Memetic Search for Identifying Critical Nodes in Sparse Graphs

Critical node problems involve finding a set of critical nodes from a graph whose removal results in optimizing a pre-defined measure over the residual graph. As useful models for a variety of practical applications, these problems are computational challenging. In this paper, we study the classic Critical Node Problem (CNP) and introduce an effective memetic algorithm for solving CNP. The proposed algorithm combines a double backbone-based crossover operator (to generate promising offspring solutions), a component-based neighborhood search procedure (to find high-quality local optima) and a rank-based pool updating strategy (to guarantee a healthy population). Extensive evaluations on 42 synthetic and real-world benchmark instances show that the proposed algorithm discovers 24 new upper bounds and matches 15 previous best-known bounds. We also demonstrate the relevance of our algorithm for effectively solving a variant of the classic CNP, called the Cardinality-Constrained Critical Node Problem (CC-CNP). Finally, we investigate the usefulness of each key algorithmic component

The distance-based critical node detection problem : models and algorithms

In the wake of terrorism and natural disasters, assessing networked systems for vulnerability to failures that arise from these events is essential to maintaining the operations of the systems. This is very crucial given the heavy dependence of daily social and economic activities on networked systems such as transport, telecommunication and energy networks as well as the interdependence of these networks. In this thesis, we explore methods to assess the vulnerability of networked systems to element failures which employ connectivity as the performance measure for vulnerability. The associated optimisation problem termed the critical node (edge) detection problem seeks to identify a subset of nodes (edges) of a network whose deletion (failure) optimises a network connectivity objective. Traditional connectivity measures employed in most studies of the critical node detection problem overlook internal cohesiveness of networks and the extent of connectivity in the network. This limits the effectiveness of the developed methods in uncovering vulnerability with regards to network connectivity. Our work therefore focuses on distance-based connectivity which is a fairly new class of connectivity introduced for studying the critical node detection problem to overcome the limitations of traditional connectivity measures. In Chapter 1, we provide an introduction outlining the motivations and the methods related to our study. In Chapter 2, we review the literature on the critical node detection problem as well as its application areas and related problems. Following this, we formally introduce the distance-based critical node detection problem in Chapter 3 where we propose new integer programming models for the case of hop-based distances and an efficient algorithm for the separation problems associated with the models. We also propose two families of valid inequalities. In Chapter 4, we consider the distance-based critical node detection problem using a heuristic approach in which we propose a centrality-based heuristic that employs a backbone crossover and a centrality-based neighbourhood search. In Chapter 5, we present generalisations of the methods proposed in Chapter 3 to edge-weighted graphs. We also introduce the edge-deletion version of the problem which we term the distance based critical edge detection problem. Throughout Chapters 3, 4 and 5, we provide computational experiments. Finally, in Chapter 6 we present conclusions as well future research directions. Keywords: Network Vulnerability, Critical Node Detection Problem, Distance-based Connectivity, Integer Programming, Lazy Constraints, Branch-and-cut, Heuristics.In the wake of terrorism and natural disasters, assessing networked systems for vulnerability to failures that arise from these events is essential to maintaining the operations of the systems. This is very crucial given the heavy dependence of daily social and economic activities on networked systems such as transport, telecommunication and energy networks as well as the interdependence of these networks. In this thesis, we explore methods to assess the vulnerability of networked systems to element failures which employ connectivity as the performance measure for vulnerability. The associated optimisation problem termed the critical node (edge) detection problem seeks to identify a subset of nodes (edges) of a network whose deletion (failure) optimises a network connectivity objective. Traditional connectivity measures employed in most studies of the critical node detection problem overlook internal cohesiveness of networks and the extent of connectivity in the network. This limits the effectiveness of the developed methods in uncovering vulnerability with regards to network connectivity. Our work therefore focuses on distance-based connectivity which is a fairly new class of connectivity introduced for studying the critical node detection problem to overcome the limitations of traditional connectivity measures. In Chapter 1, we provide an introduction outlining the motivations and the methods related to our study. In Chapter 2, we review the literature on the critical node detection problem as well as its application areas and related problems. Following this, we formally introduce the distance-based critical node detection problem in Chapter 3 where we propose new integer programming models for the case of hop-based distances and an efficient algorithm for the separation problems associated with the models. We also propose two families of valid inequalities. In Chapter 4, we consider the distance-based critical node detection problem using a heuristic approach in which we propose a centrality-based heuristic that employs a backbone crossover and a centrality-based neighbourhood search. In Chapter 5, we present generalisations of the methods proposed in Chapter 3 to edge-weighted graphs. We also introduce the edge-deletion version of the problem which we term the distance based critical edge detection problem. Throughout Chapters 3, 4 and 5, we provide computational experiments. Finally, in Chapter 6 we present conclusions as well future research directions. Keywords: Network Vulnerability, Critical Node Detection Problem, Distance-based Connectivity, Integer Programming, Lazy Constraints, Branch-and-cut, Heuristics

A novel clustering methodology based on modularity optimisation for detecting authorship affinities in Shakespearean era plays

