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Sparsification of Decomposable Submodular Functions [article]

Akbar Rafiey, Yuichi Yoshida
2022 arXiv   pre-print
Acknowledgments Akbar Rafiey was supported by NSERC. Yuichi Yoshida was supported by JST PRESTO Grant Number JPMJPR192B and JSPS KAKENHI Grant Number 20H05965.  ...  cardinality and matroid constraints in various data summarization settings Mirzasoleiman et al. [2016a,b,c] , and differential privacy settings Chaturvedi et al. [2021] , Mitrovic et al. [2017] , Rafiey  ... 
arXiv:2201.07289v1 fatcat:4gqsyaxoincvndnfhqgjz5dt3i

Approximation Algorithms for Generalized MST and TSP in Grid Clusters [article]

Binay Bhattacharya, Ante Ćustić, Akbar Rafiey, Arash Rafiey, Vladyslav Sokol
2015 arXiv   pre-print
We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is 1 × 1. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one
more » ... t from each non-empty grid cell. We give a (1+4√(2)+ϵ) and (1.5+8√(2)+ϵ)-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further.
arXiv:1507.04438v1 fatcat:bu3wz75myfevblogdzy2rs77b4

Ordering with precedence constraints and budget minimization [article]

Akbar Rafiey, Jeff Kinne, Ján Manuch, Arash Rafiey
2016 arXiv   pre-print
We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph H=(B,S). Vertices in B are thought of as goods or services that must be bought to produce items in S that are to be sold. An edge from j∈ S to i∈ B indicates that the production of j requires the purchase of i. Each vertex in B has a cost, and each vertex in S results in some gain. The goal is to obtain an ordering of
more » ... B∪ S that respects the precedence constraints and maximizes the minimal net profit encountered as the vertices are processed. We call this optimal value the budget or capital investment required for the bipartite graph, and refer to our problem as the bipartite graph ordering problem. The problem is equivalent to a version of an NP-complete molecular folding problem that has been studied recently [12]. Work on the molecular folding problem has focused on heuristic algorithms and exponential-time exact algorithms for the un-weighted problem where costs are ± 1 and when restricted to graphs arising from RNA folding. The bipartite graph present work seeks exact algorithms for solving the bipartite ordering problem. We demonstrate an algorithm that computes the optimal ordering in time O^*(2^n) when n is the number of vertices in the input bipartite graph. Our main result is a general strategy that can be used to find an optimal ordering in polynomial time for bipartite graphs that satisfy certain properties. We apply the technique to a variety of graph classes, obtaining polynomial-time solutions to the bipartite graph ordering problem for bipartite permutation graphs, trivially perfect, co-bipartite graphs, and trees.
arXiv:1507.04885v3 fatcat:redna2lncbdchiveeik7r5puea

Toward a Dichotomy for Approximation of H-coloring [article]

Akbar Rafiey, Arash Rafiey, Thiago Santos
2019 arXiv   pre-print
Given two (di)graphs G, H and a cost function c:V(G)× V(H) →Q_≥ 0∪{+∞}, in the minimum cost homomorphism problem, MinHOM(H), goal is finding a homomorphism f:V(G)→ V(H) (a.k.a H-coloring) that minimizes ∑_v∈ V(G)c(v,f(v)). The complexity of exact minimization of this problem is well understood [34], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs. In this paper, we consider the approximation of MinHOM within a constant factor.
more » ... r digraphs, MinHOM(H) is not approximable if H contains a digraph asteroidal triple (DAT). We take a major step toward a dichotomy classification of approximable cases. We give a dichotomy classification for approximating the MinHOM(H) when H is a graph. For digraphs, we provide constant factor approximation algorithms for two important classes of digraphs, namely bi-arc digraphs (digraphs with a conservative semi-lattice polymorphism or min-ordering), and k-arc digraphs (digraphs with an extended min-ordering). Specifically, we show that: 1. Dichotomy for Graphs: MinHOM(H) has a 2|V(H)|-approximation algorithm if graph H admits a conservative majority polymorphims (i.e. H is a bi-arc graph), otherwise, it is inapproximable; 2. MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a bi-arc digraph; 3. MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a k-arc digraph. In conclusion, we show the importance of these results and provide insights for achieving a dichotomy classification of approximable cases. Our constant factors depend on the size of H. However, the implementation of our algorithms provides a much better approximation ratio. It leaves open to investigate a classification of digraphs H, where MinHOM(H) admits a constant factor approximation algorithm that is independent of H.
arXiv:1902.02201v3 fatcat:hvl3idprorehvhyrt5mgydbgni

