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We live in the world of information, where huge amounts of data of diverse nature and origin arise in various spheres of life, including sports. To get useful information from this data, one should apply special techniques of summarizing... more
We live in the world of information, where huge amounts of data of diverse nature and origin arise in various spheres of life, including sports. To get useful information from this data, one should apply special techniques of summarizing and visualizing the information contained in a certain dataset. In many practical situations, a real-life dataset can be represented as a large graph (network)(Boginski et al. 2003). A graph is a set of vertices (dots) and edges (links) connecting them. In a graph representation of a dataset, certain attributes are ...
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ABSTRACT This paper explores techniques for solving the maximum clique and vertex coloring problems on very largescale real-life networks. Because of the size of such networks and the intractability of the considered problems, previously... more
ABSTRACT This paper explores techniques for solving the maximum clique and vertex coloring problems on very largescale real-life networks. Because of the size of such networks and the intractability of the considered problems, previously developed exact algorithms may not be directly applicable. The proposed approaches aim to reduce the network instances to a size that is tractable for existing solvers, while preserving optimality. Two clique relaxation structures are exploited for this purpose. In addition to the known k -core structure, a newly introduced clique relaxation, k -community, is used to further reduce the instance size. Experimental results on real-life graphs (collaboration networks, P2P networks, social networks, etc.) show the proposed procedures to be effective by finding, for the first time, exact solutions for instances with over 18 million vertices.
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Given a graph, the minimum connected dominating set problem is to flnd a mini- mum cardinality subset of vertices D such that its induced subgraph is connected and each vertex outside D has at least one neighbor in D. Approximations of... more
Given a graph, the minimum connected dominating set problem is to flnd a mini- mum cardinality subset of vertices D such that its induced subgraph is connected and each vertex outside D has at least one neighbor in D. Approximations of min- imum connected dominating sets are often used to represent a virtual routing back- bone in wireless networks. This paper proposes a constant-ratio approximation al- gorithm for the minimum connected dominating set problem in unit-ball graphs.
ABSTRACT In this article, a heuristic is said to be provably best if, assuming , no other heuristic always finds a better solution (when one exists). This extends the usual notion of “best possible” approximation algorithms to include a... more
ABSTRACT In this article, a heuristic is said to be provably best if, assuming , no other heuristic always finds a better solution (when one exists). This extends the usual notion of “best possible” approximation algorithms to include a larger class of heuristics. We illustrate the idea on several problems that are somewhat stylized versions of real-life network optimization problems, including the maximum clique, maximum k-club, minimum (connected) dominating set, and minimum vertex coloring problems. The corresponding provably best construction heuristics resemble those commonly used within popular metaheuristics. Along the way, we show that it is hard to recognize whether the clique number and the k-club number of a graph are equal, yet a polynomial-time computable function is “sandwiched” between them. This is similar to the celebrated Lovász function wherein an efficiently computable function lies between two graph invariants that are -hard to compute. © 2015 Wiley Periodicals, Inc. NETWORKS, 2015
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ABSTRACT This paper explores techniques for solving the maximum clique and vertex coloring problems on very largescale real-life networks. Because of the size of such networks and the intractability of the considered problems, previously... more
ABSTRACT This paper explores techniques for solving the maximum clique and vertex coloring problems on very largescale real-life networks. Because of the size of such networks and the intractability of the considered problems, previously developed exact algorithms may not be directly applicable. The proposed approaches aim to reduce the network instances to a size that is tractable for existing solvers, while preserving optimality. Two clique relaxation structures are exploited for this purpose. In addition to the known k -core structure, a newly introduced clique relaxation, k -community, is used to further reduce the instance size. Experimental results on real-life graphs (collaboration networks, P2P networks, social networks, etc.) show the proposed procedures to be effective by finding, for the first time, exact solutions for instances with over 18 million vertices.
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ABSTRACT This paper considers the minimum k -connected d -dominating set problem, which is a fault-tolerant generalization of the minimum connected dominating set ( MCDS) problem. Three integer programming formulations based on vertex... more
ABSTRACT This paper considers the minimum k -connected d -dominating set problem, which is a fault-tolerant generalization of the minimum connected dominating set ( MCDS) problem. Three integer programming formulations based on vertex cuts are proposed ( depending on whether d < k, d D k, or d > k) and their integer hulls are studied. The separation problem for the vertex-cut inequalities is a weighted vertex-connectivity problem and is polytime solvable, meaning that the LP relaxation can be solved in polytime despite having exponentially many constraints. A new class of valid inequalities-r-robust vertex-cut inequalities-is introduced and is shown to induce exponentially many facets. Finally, a lazy-constraint approach is shown to compare favorably with existing approaches for the MCDS problem ( the case k = d = 1), and is in fact the fastest in literature for standard test instances. A key subroutine is an algorithm for finding an inclusion-wise minimal vertex cut in linear time. Computational results for (k, d) =(2, 1), (2, 2), (3, 3), (4, 4) are provided as well.
