significant application of the method of intermittent assertions.(This paper grew out of an earlier version which was submitted to this journal on October 16, 1974)     

Hearing the clusters of a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/eigenvector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies.     

Missing data imputation in multivariate data by evolutionary algorithms

This paper presents a proposal based on an evolutionary algorithm to impute missing observations in multivariate data. A genetic algorithm based on the minimization of an error function derived from their covariance matrix and vector of means is presented.All methodological aspects of the genetic structure are presented. An extended explanation of the design of the fitness function is provided. An application example is solved by the proposed method.     

数据和计算密集混合元任务的网格调度算法

网格计算技术是继Internet计算之后出现的新兴研究领域。网格系统由异构的资源组成,一个好的任务调度方法可以充分利用网格系统的处理能力,减少任务的完成时间。根据目前网格系统的使用模式,提出了符合实际的用户任务形式,即任务由数据传输和计算两部分组成,计算在获得所有输入之后开始执行。多个这样的独立任务组成元任务,作为调度程序的最小执行单位。在实际应用中,元任务应该由数据密集型和计算密集型任务混合组成。考虑到数据传输和计算的比例关系对元任务完成的影响,提出一种新的调度算法TCR,通过提高计算资源的利用率以及任务间的并行度,减少元任务的完成时间。详细介绍了该算法,并通过模拟结果的对比验证了该算法的良好性能。     

Correct transformation: From object-based graph grammars to PROMELA

Model transformation is an approach that, among other advantages, enables the reuse of existing analysis and implementation techniques, languages and tools. The area of formal verification makes wide use of model transformation because the cost of constructing efficient model checkers is extremely high. There are various examples of translations from specification and programming languages to the input languages of prominent model checking tools, like SPIN. However, this approach provides a safe analysis method only if there is a guarantee that the transformation process preserves the semantics of the original specification/program, that is, that the transformation is correct. Depending on the source and/or target languages, this notion of correctness is not easy to achieve. In this paper, we tackle this problem in the context of Object-Based Graph Grammars (OBGG). OBGG is a formal language suitable for the specification of distributed systems, with a variety of tools and techniques centered around the transformation of OBGG models. We describe in details the model transformation from OBGG models to PROMELA, the input language of the SPIN model checker. Amongst the contributions of this paper are: (a) the correctness proof of the transformation from OBGG models to PROMELA; (b) a generalization of this process in steps that may be used as a guide to prove the correctness of transformations from different specification/programming languages to PROMELA.     

Derivation of fast algorithms via binary filtering of signals

We present a new way to derive a fast algorithm realizing the discrete Walsh transform (DWT), which can be applied both in the traditional form, i.e., to a one-dimensional numerical array, and to a multi-dimensional array, as well as for a signal of a continuous argument in the form of a function or an image. The algorithm is presented as iterated application of the primitive discrete Haar transform (DHT) over two variables. Two standard ways of arranging the results of this simplest transform lead to the fast DWT in the Hadamard or Paley enumeration in the case of splitting the signal into equal parts. Application of the algorithm to analogous shifts of the periodic source signal results in longitudinal filtering of a signal via decomposing it into a sum of simpler signals. In an incomplete version of the last algorithm, we come to an analog of the fast DHT.     

Bridging the gap between formal semantics and implementation of triple graph grammars

The correctness of model transformations is a crucial element for model-driven engineering of high-quality software. A prerequisite to verify model transformations at the level of the model transformation specification is that an unambiguous formal semantics exists and that the implementation of the model transformation language adheres to this semantics. However, for existing relational model transformation approaches, it is usually not really clear under which constraints particular implementations really conform to the formal semantics. In this paper, we will bridge this gap for the formal semantics of triple graph grammars (TGG) and an existing efficient implementation. While the formal semantics assumes backtracking and ignores non-determinism, practical implementations do not support backtracking, require rule sets that ensure determinism, and include further optimizations. Therefore, we capture how the considered TGG implementation realizes the transformation by means of operational rules, define required criteria, and show conformance to the formal semantics if these criteria are fulfilled. We further outline how static and runtime checks can be employed to guarantee these criteria.     

Learning from graph data by putting graphs on the lattice

Graph data have been of common practice in many application domains. However, it is very difficult to deal with graphs due to their intrinsic complex structure. In this paper, we propose to apply Formal Concept Analysis (FCA) to learning from graph data. We use subgraphs appearing in each of graph data as its attributes and construct a lattice based on FCA to organize subgraph attributes which are too numerous. For statistical learning purpose, we propose a similarity measure based on the concept lattice, taking into account the lattice structure explicitly. We prove that, the upper part of the lattice can provide a reliable and feasible way to compute the similarity between graphs. We also show that the similarity measure is rich enough to include some other measures as subparts. We apply the measure to a transductive learning algorithm for graph classification to prove its efficiency and effectiveness in practice. The high accuracy and low running time results confirm empirically the merit of the similarity measure based on the lattice.