On finding k-cliques in k-partite graphs

Mirghorbani, Mohammad; Krokhmal, Pavlo A.

doi:10.1007/s11590-012-0536-y

Cited by 24 publications

(14 citation statements)

References 12 publications

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“…Mirghorbani and Krokhmal [17] proposed a method for finding a k-sized clique in k-segmented graphs. This method is based on the bit pattern used to find cliques.…”

Section: Related Workmentioning

confidence: 99%

Discovering the maximum k-clique on social networks using bat optimization algorithm

Khodadadi

Saeidi

2021

Comput Soc Netw

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The k-clique problem is identifying the largest complete subgraph of size k on a network, and it has many applications in Social Network Analysis (SNA), coding theory, geometry, etc. Due to the NP-Complete nature of the problem, the meta-heuristic approaches have raised the interest of the researchers and some algorithms are developed. In this paper, a new algorithm based on the Bat optimization approach is developed for finding the maximum k-clique on a social network to increase the convergence speed and evaluation criteria such as Precision, Recall, and F1-score. The proposed algorithm is simulated in Matlab® software over Dolphin social network and DIMACS dataset for k = 3, 4, 5. The computational results show that the convergence speed on the former dataset is increased in comparison with the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) approaches. Besides, the evaluation criteria are also modified on the latter dataset and the F1-score is obtained as 100% for k = 5.

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“…Mirghorbani and Krokhmal [17] proposed a method for finding a k-sized clique in k-segmented graphs. This method is based on the bit pattern used to find cliques.…”

Section: Related Workmentioning

confidence: 99%

Discovering the maximum k-clique on social networks using bat optimization algorithm

Khodadadi

Saeidi

2021

Comput Soc Netw

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“…In an intermediate paper Mirghorbani and Krokhmal [9] proposed to improve the data structure of FindClique. They reported that using arrays and bitsets could each gain a factor of about 3.…”

Section: Benchmarks On Random Graphsmentioning

confidence: 99%

A new $k$-partite graph $k$-clique iterator and the optimal colored Tverberg problem for ten colored points

Kliem¹

2021

Preprint

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We provide an algorithm that solves the optimal colored Tverberg problem for 10 points in the plane: Every 10 points in the plane in color classes of size at most 3 can be partitioned in 4 rainbow pieces such that their convex hulls intersect in a common point. This is achieved by translating the problem to k-partite graphs and using a new algorithm to verify that those graphs do not have a k-clique.

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“…In the worst case, the number of candidates can grow exponentially in the number of bigrams collected. The problem of efficiently finding kcliques in a k-partite graph has been studied in the context of braiding in the textile industry [20]; this approach significantly outperforms traditional branch-and-bound algorithms.…”

Section: )mentioning

confidence: 99%

Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries

Fanti

Pihur

Erlingsson

2016

Proceedings on Privacy Enhancing Technologies

232

202

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Techniques based on randomized response enable the collection of potentially sensitive data from clients in a privacy-preserving manner with strong local differential privacy guarantees. A recent such technology, RAPPOR [12], enables estimation of the marginal frequencies of a set of strings via privacy-preserving crowdsourcing. However, this original estimation process relies on a known dictionary of possible strings; in practice, this dictionary can be extremely large and/or unknown. In this paper, we propose a novel decoding algorithm for the RAPPOR mechanism that enables the estimation of "unknown unknowns," i.e., strings we do not know we should be estimating. To enable learning without explicit dictionary knowledge, we develop methodology for estimating the joint distribution of multiple variables collected with RAPPOR. Our contributions are not RAPPOR-specific, and can be generalized to other local differential privacy mechanisms for learning distributions of string-valued random variables.

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On finding k-cliques in k-partite graphs

Cited by 24 publications

References 12 publications

Discovering the maximum k-clique on social networks using bat optimization algorithm

Discovering the maximum k-clique on social networks using bat optimization algorithm

A new $k$-partite graph $k$-clique iterator and the optimal colored Tverberg problem for ten colored points

Building a RAPPOR with the Unknown: Privacy-Preserving Learning of Associations and Data Dictionaries

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