Context-free graph languages of bounded degree are generated by apex graph grammars

The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph grammars. The main feature of apex graph grammars is that nodes cannot be passed from nonterminal to nonterminal. The proof is based on a normal form result for arbitrary hyperedge replacement systems that forbids passing chains. This generalizes Greibach Normal Form.     

Hierarchical reachability graph of bounded Petri nets forconcurrent-software analysis

Petri nets have been proposed as a promising tool for modeling and analyzing concurrent-software systems such as Ada programs and communication protocol software. Among analysis techniques available for Petri nets, the most general approach is to generate all possible states (markings) of the system in a form of a so-called reachability graph. However, this conventional reachability graph approach is inefficient or intractable, even for a bounded Petri net, due to state explosion in many practical applications. To cope with this problem, this paper proposes a method for constructing a hierarchically organized state space called the hierarchical reachability graph (HRG). Using the HRG, we obtain necessary and sufficient conditions for reachability and deadlock, as well as algorithms to test whether a given state or marking is reachable from the initial state and whether there is a deadlock state (a state with no successor states)     

String and graph grammar characterizations of bounded regular languages

Two grammatical characterizations of the bounded regular languages are presented: one in terms of graph grammars, the other using string grammars. First it is shown that a class of state graphs recognizing the bounded regular languages can be generated by a particular second-order contextfree graph grammar. Next we call uniquely recursive a right-linear (string) grammar having at most one right-recursive production for each of its nonterminals. It is then established that the class of languages generated by uniquely recursive, sequential right-linear grammars is exactly the bounded regular languages. Some comments on the relationship between string and graph grammars are made.     

A history of graph entropy measures

This survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures. Setting the scene with a review of classical measures for determining the structural information content of graphs, we discuss graph entropy measures which play an important role in a variety of problem areas, including biology, chemistry, and sociology. In addition, we examine relationships between selected entropy measures, illustrating differences quantitatively with concrete examples.     

Support measures for graph data*

The concept of support is central to data mining. While the definition of support in transaction databases is intuitive and simple, that is not the case in graph datasets and databases. Most mining algorithms require the support of a pattern to be no greater than that of its subpatterns, a property called anti-monotonicity, or admissibility. This paper examines the requirements for admissibility of a support measure. Support measures for mining graphs are usually based on the notion of an instance graph---a graph representing all the instances of the pattern in a database and their intersection properties. Necessary and sufficient conditions for support measure admissibility, based on operations on instance graphs, are developed and proved. The sufficient conditions are used to prove admissibility of one support measure—the size of the independent set in the instance graph. Conversely, the necessary conditions are used to quickly show that some other support measures, such as weighted count of instances, are not admissible. ^*Partially supported by the KITE consortium under contract to the Israeli Ministry of Trade and Industry, and by the Paul Ivanier Center for Robotics and Production Management.     

Subtree filament graphs are subtree overlap graphs

We show that the class of intersection graphs of subtree filaments in a tree is identical to the class of overlap graphs of subtrees in a tree.     

All Creative People are Not Alike

The prime purpose of this article is to identify the differences we expect to find among highly gifted scientists and thus to guide us in supporting and managing their efforts. Differences that are important to this purpose can be grouped into those which describe:

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偷来的金点子

为了提高你的工业控制能力,最好的方法就是学习别人的技术和技巧。以下是一些你可以尝试的方法。[编者按]     

All agents are not created equal

As the technology advances, we can expect the development of specialized agents to be used as standardized building blocks for information systems. Two trends lend credence to such a prediction. First, software systems in general are being constructed with larger components, such as ActiveX and JavaBeans, which are becoming closer to being agents themselves. They have more functionality than simple objects, respond to events autonomously, and, most importantly, respond to system builders at development time, as well as to events at runtime. Moreover, there is a move toward more cooperative information systems, in which the architecture itself plays an important role in the effectiveness of the system, as opposed to traditional software systems where effectiveness depends on the quality of the individual components. These architectures are generating a set of standardized agents. Architectures based on standardized agent types should be easier to develop, understand, and use. Perhaps most important of all, these architectures will make it easier for separately developed information systems to interoperate     

Structure-based graph distance measures of high degree of precision

In recent years, evaluating graph distance has become more and more important in a variety of real applications and many graph distance measures have been proposed. Among all of those measures, structure-based graph distance measures have become the research focus due to their independence of the definition of cost functions. However, existing structure-based graph distance measures have low degree of precision because only node and edge information of graphs are employed in these measures. To improve the precision of graph distance measures, we define substructure abundance vector (SAV) to capture more substructure information of a graph. Furthermore, based on SAV, we propose unified graph distance measures which are generalization of the existing structure-based graph distance measures. In general, the unified graph distance measures can evaluate graph distance in much finer grain. We also show that unified graph distance measures based on occurrence mapping and some of their variants are metrics. Finally, we apply the unified graph distance metric and its variants to the population evolution analysis and construct distance graphs of marker networks in three populations, which reflect the single nucleotide polymorphism (SNP) linkage disequilibrium (LD) differences among these populations.     