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Abstract Given a simple undirected graph G, a k-club is a subset of vertices inducing a subgraph of diameter at most k. The maximum k-club problem (MkCP) is to find a k-club of maximum cardinality in G. These structures, originally... more
Abstract Given a simple undirected graph G, a k-club is a subset of vertices inducing a subgraph of diameter at most k. The maximum k-club problem (MkCP) is to find a k-club of maximum cardinality in G. These structures, originally introduced to model cohesive subgroups in social network analysis, are of interest in network-based data mining and clustering applications. The maximum k-club problem is NP-hard, moreover, determining whether a given k-club is maximal (by inclusion) is NP-hard as well. This paper first ...
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ABSTRACT A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no... more
ABSTRACT A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s -club. We prove that for any fixed positive integer s it is NP-complete to determine if a graph has a dominating s -club, even when the graph has diameter s+1s+1. As a special case it is NP-complete to determine if a graph of diameter two has a dominating clique. We then propose a compact integer programming formulation for the related minimization problem, enhance the approach with variable fixing rules and valid inequalities, and present computational results.
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ABSTRACT This paper presents a computational study of global characteristics of the US stock market using a network-based model referred to as the market graph. The market graph reflects similarity patterns between stock return... more
ABSTRACT This paper presents a computational study of global characteristics of the US stock market using a network-based model referred to as the market graph. The market graph reflects similarity patterns between stock return fluctuations via linking pairs of stocks that exhibit “coordinated” behavior over a specified period of time. We utilized Spearman rank correlation as a measure of similarity between stocks and considered the evolution of the market graph over the recent decade between 2001–2011. The observed market graph characteristics reveal interesting trends in the stock market over time, as well as allow one to use this model to identify cohesive clusters of stocks in the market.
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A Greedy Randomized Adaptive Search Procedure (GRASP) is a randomized heuristic that has produced high quality solutions for a wide range of combinatorial optimization problems. The NP-complete Feedback Vertex Set (FVS) Problem is to find... more
A Greedy Randomized Adaptive Search Procedure (GRASP) is a randomized heuristic that has produced high quality solutions for a wide range of combinatorial optimization problems. The NP-complete Feedback Vertex Set (FVS) Problem is to find the minimum number of vertices that need to be removed from a directed graph so that the resulting graph has no directed cycle. The FVS problem has found applications in many fields, including VLSI design, program verification, and statistical inference.
Abstract: The objective of this research is to develop a general methodological framework for planning and evaluating the effectiveness of highway reconstruction strategies on the system's performance measures, in particular safety,... more
Abstract: The objective of this research is to develop a general methodological framework for planning and evaluating the effectiveness of highway reconstruction strategies on the system's performance measures, in particular safety, mobility, and the total cost of network rehabilitation. Transportation networks are characterized by uncertainty that stems from different sources and transportation planners should consider risks involved in uncertainty in model parameters.
We address a new approach to the problem of improvement of the quality of multi-grade spatial-spectral images provided by several remote sensing (RS) systems as required for environmental resource management with the use of multisource RS... more
We address a new approach to the problem of improvement of the quality of multi-grade spatial-spectral images provided by several remote sensing (RS) systems as required for environmental resource management with the use of multisource RS data.
As for the material included in each of the sections, I believe that it is an excellent primer for young researchers who seek for introductory literature on applying optimization to solving problems in biomedicine. The part on radiation... more
As for the material included in each of the sections, I believe that it is an excellent primer for young researchers who seek for introductory literature on applying optimization to solving problems in biomedicine. The part on radiation therapy introduces the background on the application and the underlying optimization techniques with references to the medical instrumentation. Then models and solution approaches are presented and discussed. The theoretical results discussed by Busygin et al.
The maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems are classical problems in combinatorial optimization. Owing to their important role in several theoretical fields and applicability in a... more
The maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems are classical problems in combinatorial optimization. Owing to their important role in several theoretical fields and applicability in a wide variety of practical settings, these problems have been extensively studied from different perspectives by mathematicians, computer scientists, operations researchers, engineers, biologists, and social scientists.
Abstract This paper studies the sum-of-ratios version of the classical minimum spanning tree problem. We describe a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The... more
Abstract This paper studies the sum-of-ratios version of the classical minimum spanning tree problem. We describe a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on randomly generated complete and sparse graph instances.
Abstract: This paper presents a method of constructing risk-based rehabilitation policies for a network of pavement facilities that ensure a specific quality level. The model is formulated in the Markov Decision Process framework with... more
Abstract: This paper presents a method of constructing risk-based rehabilitation policies for a network of pavement facilities that ensure a specific quality level. The model is formulated in the Markov Decision Process framework with risk-averse actions and transitional probabilities that are subjected to the uncertainty in the pavement performance model. A well known Conditional Value at Risk (CVaR) is used as a measure of risk to represent risk averseness of the decision maker.
