Graph Theoretic Clique Relaxations and Applications

Balasundaram, Balabhaskar; Pajouh, Foad Mahdavi

doi:10.1007/978-1-4419-7997-1_9

Cited by 16 publications

(11 citation statements)

References 106 publications

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“…A survey by Balasundaram and Pajouh [9] gives an overview of NP-hardness results and approximation hardness results for different clique relaxations. Moreover, for some clique relaxations, integer programming formulations of the corresponding computational problems are given.…”

Section: Related Workmentioning

confidence: 99%

Multivariate Algorithmics for Finding Cohesive Subnetworks

Komusiewicz

2016

Algorithms

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Community detection is an important task in the analysis of biological, social or technical networks. We survey different models of cohesive graphs, commonly referred to as clique relaxations, that are used in the detection of network communities. For each clique relaxation, we give an overview of basic model properties and of the complexity of the problem of finding large cohesive subgraphs under this model. Since this problem is usually NP-hard, we focus on combinatorial fixed-parameter algorithms exploiting typical structural properties of input networks.

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Section: Related Workmentioning

confidence: 99%

Multivariate Algorithmics for Finding Cohesive Subnetworks

Komusiewicz

2016

Algorithms

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“…For example, if we take φ G (S) to be the diameter of G[S], we arrive at an optimization version of the s-Club problem [4,5,44] which asks to find a subgraph of order k that has diameter at most s. Note that this problem is nontrivial only if k > ∆. As a consequence, the above theorem improves on the previously reported overall running time of O((k − 2) k · k!…”

Section: Proofmentioning

confidence: 52%

“…Surveys of different types of clique relaxations and the computational problems associated with finding such subgraphs were given by Balasundaram and Pajouh [5] and Kosub [38].…”

Section: Fixed-cardinality Optimizationmentioning

confidence: 99%

An algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problems

Komusiewicz

Sorge

2015

Discrete Applied Mathematics

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“…A more practical variation of isomorphism is the maximum weighted common subgraph (MWCS), which identifies the largest weighted subgraph of G 1 that is isomorphic to a subgraph of G 2 . There is a correspondence between the MWCS problem and another well-known problem-the maximum weighted independent set (MWIS) of a third graph, which can be induced from the graphs being compared [22,23]. The vertices and edges of the third graph, called a conflict graph, represent possible mappings and the conflicts between them, respectively.…”

Section: Molecular Similaritymentioning

confidence: 99%

“…One of the relaxations is known as the maximum weighted co-k-plex problem, in which the goal is to find the largest weighted set of vertices in the graph such that each vertex has at most k −1 edges connecting it to the other vertices. It is clear that the maximum weighted co-1-plex problem is the MWIS problem [23]. The majority of the similarity methods discussed above, including the MWIS and maximum weighted co-k-plex problems, are in general NP-hard, having exponentially increasing computational complexity due to the combinatorial nature of the graphs involved [25,26].…”

Section: Molecular Similaritymentioning

confidence: 99%

Enhancing quantum annealing performance for the molecular similarity problem

Hernandez

Aramon²

2017

Quantum Inf Process

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Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length, and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware's performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches, and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

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Graph Theoretic Clique Relaxations and Applications

Cited by 16 publications

References 106 publications

Multivariate Algorithmics for Finding Cohesive Subnetworks

Multivariate Algorithmics for Finding Cohesive Subnetworks

An algorithmic framework for fixed-cardinality optimization in sparse graphs applied to dense subgraph problems

Enhancing quantum annealing performance for the molecular similarity problem

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