Toward a Dichotomy for Approximation of H-Coloring

Akbar Rafiey, Arash Rafiey, Thiago Santos, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
Rafiey, A. Rafiey, and T. Santos 91:5 then the HOM(H) problem is polynomial time solvable.  ...  Rafiey, A. Rafiey, and T. Santos 91:9 proportional to the difference of the fractional values v t − v t+1 .  ... 
doi:10.4230/lipics.icalp.2019.91 dblp:conf/icalp/RafieyRS19 fatcat:fpz3mb6v25d3bgyhz2fkjzbbam

Private Boosted Decision Trees via Smooth Re-Weighting [article]

Vahid R. Asadi, Marco L. Carmosino, Mohammadmahdi Jahanara, Akbar Rafiey, Bahar Salamatian
2022 arXiv   pre-print
Protecting the privacy of people whose data is used by machine learning algorithms is important. Differential Privacy is the appropriate mathematical framework for formal guarantees of privacy, and boosted decision trees are a popular machine learning technique. So we propose and test a practical algorithm for boosting decision trees that guarantees differential privacy. Privacy is enforced because our booster never puts too much weight on any one example; this ensures that each individual's
more » ... a never influences a single tree "too much." Experiments show that this boosting algorithm can produce better model sparsity and accuracy than other differentially private ensemble classifiers.
arXiv:2201.12648v1 fatcat:wisntaltdndx7fnkja6pdeln34

Fast and Private Submodular and k-Submodular Functions Maximization with Matroid Constraints [article]

Akbar Rafiey, Yuichi Yoshida
2020 arXiv   pre-print
The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem. Many machine learning problems, including data summarization and influence maximization, can be naturally modeled as the problem of maximizing monotone submodular functions. However, when such applications involve sensitive data about individuals, their privacy
more » ... oncerns should be addressed. In this paper, we study the problem of maximizing monotone submodular functions subject to matroid constraints in the framework of differential privacy. We provide (1-1/e)-approximation algorithm which improves upon the previous results in terms of approximation guarantee. This is done with an almost cubic number of function evaluations in our algorithm. Moreover, we study k-submodularity, a natural generalization of submodularity. We give the first 1/2-approximation algorithm that preserves differential privacy for maximizing monotone k-submodular functions subject to matroid constraints. The approximation ratio is asymptotically tight and is obtained with an almost linear number of function evaluations.
arXiv:2006.15744v1 fatcat:vgjyf2cfuvecbhqtmxjzjfjv24

Bi-Arc Digraphs and Conservative Polymorphisms [article]

Pavol Hell and Akbar Rafiey and Arash Rafiey
2020 arXiv   pre-print
[RRS19a] Akbar Rafiey, Arash Rafiey, and Thiago Santos. Toward a dichotomy for approximation of h-coloring.  ...  CoRR, abs/1902.02201, 2019. 56 [RRS19b] Akbar Rafiey, Arash Rafiey, and Tiago Santos. Toward a dichotomy for approximation of h-coloring.  ... 
arXiv:1608.03368v5 fatcat:es537slt4fgz5d6ke25aqcdjby