Abstract Some of the most popular routing protocols for wireless sensor networks require a virtual backbone for efficient communication between the sensors. Connected dominating sets (CDS) have been studied as a method of choosing nodes... more
Abstract Some of the most popular routing protocols for wireless sensor networks require a virtual backbone for efficient communication between the sensors. Connected dominating sets (CDS) have been studied as a method of choosing nodes to be in the backbone. The traditional approach is to assume that the transmission range of each node is given and to minimize the number of nodes in the CDS representing the backbone.
Clique relaxation models that were originally introduced in the literature on social network analysis are not only gaining increasing popularity in a wide spectrum of complex network applications, but also keep garnering attention of... more
Clique relaxation models that were originally introduced in the literature on social network analysis are not only gaining increasing popularity in a wide spectrum of complex network applications, but also keep garnering attention of mathematicians, computer scientists, and operations researchers as a promising avenue for fruitful theoretical investigations.
Abstract Given a simple undirected graph G=(V, E) and a constant γ∈(0, 1), a subset of vertices is called a γ-quasi-clique or, simply, a γ-clique if it induces a subgraph with the edge density of at least γ. The maximum γ-clique problem... more
Abstract Given a simple undirected graph G=(V, E) and a constant γ∈(0, 1), a subset of vertices is called a γ-quasi-clique or, simply, a γ-clique if it induces a subgraph with the edge density of at least γ. The maximum γ-clique problem consists in finding a γ-clique of largest cardinality in the graph. Despite numerous practical applications, this problem has not been rigorously studied from the mathematical perspective, and no exact solution methods have been proposed in the literature.
A method for determining optimal risk-based maintenance and rehabilitation (M&R) policies for transportation infrastructure is presented. The proposed policies guarantee a certain performance level across the network under a predefined... more
A method for determining optimal risk-based maintenance and rehabilitation (M&R) policies for transportation infrastructure is presented. The proposed policies guarantee a certain performance level across the network under a predefined level of risk. The long-term model is formulated in the Markov Decision Process framework with risk-averse actions and transitional probabilities describing the uncertainty in the deterioration process. The well known Conditional Value at Risk (CVaR) is used as the measure of risk.
In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear... more
In this paper we present the application of a method of adaptive estimation using an algebra–geometric approach, to the study of dynamic processes in the brain. It is assumed that the brain dynamic processes can be described by nonlinear or bilinear lattice models. Our research focuses on the development of an estimation algorithm for a signal process in the lattice models with background additive white noise, and with different assumptions regarding the characteristics of the signal process.
This book presents the up-to-date research developments in economics, management and optimization applied to sports, which would be of interest to researchers and practitioners in sports industry, and could be used as supplementary... more
This book presents the up-to-date research developments in economics, management and optimization applied to sports, which would be of interest to researchers and practitioners in sports industry, and could be used as supplementary reading in related courses and seminars.
Abstract New results are presented concerning binary correcting codes, such as deletion-correcting codes, transposition-correction codes, and codes for the Z-channel. These codes are important due to the possibility of packet loss and... more
Abstract New results are presented concerning binary correcting codes, such as deletion-correcting codes, transposition-correction codes, and codes for the Z-channel. These codes are important due to the possibility of packet loss and corruption on internet transmissions. It is known that the problem of finding the largest correcting codes can be reduced to a well-known combinatorial optimization problem on graphs, the maximum independent set problem.
National Collegiate Athletic Association (NCAA) Division IA football championship features more than 100 top college football programs in the United States. Competitions for the national title are surrounded by enormous fan interest and... more
National Collegiate Athletic Association (NCAA) Division IA football championship features more than 100 top college football programs in the United States. Competitions for the national title are surrounded by enormous fan interest and receive extensive media coverage. Many of the games are attended by tens of thousands of spectators and are followed by millions through the media.
Abstract. Massive data sets arise in a great variety of scientific, engineering and commercial applications. In many cases they can be modeled as very large graphs. whose properties are then studied in order to extract information about... more
Abstract. Massive data sets arise in a great variety of scientific, engineering and commercial applications. In many cases they can be modeled as very large graphs. whose properties are then studied in order to extract information about the application they represent. We discuss recent advances and challenges in modeling and optimixation for massive graphs arising in telecommunications. Internet and finance.
The problem of a recursive realization of Bayesian estimation for incomplete experimental data is considered. A differential-geometric structure of nonlinear estimation is studied. It is shown that the use of a rationally chosen... more
The problem of a recursive realization of Bayesian estimation for incomplete experimental data is considered. A differential-geometric structure of nonlinear estimation is studied. It is shown that the use of a rationally chosen description of the true posterior density produces a geometrical structure defined on the family of possible posteriors. Pythagorean-like relations valid for probability distributions are presented and their importance for estimation under reduced data is indicated.
This volume presents a collection of papers dealing with various aspects of clustering in biological networks and other related problems in computational biology. It consists of two parts, with the first part containing surveys of... more
This volume presents a collection of papers dealing with various aspects of clustering in biological networks and other related problems in computational biology. It consists of two parts, with the first part containing surveys of selected topics and the second part presenting original research contributions.
This volume presents original contributions from renowned researchers in sports economics, management, and optimization.