Combinatorial search versus genetic algorithms: A case study based on the generalized median graph problem

The computation of generalized median graphs (the graph with the smallest average edit distance to all graphs in a given set of graphs) is highly computationally complex. As a matter of fact, it is exponential in the number of nodes of the union of all graphs under consideration. Thus, the generalized median graph computation problem seems to be a suitable and challenging testbed for a comparison of combinatorial search and genetic algorithms. Two solutions are described in this paper. The first is an exact algorithm based on combinatorial search, while the second is a genetic algorithm. Both approaches are compared to each other in a series of experiments.     

Median graph computation for graph clustering

In this paper, we are interested in the problem of graph clustering. We propose a new algorithm for computing the median of a set of graphs. The concept of median allows the extension of conventional algorithms such as the k-means to graph clustering, helping to bridge the gap between statistical and structural approaches to pattern recognition. Experimental results show the efficiency of the new median graph algorithm compared to the (only) existing algorithm in the literature. We also show its effective use in clustering a set of random graphs and in a content-based synthetic image retrieval system.     

Median graphs: A genetic approach based on new theoretical properties

Given a set of graphs, the median graph has been theoretically presented as a useful concept to infer a representative of the set. However, the computation of the median graph is a highly complex task and its practical application has been very limited up to now. In this work we present two major contributions. On one side, and from a theoretical point of view, we show new theoretical properties of the median graph. On the other side, using these new properties, we present a new approximate algorithm based on the genetic search, that improves the computation of the median graph. Finally, we perform a set of experiments on real data, where none of the existing algorithms for the median graph computation could be applied up to now due to their computational complexity. With these results, we show how the concept of the median graph can be used in real applications and leaves the box of the only-theoretical concepts, demonstrating, from a practical point of view, that can be a useful tool to represent a set of graphs.     

Learning graph prototypes for shape recognition

This paper presents some new approaches for computing graph prototypes in the context of the design of a structural nearest prototype classifier. Four kinds of prototypes are investigated and compared: set median graphs, generalized median graphs, set discriminative graphs and generalized discriminative graphs. They differ according to (i) the graph space where they are searched for and (ii) the objective function which is used for their computation. The first criterion allows to distinguish set prototypes which are selected in the initial graph training set from generalized prototypes which are generated in an infinite set of graphs. The second criterion allows to distinguish median graphs which minimize the sum of distances to all input graphs of a given class from discriminative graphs, which are computed using classification performance as criterion, taking into account the inter-class distribution. For each kind of prototype, the proposed approach allows to identify one or many prototypes per class, in order to manage the trade-off between the classification accuracy and the classification time.Each graph prototype generation/selection is performed through a genetic algorithm which can be specialized to each case by setting the appropriate encoding scheme, fitness and genetic operators.An experimental study performed on several graph databases shows the superiority of the generation approach over the selection one. On the other hand, discriminative prototypes outperform the generative ones. Moreover, we show that the classification rates are improved while the number of prototypes increases. Finally, we show that discriminative prototypes give better results than the median graph based classifier.     

Hypergraph-based image retrieval for graph-based representation

In this paper, we introduce a novel method for graph indexing. We propose a hypergraph-based model for graph data sets by allowing cluster overlapping. More precisely, in this representation one graph can be assigned to more than one cluster. Using the concept of the graph median and a given threshold, the proposed algorithm detects automatically the number of classes in the graph database. We consider clusters as hyperedges in our hypergraph model and we index the graph set by the hyperedge centroids. This model is interesting to traverse the data set and efficient to retrieve graphs.     

A Puzzle-Based Genetic Algorithm with Block Mining and Recombination Heuristic for the Traveling Salesman Problem

In this research, we introduce a new heuristic approach using the concept of ant colony optimization (ACO) to extract patterns from the chromosomes generated by previous generations for solving the generalized traveling salesman problem. The proposed heuristic is composed of two phases. In the first phase the ACO technique is adopted to establish an archive consisting of a set of non-overlapping blocks and of a set of remaining cities (nodes) to be visited. The second phase is a block recombination phase where the set of blocks and the rest of cities are combined to form an artificial chromosome. The generated artificial chromosomes (ACs) will then be injected into a standard genetic algorithm (SGA) to speed up the convergence. The proposed method is called "Puzzle-Based Genetic Algorithm" or "p-ACGA". We demonstrate that p-ACGA performs very well on all TSPLIB problems, which have been solved to optimality by other researchers. The proposed approach can prevent the early convergence of the genetic algorithm (GA) and lead the algorithm to explore and exploit the search space by taking advantage of the artificial chromosomes.     