Cardiac repolarization changes in the children with breath-holding spells

Hamid Amoozgar, Fazl Saleh, Nahal Farhani, Mohammad Rafiei, Soroor Inaloo, Ali-Akbar Asadipooya
2013 Iranian Journal of Pediatrics  
Breath-holding spells are known as benign attacks, frequencies of which decrease by the development of the autonomic nervous system. The present study aims to compare the electrocardiographic repolarization in children with breath-holding spells. In this study, QT dispersion, QTc dispersion, T peak to T end dispersion, and P wave dispersion of the twelve-lead surface electrocardiography of fifty children who had breath-holding spells were measured and compared with normal children from April
more » ... 1 to August 2012. Forty-four (88%) patients had cyanotic spells, while 6 (12%) had pallid spells. QTc dispersion was increased in the patients with breath-holding spells (148.2±33.1) compared to the healthy children (132±27.3) and the difference was statically significant (P = 0.01). Meanwhile, no statistically significant differences were observed between the patients and the control subjects regarding the other parameters (P > 0.05). QTc dispersion was significantly increased in the patients with breath-holding spells compared to normal children and this is a sign of cardiac repolarization abnormality as well as the increased risk of cardiac arrhythmia in patients with breath-holding spells.
pmid:24910749 pmcid:PMC4025128 fatcat:gh7gqyd325bhbi63vqwt2kwssm

Prediction of microRNA target genes using an efficient genetic algorithm-based decision tree

Behzad Rabiee-Ghahfarrokhi, Fariba Rafiei, Ali Akbar Niknafs, Behzad Zamani
2015 FEBS Open Bio  
MicroRNAs (miRNAs) are small, non-coding RNA molecules that regulate gene expression in almost all plants and animals. They play an important role in key processes, such as proliferation, apoptosis, and pathogen-host interactions. Nevertheless, the mechanisms by which miRNAs act are not fully understood. The first step toward unraveling the function of a particular miRNA is the identification of its direct targets. This step has shown to be quite challenging in animals primarily because of
more » ... plete complementarities between miRNA and target mRNAs. In recent years, the use of machine-learning techniques has greatly increased the prediction of miRNA targets, avoiding the need for costly and time-consuming experiments to achieve miRNA targets experimentally. Among the most important machine-learning algorithms are decision trees, which classify data based on extracted rules. In the present work, we used a genetic algorithm in combination with C4.5 decision tree for prediction of miRNA targets. We applied our proposed method to a validated human datasets. We nearly achieved 93.9% accuracy of classification, which could be related to the selection of best rules.
doi:10.1016/j.fob.2015.10.003 pmid:26649272 pmcid:PMC4643183 fatcat:byaapii3ejhvvejaw4vurmukyu

Short-term load forecasting using mixed lazy learning method

Seyed-Masoud BARAKATI, Ali Akbar GHARAVEISI, Seyed Mohammad Reza RAFIEI
2015 Turkish Journal of Electrical Engineering and Computer Sciences  
A novel short-term load forecasting method based on the lazy learning (LL) algorithm is proposed. The LL algorithm's input data are electrical load information, daily electricity consumption patterns, and temperatures in a specified region. In order to verify the ability of the proposed method, a load forecasting problem, using the Pennsylvania-New Jersey-Maryland Interconnection electrical load data, is carried out. Three LL models are proposed: constant, linear, and mixed models. First, the
more » ... rformances of the 3 developed models are compared using the root mean square error technique. The best technique is then selected to compete with the state-of-the-art neural network (NN) load forecasting models. A comparison is made between the performances of the proposed mixed-model LL as the superior LL model and the radial basis function and multilayer perceptron NN models. The results reveal significant improvements in the precision and efficiency of the proposed forecasting model when compared with the NN techniques.
doi:10.3906/elk-1301-134 fatcat:ljsazfc6lzhcfhpy2gndg33f6u

Counting maximal near perfect matchings in quasirandom and dense graphs [article]

Yifan Jing, Akbar Rafiey
2019 arXiv   pre-print
A maximal ε-near perfect matching is a maximal matching which covers at least (1-ε)|V(G)| vertices. In this paper, we study the number of maximal near perfect matchings in generalized quasirandom and dense graphs. We provide tight lower and upper bounds on the number of ε-near perfect matchings in generalized quasirandom graphs. Moreover, based on these results, we provide a deterministic polynomial time algorithm that for a given dense graph G of order n and a real number ε>0, returns either a
more » ... conclusion that G has no ε-near perfect matching, or a positive non-trivial number ℓ such that the number of maximal ε-near perfect matchings in G is at least n^ℓ n. Our algorithm uses algorithmic version of Szemerédi Regularity Lemma, and has O(f(ε)n^5/2) time complexity. Here f(·) is an explicit function depending only on ε.
arXiv:1807.04803v3 fatcat:ptxbgs7yzfbhzpid5vme3ex7ze