© 2016 Naeni et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. In this study we propose a novel, unsupervised clustering methodology for analyzing large datasets. This new, efficient methodology converts the general clustering problem into the community detection problem in graph by using the Jensen-Shannon distance, a dissimilarity measure originating in Information Theory. Moreover, we use graph theoretic concepts for the generation and analysis of proximity graphs. Our methodology is based on a newly proposed memetic algorithm (iMA-Net) for discovering clusters of data elements by maximizing the modularity function in proximity graphs of literary works. To test the effectiveness of this general methodology, we apply it to a text corpus dataset, which contains frequencies of approximately 55,114 unique words across all 168 written in the Shakespearean era (16th and 17th centuries), to analyze and detect clusters of similar plays. Experimental results and comparison with state-of-the-art clustering methods demonstrate the remarkable performance of our new method for identifying high quality clusters which reflect the commonalities in the literary style of the plays

High-Quality Hypergraph Partitioning

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric. Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution. With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space. All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time

Finding Near-Optimal Weight Independent Sets at Scale

Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise, state-of-the-art branch-and-reduce algorithms can solve many large-scale graphs if reductions are applicable. Otherwise, their performance quickly degrades due to branching requiring exponential time. In this paper, we develop an advanced memetic algorithm to tackle the problem, which incorporates recent data reduction techniques to compute near-optimal weighted independent sets in huge sparse networks. More precisely, we use a memetic approach to recursively choose vertices that are likely to be in a large-weight independent set. We include these vertices into the solution, and further reduce the graph. We show that identifying and removing vertices likely to be in large-weight independent sets opens up the reduction space and speeds up the computation of large-weight independent sets remarkably. Our experimental evaluation indicates that we are able to outperform state-of-the-art algorithms. For example, our two algorithm configurations compute the best results among all competing algorithms for 205 out of 207 instances. Thus can be seen as a useful tool when large-weight independent sets need to be computed in~practice

A heuristic approach for the distance-based critical node detection problem in complex networks

The distance-based critical node problem involves identifying a subset of nodes in a network whose removal minimises a pre-defined distance-based connectivity measure. Having the classical critical node problem as a special case, the distance-based critical node problem is computationally challenging. In this article, we study the distance-based critical node problem from a heuristic algorithm perspective. We consider the distance-based connectivity objective whose goal is to minimise the number of node pairs connected by a path of length at most k, subject to budgetary constraints. We propose a centrality based heuristic which combines a backbone-based crossover procedure to generate good offspring solutions and a centrality-based neighbourhood search to improve the solution. Extensive computational experiments on real-world and synthetic graphs show the effectiveness of the developed heuristic in generating good solutions when compared to exact solution. Our empirical results also provide useful insights for future algorithm development

Streaming, Local, and Multi­Level (Hyper)Graph Decomposition

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex (hyper)graphs, such as social networks, chemical compounds, and computer networks. This dissertation explores several types of (hyper)graph decomposition problems, including graph partitioning, hypergraph partitioning, local graph clustering, process mapping, and signed graph clustering. Our main focus is on streaming algorithms, local algorithms and multilevel algorithms. In terms of streaming algorithms, we make contributions with highly efficient and effective algorithms for (hyper)graph partitioning and process mapping. In terms of local algorithms, we propose sub-linear algorithms which are effective in detecting high-quality local communities around a given seed node in a graph based on the distribution of a given motif. In terms of multilevel algorithms, we engineer high-quality multilevel algorithms for process mapping and signed graph clustering. We provide a thorough discussion of each algorithm along with experimental results demonstrating their superiority over existing state-of-the-art techniques. The results show that the proposed algorithms achieve improved performance and better solutions in various metrics, making them highly promising for practical applications. Overall, this dissertation showcases the effectiveness of advanced combinatorial algorithmic techniques in solving challenging (hyper)graph decomposition problems

AntNetAlign: Ant colony optimization for network alignment

The code (and data) in this article has been certified as Reproducible by Code Ocean: (https://codeocean.com/). More information on the Reproducibility Badge Initiative is available at https://www.elsevier.com/physical-sciences-andengineering/computer-science/journalsNetwork Alignment (NA) is a hard optimization problem with important applications such as, for example, the identification of orthologous relationships between different proteins and of phylogenetic relationships between species. Given two (or more) networks, the goal is to find an alignment between them, that is, a mapping between their respective nodes such that the topological and functional structure is well preserved. Although the problem has received great interest in recent years, there is still a need to unify the different trends that have emerged from diverse research areas. In this paper, we introduce AntNetAlign, an Ant Colony Optimization (ACO) approach for solving the problem. The proposed approach makes use of similarity information extracted from the input networks to guide the construction process. Combined with an improvement measure that depends on the current construction state, it is able to optimize any of the three main topological quality measures. We provide an extensive experimental evaluation using real-world instances that range from Protein–Protein Interaction (PPI) networks to Social Networks. Results show that our method outperforms other state-of-the-art approaches in two out of three of the tested scores within a reasonable amount of time, specially in the important score. Moreover, it is able to obtain near-optimal results when aligning networks with themselves. Furthermore, in larger instances, our algorithm was still able to compete with the best performing method in this regard.Christian Blum and Guillem Rodríguez Corominas, Spain were supported by grants PID2019-104156GB-I00 and TED2021- 129319B-I00 funded by MCIN/AEI/10.13039/501100011033. Maria J. Blesa acknowledges support from AEI, Spain under grant PID2020-112581GB-C21 (MOTION) and the Catalan Agency for Management of University and Research Grants (AGAUR), Spain under grant 2017-SGR-786 (ALBCOM).Peer ReviewedPostprint (published version