关联图与主动规则集的终止性分析

终止性反映了主动数据库系统良好的行为特性.目前有关主动规则集终止性分析的主要依据是触发图和活化图,其分析结果是保守的.为表达一个规则的动作可能使另一规则的条件为假的事实,引入了惰化图(deactivationgraph),并与触发图和活化图相结合,定义了更为一般的关联图(relationshipgraph).同时,给出了基于关联图的主动规则集终止性静态分析算法,提高了终止性判定的准确性.     

Generalized median graph computation by means of graph embedding in vector spaces

The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.     

Learning and discovery: one system's search for mathematical knowledge

The Graph Theorist, GT, is a system that performs mathematical research in graph theory. From the definitions in its input knowledge base, GT constructs examples of mathematical concepts, conjectures and proves mathematical theorems about concepts, and discovers new concepts. Discovery is driven both by examples and by definitional form. The discovery processes construct a semantic net that links all of GT's concepts together.
Each definition is an algebraic expression whose semantic interpretation is a stylized algorithm to generate a class of graphs correctly and completely. From a knowledge base of these concept definitions, GT is able to conjecture and prove such theorems as "The set of acyclic, connected graphs is precisely the set of trees" and "There is no odd-regular graph on an odd number of vertices." GT explores new concepts either to develop an area of knowledge or to link a newly acquired concept into a pre-existing knowledge base. New concepts arise from the specialization of an existing concept, the generalization of an existing concept, and the merger of two or more existing concepts. From an initial knowledge base containing only the definition of "graph," GT discovers such concepts as acyclic graphs, connected graphs, and bipartite graphs.     

Distributed scheduling strategy for divisible loads on arbitrarily configured distributed networks using load balancing via virtual routing

In this paper, we consider a scheduling problem for divisible loads originating from single or multiple sites on arbitrary networks. We first propose a generalized mathematical model and formulate the scheduling problem as an optimization problem with an objective to minimize the processing time of the loads. We derive a number of theoretical results on the solution of the optimization problem. On the basis of these first set of results, we propose an efficient algorithm for scheduling divisible loads using the concept of load balancing via virtual routing for an arbitrary network configuration. The proposed algorithm has three major attractive features. Firstly, the algorithm is simple to realize and can be implemented in a distributed fashion. The second one is in its style of working by avoiding the need for generating a timing diagram explicitly for any complex networks having an arbitrary network topology. The last one is its capability of handling divisible loads originating from both single and multiple sites. When divisible loads originate from a single node, we compare the proposed algorithm with a recently proposed RAOLD algorithm which is based on minimum cost spanning tree [J. Yao, V. Bharadwaj, Design and performance analysis of divisible load scheduling strategies on arbitrary graphs, Cluster Computing 7(2) (2004) 191–207]. When divisible loads originate from multiple sites, we test the performance on sparse, medium and densely connected networks. This is the first time in the divisible load theory (DLT) literature that such a generic approach for handling divisible loads originating from multiple sites on arbitrary networks employing load balancing via virtual routing is attempted.     

Two algorithms for determining a minimum independent dominating set

The problem of determining a minimum independent dominating set is fundamental to both the theory and applications of graphs. Computationally it belongs to the class of hard combinatorial optimization problems known as NP-hard. In this paper, we develop a backtracking algorithm and a dynamic programming algorithm to determine a minimum independent dominating set. Computational experience with the backtracking algorithm on more than 1000 randomly generated graphs ranging from 100 to 200 vertices and from 10% to 60% densities has shown that the algorithm is effective.     

A RKHS interpolator-based graph matching algorithm

We present an algorithm for performing attributed graph matching. This algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel Hilbert spaces (RKHS). The algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs, allowing the structure of the graphs to be based on multiple sets of attributes. No assumption is made about the adjacency structure of the graphs to be matched     

State agnostic planning graphs: deterministic,non-deterministic,and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source.We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.     