Unnormalized and normalized forms of gefura measures in directed and undirected networks

In some networks nodes belong to predefined groups(e.g.,authors belong to institutions).Common network centrality measures do not take this structure into account.Gefura measures are designed as indicators of a node’s brokerage role between such groups.They are defined as variants of betweenness centrality and consider to what extent a node belongs to shortest paths between nodes from different groups.In this article we make the following new contributions to their study:(1) We systematically study unnormalized gefura measures and show that,next to the ‘structural’ normalization that has hitherto been applied,a ‘basic’ normalization procedure is possible.While the former normalizes at the level of groups,the latter normalizes at the level of nodes.(2) Treating undirected networks as equivalent to symmetric directed networks,we expand the definition of gefura measures to the directed case.(3) It is shown how Brandes’ algorithm for betweenness centrality can be adjusted to cover these cases.     

Commutative bounded integral residuated orthomodular lattices are Boolean algebras

We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of (Ward, Dilworth in Trans Am Math Soc 45, 336–354, 1939, Theorem 7.31); however, out proof is independent and uses other instruments.     

Parallei graph algorithms that are efficient on average

The following three problems concerning random graphs can be solved in (log n)^O(1) expected time using linearly many processors: (1) finding the lexicographically first maximal independent set, (2) coloring the vertices using a number of colors that is almost surely within twice the chromatic number, and (3) finding a Hamiltonian circuit.     

An in-depth study of graph partitioning measures for perceptual organization

In recent years, one of the effective engines for perceptual organization of low-level image features is based on the partitioning of a graph representation that captures Gestalt inspired local structures, such as similarity, proximity, continuity, parallelism, and perpendicularity, over the low-level image features. Mainly motivated by computational efficiency considerations, this graph partitioning process is usually implemented as a recursive bipartitioning process, where, at each step, the graph is broken into two parts based on a partitioning measure. We focus on three such measures, namely, the minimum, average, and normalized cuts. The minimum cut partition seeks to minimize the total link weights cut. The average cut measure is proportional to the total link weight cut, normalized by the sizes of the partitions. The normalized cut measure is normalized by the product of the total connectivity (valencies) of the nodes in each partition. We provide theoretical and empirical insight into the nature of the three partitioning measures in terms of the underlying image statistics. In particular, we consider for what kinds of image statistics would optimizing a measure, irrespective of the particular algorithm used, result in correct partitioning. Are the quality of the groups significantly different for each cut measure? Are there classes of images for which grouping by partitioning does not work well? Also, can the recursive bipartitioning strategy separate out groups corresponding to K objects from each other? In the analysis, we draw from probability theory and the rich body of work on stochastic ordering of random variables. Our major conclusion is that optimization of none of the three measures is guaranteed to result in the correct partitioning of K objects, in the strict stochastic order sense, for all image statistics.     

Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable

Recognition of minimal unsatisfiable CNF formulas (unsatisfiable CNF formulas which become satisfiable if any clause is removed) is a classical D^P-complete problem. It was shown recently that minimal unsatisfiable formulas with n variables and n+k clauses can be recognized in time . We improve this result and present an algorithm with time complexity ; hence the problem turns out to be fixed-parameter tractable (FTP) in the sense of Downey and Fellows (Parameterized Complexity, 1999).Our algorithm gives rise to a fixed-parameter tractable parameterization of the satisfiability problem: If for a given set of clauses F, the number of clauses in each of its subsets exceeds the number of variables occurring in the subset at most by k, then we can decide in time whether F is satisfiable; k is called the maximum deficiency of F and can be efficiently computed by means of graph matching algorithms. Known parameters for fixed-parameter tractable satisfiability decision are tree-width or related to tree-width. Tree-width and maximum deficiency are incomparable in the sense that we can find formulas with constant maximum deficiency and arbitrarily high tree-width, and formulas where the converse prevails.     

Use of graph theory measures to identify errors in record linkage

Ensuring high linkage quality is important in many record linkage applications. Current methods for ensuring quality are manual and resource intensive. This paper seeks to determine the effectiveness of graph theory techniques in identifying record linkage errors. A range of graph theory techniques was applied to two linked datasets, with known truth sets. The ability of graph theory techniques to identify groups containing errors was compared to a widely used threshold setting technique. This methodology shows promise; however, further investigations into graph theory techniques are required. The development of more efficient and effective methods of improving linkage quality will result in higher quality datasets that can be delivered to researchers in shorter timeframes.