An exact algorithm for the maximum probabilistic clique problem

Miao, Zhuqi; Balasundaram, Balabhaskar; Pasiliao, Eduardo L.

doi:10.1007/s10878-013-9699-4

Cited by 11 publications

(4 citation statements)

References 37 publications

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“…Investigating this could lead to significant contributions. Additionally, there is a clear path towards exploring probabilistic group centrality metrics, such as examining the problem of maximum probabilistic clique (Miao et al, 2014) from a group centrality perspective. Assuming static, unchanging conditions in large-scale network can be a significant limitation in real-world scenarios where uncertainty and variability are inherent.…”

Section: Future Workmentioning

confidence: 99%

“…This probability can be viewed as the equivalent of the probability of all edges between the designated center and stars to exist, as well as no edges between any two leaves existing. We note here the similarity between the pseudo-star and a probabilistic clique (Miao et al, 2014). A probabilistic clique is defined as a set of nodes that form a clique with at least probability θ ∈ [0, 1].…”

Section: Brief History On Group Centralitymentioning

confidence: 99%

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The Star Degree Centrality Problem: A Decomposition Approach

Camur

Sharkey

Vogiatzis

2022

INFORMS Journal on Computing

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We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, is shown to be [Formula: see text]-complete. In this work, we first propose a new integer programming (IP) formulation, which has a smaller number of constraints and nonzero coefficients in them than the existing formulation in the literature. We present classes of networks in which the problem is solvable in polynomial time and offer a new proof of [Formula: see text]-completeness that shows the problem remains [Formula: see text]-complete for both bipartite and split graphs. In addition, we propose a decomposition framework that is suitable for both the existing and our formulations. We implement several acceleration techniques in this framework, motivated by techniques used in Benders decomposition. We test our approaches on networks generated based on the Barabási–Albert, Erdös–Rényi, and Watts–Strogatz models. Our decomposition approach outperforms solving the IP formulations in most of the instances in terms of both solution time and quality; this is especially true for larger and denser graphs. We then test the decomposition algorithm on large-scale protein–protein interaction networks, for which SDC is shown to be an important centrality metric. Summary of Contribution: In this study, we first introduce a new integer programming (NIP) formulation for the star degree centrality (SDC) problem in which the goal is to identify the induced star with the largest open neighborhood. We then show that, although the SDC can be efficiently solved in tree graphs, it remains [Formula: see text]-complete in both split and bipartite graphs via a reduction performed from the set cover problem. In addition, we implement a decomposition algorithm motivated by Benders decomposition together with several acceleration techniques to both the NIP formulation and the existing formulation in the literature. Our experimental results indicate that the decomposition implementation on the NIP is the best solution method in terms of both solution time and quality.

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Section: Future Workmentioning

confidence: 99%

Section: Brief History On Group Centralitymentioning

confidence: 99%

The Star Degree Centrality Problem: A Decomposition Approach

Camur

Sharkey

Vogiatzis

2022

INFORMS Journal on Computing

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“…Therefore, in the presence of uncertainties, formulation (1) has to be modified to explicitly specify the conditions under which its solution can be considered a -subgraph of (stochastic) graph G. One common approach in the literature is to require that the solution of an optimization problem with stochastic data satisfies the required properties with a prescribed probability. An application of this approach to a maximum clique problem on stochastic graphs was considered in [20].…”

Section: A Two-stage Stochastic Maximum Subgraph Problemmentioning

confidence: 99%

“…Although uncertainty in the aforementioned studies mostly influenced decisions related to directed flows and routing, less focus has been put on developing two-stage recourse constructs for designing/identifying graphs that are adept at maintaining their connection properties in situations when random factors affect/alter/damage their original physical characteristics. A notable non-recourse problem of finding the largest subset of vertices that form a clique with a specified probability, given that edges in the graph can fail with some probabilities, was studied in [20]. A similar approach in application to certain clique relaxations was pursued in [35].…”

Section: Introductionmentioning

confidence: 99%

Detecting resilient structures in stochastic networks: A two‐stage stochastic optimization approach

2017

Self Cite

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We propose a two-stage stochastic programming framework for designing or identifying "resilient," or "reparable" structures in graphs whose topology may undergo a stochastic transformation. The reparability of a subgraph satisfying a given property is defined in terms of a budget constraint, which allows for a prescribed number of vertices to be added to or removed from the subgraph so as to restore its structural properties after the observation of random changes to the graph's set of edges. A two-stage stochastic programming model is formulated and is shown to be N P -complete for a broad range of graph-theoretical properties that the resilient subgraph is required to satisfy. A general combinatorial branch-and-bound algorithm is developed, and its computational performance is illustrated on the example of a two-stage stochastic maximum clique problem.

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A survey on optimization studies of group centrality metrics

Camur,

Vogiatzis

2024

Networks

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Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of centrality have started attracting scientific and practitioner interest. The identification of sets of nodes that are influential within a network is becoming increasingly more important. This is even more pronounced when these sets of nodes are required to induce a certain motif or structure. In this study, we review group centrality metrics from an operations research and optimization perspective for the first time. This is particularly interesting due to the rapid evolution and development of this area in the operations research community over the last decade. We first present a historical overview of how we have reached this point in the study of group centrality. We then discuss the different structures and motifs that appear prominently in the literature, alongside the techniques and methodologies that are popular. We finally present possible avenues and directions for future work, mainly in three areas: (i) probabilistic metrics to account for randomness along with stochastic optimization techniques; (ii) structures and relaxations that have not been yet studied; and (iii) new emerging applications that can take advantage of group centrality. Our survey offers a concise review of group centrality and its intersection with network analysis and optimization.

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An exact algorithm for the maximum probabilistic clique problem

Cited by 11 publications

References 37 publications

The Star Degree Centrality Problem: A Decomposition Approach

The Star Degree Centrality Problem: A Decomposition Approach

Detecting resilient structures in stochastic networks: A two‐stage stochastic optimization approach

A survey on optimization studies of group centrality metrics

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