A simple group mutual l-exclusion algorithm

This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating sets for undirected graphs. Whereas dominating sets for digraphs have more applications than those for undirected graphs. We construct dominating sets of generalized de Bruijn digraphs where obtained dominating sets have some qualifications. For generalized Kautz digraphs, there is a minimum dominating set in those constructed dominating sets.     

基于本体分割的语义图概要方法

语义图概要的目的是提取语义图的关键信息,形成原数据集的概要模型以解决大规模语义图的理解、查询、应用难题。为提升现有语义图概要方法效率,提出一种基于本体分割的概要方法。通过本体分割算法对语义图进行分割生成扩展子图。采用形式概念分析对每个扩展子图生成元素的偏序格（又称特征集格）。在此基础上,由所有子图的特征集格形成了原语义图的概要。在关联开放数据集和Berlin SPARQL Benchmark数据集上的实验结果表明,该方法具有较好的可扩展性,有效提高了概要方法的效率。     

Central Clustering of Attributed Graphs

Partitioning a data set of attributed graphs into clusters arises in different application areas of structural pattern recognition and computer vision. Despite its importance, graph clustering is currently an underdeveloped research area in machine learning due to the lack of theoretical analysis and the high computational cost of measuring structural proximities. To address the first issue, we introduce the concept of metric graph spaces that enables central (or center-based) clustering algorithms to be applied to the domain of attributed graphs. The key idea is to embed attributed graphs into Euclidean space without loss of structural information. In addressing the second issue of computational complexity, we propose a neural network solution of the K-means algorithm for structures (KMS). As a distinguishing feature to improve the computational time, the proposed algorithm classifies the data graphs according to the principle of elimination of competition where the input graph is assigned to the winning model of the competition. In experiments we investigate the behavior and performance of the neural KMS algorithm.     

Fitness landscapes, memetic algorithms, and greedy operators for graph bipartitioning

The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced. In particular, the local structure and the regularity of the dependency graph seems to be important for the performance of an algorithm, and in fact, algorithms that exploit these properties perform significantly better than others which do not. It will be shown that a simple hybrid multi-start local search exploiting locality in the structure of the graphs is able to find optimum or near optimum solutions very quickly. However, if the problem size increases or the graphs become unstructured, a memetic algorithm (a genetic algorithm incorporating local search) is shown to be much more effective.     

A randomized algorithm for determining dominating sets in graphs of maximum degree five

The paper is devoted to demonstrating a randomized algorithm for determining a dominating set in a given graph having a maximum degree of five. The algorithm follows the Las Vegas technique. Furthermore, the concept of a 2-separated collection of subsets of vertices in graphs is used. The suggested algorithm is based on a condition of the upper bound of the cardinality of a local dominating set. If the condition is not satisfied, then the algorithm halts with an appropriate message. Otherwise, the algorithm determines the dominating set. The given algorithm is considered a polynomial-time approximation one.     

广义模糊Gibbs随机场与MR图像分割算法研究

为了对图像进行准确、可靠的分割,提出了一种基于广义模糊集的软分割算法,并将广义模糊集和G ibbs场结合起来,提出了广义模糊G ibbs随机场模型,同时建立了广义模糊G ibbs分割(GFGS)算法。该算法是首先把每一个分割类看作是广义模糊类,并以最大后验概率(MAP)为判别准则来决定每一个像素值的归类以及它属于该类的隶属度;然后用广义隶属度函数中负的部分来刻划数据中的异常值,使得该算法能有效地处理异常值;最后用该模糊类的质心来更新类的中心,并以人脑的仿真图像和临床MR图像进行了实验。实验结果表明,该算法能有效地滤除噪声和处理部分容积效应,是一个分割能力强、稳健性好的算法。     

Single-edge monotonic sequences of graphs and linear-time algorithms for minimal completions and deletions

We study graph properties that admit an increasing, or equivalently decreasing, sequence of graphs on the same vertex set such that for any two consecutive graphs in the sequence their difference is a single edge. This is useful for characterizing and computing minimal completions and deletions of arbitrary graphs into having these properties. We prove that threshold graphs and chain graphs admit such sequences. Based on this characterization and other structural properties, we present linear-time algorithms both for computing minimal completions and deletions into threshold, chain, and bipartite graphs, and for extracting a minimal completion or deletion from a given completion or deletion. Minimum completions and deletions into these classes are NP-hard to compute.