MaxTiC: Fast Ranking Of A Phylogenetic Tree By Maximum Time Consistency With Lateral Gene Transfers [article]

Cedric Chauve, Akbar Rafiey, Adrian A. Davin, Celine Scornavacca, Philippe Veber, Bastien Boussau, Gergely Szollosi, Vincent Daubin, Eric Tannier
2017 bioRxiv   pre-print
This article has been peer-reviewed and recommended by Peer Community In Evolutionary Biology (\url{}). Lateral gene transfers between ancient species contain information about the relative timing of species diversification. Specifically, the ancestors of a donor species must have existed before the descendants of the recipient species. Hence, the detection of a transfer event can be translated into a time constraint between nodes of a phylogeny if
more » ... he donor and recipient can be identified. When a set of transfers is detected by interpreting the phylogenetic discordance between gene trees and a species tree, the set of all deduced time constraints can be used to rank the species tree, {\em i.e.} order totally its internal nodes. Unfortunately lateral gene transfer detection is challenging and current methods produce a significant proportion of false positives. As a result, often, no ranking of the species tree is compatible with the full set of time constraints deduced from predicted transfers. Here we propose a method, implemented in a software called MaxTiC (Maximum Time Consistency), which takes as input a species tree and a series of (possibly inconsistent) time constraints between its internal nodes, weighted by confidence scores. MaxTiC outputs a ranked species tree compatible with a subset of constraints with maximum cumulated confidence score. We extensively tested the method on simulated datasets, under a wide range of conditions that we compare to measures on biological datasets. In most conditions the obtained ranked tree is very close to the real one, confirming the potential of dating the history of life with transfers by maximizing time consistency. MaxTiC is freely available, distributed along with a documentation and several examples:
doi:10.1101/127548 fatcat:f4lwbd4arrh3ljgl2hf5oyyuze

High-fat milk consumption in Iran: Lessons from a recent policy affecting public health

Sima Rafiei, Sina Abdollahzade, Ali Akbar Zeinaloo, Hoda Mojazi Amiri
2010 Journal of Public Health Policy  
doi:10.1057/jphp.2010.1 pmid:20200531 fatcat:jvhrkehfqnflfehqdanszg6kay

Genotype Analysis of Giardia lamblia Isolated From Children in Ahvaz, Southwest of Iran

Elham Sadat Roointan, Abdollah Rafiei, Ali Reza Samarbaf-Zadeh, Ali Akbar Shayesteh, Ahmad Shamsizadeh, Mahdi Pourmahdi Borujeni
2013 Jundishapur Journal of Microbiology  
Giardia lamblia is a flagellated protozoa that infects the intestinal tract of a wide range of mammalian hosts, including both wild and domestic animals as well as humans. Two genotypes A and B are commonly reported among humans. The purpose of this study was to investigate the genotypes of G. lamblia among adult infected cases in Ahvaz, southwest of Iran. Fecal samples were collected from 50 patients who had been tested positive to G. lamblia. The samples were analyzed by semi-nested
more » ... chain reaction (PCR) and restriction fragment length polymorphism (RFLP) using the gdh gene. Our results indicate 38 and 16% assemblages of BIII and AII, respectively. Mixed infections with both assemblages AII and BIII were also detected in 46% of the positive samples. This higher rate of mixed infection in the region may be explained by the common occurrence of repeated and cumulative infection by the parasite in the study area or may reflect environmental contamination of water resources. Therefore, it seems further studies are needed to clarify the route of infection in the study area.
doi:10.5812/jjm.6443 fatcat:v2whf7qxejg5pnsjjzp3vf56sy
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