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Abstract. A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique called continuous scaling. The main measure of progress [...]

A caterpillar network (or graph) G is a tree with the property that removal of the leaf edges of G leaves one with a path. Here we focus on minimum [...]

An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC algorithm and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow ties, tripartite graphs, and complete graphs. Keywords Causal inference * Real log canonical threshold * Resolution of singularities * Gaussian graphical model * Algebraic statistics * Singular learning theory Mathematics Subject Classification 62H05 * 62H20 * 14Q10, 1 Introduction Extensive theory has been established in recent years for causal inference based on directed acyclic graph (DAG) models. A popular method for estimating a DAG model from observational [...]

Qperational problems arising in the planning of integrated supply chains have been increasingly studied in the past decade. Among these, the production routing problem (PRP) is a difficult problem that [...]

We consider the weighted maximum multiflow problem with respect to a terminal weight. We show that if the dimension of the tight span associated with the weight is at most [...]

Let G be a(p, q) graph. Let f be a map from V(G) to {1, 2, ..., p}. For each edge xy, assign the label [absolute value of f(x) - f(y)]. f is called a difference cordial labeling if f is a one to one map and [absolute value of [e.sub.f](0) - [e.sub.f](1)] ≤ 1 where [e.sub.f](1) and [e.sub.f](0) denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with a difference cordial labeling is called a difference cordial graph. In this paper we investigate the difference cordial labeling behavior of subdivision of some graphs. Keywords Subdivision, web, wheel, book, corona. 2000 Mathematics Subject Classification: 05C78, §1. Introduction and preliminaries Let G = (V, E) be (p, q) graph. In this paper we have considered only simple and undirected graphs. The number of vertices of G [...]

The Resource Constrained Shortest Path Problem (RCSPP) is a variant of the classical shortest path problem and is of great practical importance. The aim is to find the shortest path [...]

A hypergraph is called box-Mengerian if the linear system Ax ≥ 1, x ≥ 0 is box-totally dual integral (box-TDI), where A is the edge-vertex incidence matrix of the hypergraph. [...]

For a simple bipartite graph and an integer t ≥ 2, we consider the problem of finding a minimum-weight [K.sub.t,t]-free t-factor, which is a t-factor containing no complete bipartite graph [...]

Evidential networks are described for managing imprecise probabilities, where these networks are directed acyclic graphs that handle random and epistemic uncertainties due to Dempster-Shafer structures. Evidential networks are extended with imprecise utility functions to deal with system performance evaluation problems and also for system reliability evaluation problems.

The Capacitated Minimum Spanning Tree Problem is NP-hard and several heuristic solution methods have been proposed. They can be classified as classical ones and metaheuristics. Recent developments have shown that metaheuristics outperform classical heuristics. However, they require long computation times and there are difficulties in their parameter calibration and coding phases. This explains the popularity of the Esau-Williams (EW) heuristic in practice, and its use in many successful metaheuristics and second-order greedy methods. In this work, we are concerned with the EW heuristic and we propose simple new enhancements. Based on our computational experiments, we can say that they considerably improve its accuracy with minor increase in computation time, and without harming its simplicity. Keywords: capacitated minimal spanning tree problem; Esau-Williams heuristic

Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3-20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks. dynamics and topology | feedback loops | network theory

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained [l.sub.1] norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between graph cuts and other related continuous optimization problems. Eventually, the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided. Index Terms--Convex optimization, computer vision, graph-theoretic methods, linear programming.

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent are failure probabilities exist, a secondary objective must be present to retain some measure of […]

Packet radio networks use spatial time-division multiple-access to enable multiple network stations to communicate via the same frequency within the same time slot. Stations in close proximity are not allowed […]

Many graph-and set-theoretic problems, because of their tremendous application potential and theoretical appeal, have been well investigated by the researchers in complexity theory and were found to be NP-hard. Since the combinatorial complexity of these problems does not permit exhaustive searches for optimal solutions, only near-optimal solutions can be explored using either various problem-specific heuristic strategies or metaheuristic global-optimization methods, such as simulated annealing, genetic algorithms, etc. In this paper, we propose a unified evolutionary algorithm (EA) to the problems of maximum clique finding, maximum independent set, minimum vertex cover, subgraph and double subgraph isomorphism, set packing, set partitioning, and set cover. In the proposed approach, we first map these problems onto the maximum clique-finding problem (MCP), which is later solved using an evolutionary strategy. The proposed impatient EA with probabilistic tabu search (IEA-PTS) for the MCP integrates the best features of earlier successful approaches with a number of new heuristics that we developed to yield a performance that advances the state of the art in EAs for the exploration of the maximum cliques in a graph. Results of experimentation with the 37 DIMACS benchmark graphs and comparative analyses with six state-of-the-art algorithms, including two from the smaller EA community and four from the larger metaheuristics community, indicate that the IEA-PTS outperforms the EAs with respect to a Pareto-lexicographic ranking criterion and offers competitive performance on some graph instances when individually compared to the other heuristic algorithms. It has also successfully set a new benchmark on one graph instance. On another benchmark suite called Benchmarks with Hidden Optimal Solutions, IEA-PTS ranks second, after a very recent algorithm called COVER, among its peers that have experimented with this suite. Index Terms--Clique finding, evolutionary algorithms (EAs), NP-hard problems in set and graph theory.

The optimal scheduling of IC via the range of DAGs is discussed.

This paper studies a repeated minority game with public signals, symmetric bounded recall, and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. [...]

A report on the optimization problem of the grid computing system is solved using an algorithm based on graph theory, Bayesian approach, and evolutionary approach taking into account the failure correlation in common communication channels and illustrated with examples is presented.

A report on balanced overlay networks's scalability for large-scale networks using a new algorithm shows that the structures approach the ideal case of d-regular random graph.

The risk of blackouts is inherent in complex power systems, despite all efforts to prevent their occurrence. To mitigate the consequences of major blackouts, better restoration plans have been demanded. Commonly, these plans consist of a set of actions textually described. In order to enhance the operating staff comprehension about the restoration plan, this paper proposes a methodology, based on CPM/PERT graph theory, that allows power system restoration plans to be graphically visualized. This approach permits to clearly see the precedence relations among activities and to graphically follow the restoration process during its execution. The methodology can also take advantage of calculations involved with CPM/PERT methods to evaluate the restoration duration and the plan critical path. The application of the proposed approach is illustrated using the IEEE 30-bus network and the restoration plan developed for a portion of the Brazilian interconnected power system. Index Terms--Blackout mitigation, CPM/PERT, graphical user interface, graph theory, power system restoration.

The use of cross section sequence graph algorithm gave better feature extraction and classification which improved the performance of optical character recognition.

The control of mobile networks of multiple agents raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In this paper, we consider the problem of controlling a network of agents so that the resulting motion always preserves the connectivity property of the network. In particular, the connectivity condition is translated to differentiable constraints on individual agent motion by considering the dynamics of the Laplacian matrix and its spectral properties. Artificial potential fields are then used to drive the agents to configurations away from the undesired space of disconnected networks while avoiding collisions with each other. We conclude by illustrating a class of interesting problems that can be achieved while preserving connectivity constraints. Index Terms--Dynamic graphs, graph connectivity, Laplacian matrix, potential fields.

A policy equilibrium is defined, and its properties investigated, for conflicts with more than two decision makers (DMs). A fundamental construction is the metarational tree, which expresses DMs' interactions as sequences of rounds, each consisting of an initial move by the focal DM followed by countermoves by the opponents. Using the metarational tree, the stability definitions of the graph model for conflict resolution can be adapted to apply to policies. These generalized metarational stabilities are shown to generalize Nash, general metarational, and symmetric metarational stabilities. Relationships among generalized metarationalities are derived, as are their connections with policy equilibria. Finally, the refinement that allows only credible moves (moves that are in the immediate interest of the mover) produces a new family of credible generalized metarational stabilities that generalizes the concept of sequential stability in the graph model. Index Terms--Conflict, graph model for conflict resolution, metarational tree, multiple decision makers (DMs), policy analysis, policy equilibrium.

Connected filters are edge-preserving morphological operators, which rely on a notion of connectivity. This is usually the standard 4 and 8-connectivity, which is often too rigid since it cannot model generalized groupings such as object clusters or partitions. In the set-theoretical framework of connectivity, these groupings are modeled by the more general second-generation connectivity. In this paper, we present both an extension of this theory, and provide an efficient algorithm based on the Max-Tree to compute attribute filters based on these connectivities. We first look into the drawbacks of the existing framework that separates clustering and partitioning and is directly dependent on the properties of a preselected operator. We then propose a new type of second-generation connectivity termed mask-based connectivity which eliminates all previous dependencies and extends the ways the image domain can be connected. A previously developed Dual-Input Max-Tree algorithm for area openings is adapted for the wider class of attribute filters on images characterized by second-generation connectivity. CPU-times for the new algorithm are comparable to the original algorithm, typically deviating less than 10 percent either way. Index Terms--Mathematical morphology, second-generation connectivity, connectivity class, clustering, partitioning, dual input max-tree, attribute filter.

A novel patch-based correspondence model is presented in this paper. Many segment-based correspondence approaches have been proposed in recent years. Untextured pixels and boundaries of discontinuities are imposed with hard constraints by the discontinuity assumption that large disparity variation only happens at the boundaries of segments in the above approaches. Significant improvements on performance of untextured and discontinuity area have been reported. But, the performance near occlusion is not satisfactory because a segmented region in one image may be only partially visible in the other one. To solve this problem, we utilize the observation that the shared edge of a visible area and an occluded area corresponds to the discontinuity in the other image. So, the proposed model conducts color segmentation on both images first and then a segment in one image is further cut into smaller patches corresponding to the boundaries of segments in the other when it is assigned with a disparity. Different visibility of patches in one segment is allowed. The uniqueness constraint in a segment level is used to compute the occlusions. An energy minimization framework using graph-cuts is proposed to find a global optimal configuration including both disparities and occlusions. Besides, some measurements are taken to make our segment-based algorithm suffer less from violation of the discontinuity assumption. Experimental results have shown superior performance of the proposed approach, especially on occlusions, untextured areas, and near discontinuities. Index Terms--Stereo, correspondence, segmentation, graph-cuts, occlusion, energy minimization.

Unsupervised image segmentation is an important component in many image understanding algorithms and practical vision systems. However, evaluation of segmentation algorithms thus far has been largely subjective, leaving a system designer to judge the effectiveness of a technique based only on intuition and results in the form of a few example segmented images. This is largely due to image segmentation being an ill-defined problem--there is no unique ground-truth segmentation of an image against which the output of an algorithm may be compared. This paper demonstrates how a recently proposed measure of similarity, the Normalized Probabilistic Rand (NPR) index, can be used to perform a quantitative comparison between image segmentation algorithms using a hand-labeled set of ground-truth segmentations. We show that the measure allows principled comparisons between segmentations created by different algorithms, as well as segmentations on different images. We outline a procedure for algorithm evaluation through an example evaluation of some familiar algorithms--the mean-shift-based algorithm, an efficient graph-based segmentation algorithm, a hybrid algorithm that combines the strengths of both methods, and expectation maximization. Results are presented on the 300 images in the publicly available Berkeley Segmentation Data Set. Index Terms--Computer vision, image segmentation, performance evaluation of algorithms.