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  1. Book ; Online: Addressing the cold start problem in privacy preserving content-based recommender systems using hypercube graphs

    Tuval, Noa / Hertz, Alain / Kuflik, Tsvi

    2023  

    Abstract: The initial interaction of a user with a recommender system is problematic because, in such a so-called cold start situation, the recommender system has very little information about the user, if any. Moreover, in collaborative filtering, users need to ... ...

    Abstract The initial interaction of a user with a recommender system is problematic because, in such a so-called cold start situation, the recommender system has very little information about the user, if any. Moreover, in collaborative filtering, users need to share their preferences with the service provider by rating items while in content-based filtering there is no need for such information sharing. We have recently shown that a content-based model that uses hypercube graphs can determine user preferences with a very limited number of ratings while better preserving user privacy. In this paper, we confirm these findings on the basis of experiments with more than 1,000 users in the restaurant and movie domains. We show that the proposed method outperforms standard machine learning algorithms when the number of available ratings is at most 10, which often happens, and is competitive with larger training sets. In addition, training is simple and does not require large computational efforts.

    Comment: 22 pages, 6 figures, 9 tables
    Keywords Computer Science - Information Retrieval ; Mathematics - Combinatorics
    Subject code 005
    Publishing date 2023-10-13
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Book ; Online: A machine learning framework for neighbor generation in metaheuristic search

    Liu, Defeng / Perreault, Vincent / Hertz, Alain / Lodi, Andrea

    2022  

    Abstract: This paper presents a methodology for integrating machine learning techniques into metaheuristics for solving combinatorial optimization problems. Namely, we propose a general machine learning framework for neighbor generation in metaheuristic search. We ...

    Abstract This paper presents a methodology for integrating machine learning techniques into metaheuristics for solving combinatorial optimization problems. Namely, we propose a general machine learning framework for neighbor generation in metaheuristic search. We first define an efficient neighborhood structure constructed by applying a transformation to a selected subset of variables from the current solution. Then, the key of the proposed methodology is to generate promising neighbors by selecting a proper subset of variables that contains a descent of the objective in the solution space. To learn a good variable selection strategy, we formulate the problem as a classification task that exploits structural information from the characteristics of the problem and from high-quality solutions. We validate our methodology on two metaheuristic applications: a Tabu Search scheme for solving a Wireless Network Optimization problem and a Large Neighborhood Search heuristic for solving Mixed-Integer Programs. The experimental results show that our approach is able to achieve a satisfactory trade-off between the exploration of a larger solution space and the exploitation of high-quality solution regions on both applications.
    Keywords Mathematics - Optimization and Control ; Computer Science - Artificial Intelligence ; Computer Science - Machine Learning
    Subject code 006
    Publishing date 2022-12-21
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: The average size of maximal matchings in graphs

    Hertz, Alain / Bonte, Sébastien / Devillez, Gauvain / Mélot, Hadrien

    2022  

    Abstract: We investigate the ratio $I(G)$ of the average size of a maximal matching to the size of a maximum matching in a graph $G$. If many maximal matchings have a size close to $\mu(G)$, this graph invariant has a value close to 1. Conversely, if many maximal ... ...

    Abstract We investigate the ratio $I(G)$ of the average size of a maximal matching to the size of a maximum matching in a graph $G$. If many maximal matchings have a size close to $\mu(G)$, this graph invariant has a value close to 1. Conversely, if many maximal matchings have a small size, $I(G)$ approaches $\frac{1}{2}$. We propose a general technique to determine the asymptotic behavior of $\avM(G)$ for various classes of graphs. To illustrate the use of this technique, we first show how it makes it possible to find known asymptotic values of $I(G)$ which were typically obtained using generating functions, and we then determine the asymptotic value of $I(G)$ for other families of graphs, highlighting the spectrum of possible values of this graph invariant between $\frac{1}{2}$ and $1$.

    Comment: 27 pages
    Keywords Mathematics - Combinatorics ; Computer Science - Discrete Mathematics
    Publishing date 2022-04-21
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: Lower Bounds and properties for the average number of colors in the non-equivalent colorings of a graph

    Hertz, Alain / Mélot, Hadrien / Bonte, Sébastien / Devillez, Gauvain

    2021  

    Abstract: We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent colorings of a graph $G$. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on $ ...

    Abstract We study the average number $\mathcal{A}(G)$ of colors in the non-equivalent colorings of a graph $G$. We show some general properties of this graph invariant and determine its value for some classes of graphs. We then conjecture several lower bounds on $\mathcal{A}(G)$ and prove that these conjectures are true for specific classes of graphs such as triangulated graphs and graphs with maximum degree at most 2.

    Comment: 20 pages, 2 figures
    Keywords Mathematics - Combinatorics ; Computer Science - Discrete Mathematics
    Publishing date 2021-04-29
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Using Graph Theory to Derive Inequalities for the Bell Numbers

    Hertz, Alain / Hertz, Anaelle / Mélot, Hadrien

    2021  

    Abstract: The Bell numbers count the number of different ways to partition a set of $n$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and ... ...

    Abstract The Bell numbers count the number of different ways to partition a set of $n$ elements while the graphical Bell numbers count the number of non-equivalent partitions of the vertex set of a graph into stable sets. This relation between graph theory and integer sequences has motivated us to study properties on the average number of colors in the non-equivalent colorings of a graph to discover new non trivial inequalities for the Bell numbers. Example are given to illustrate our approach.
    Keywords Computer Science - Discrete Mathematics ; Mathematics - Combinatorics
    Publishing date 2021-04-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article ; Online: A note on r-equitable k-colorings of trees

    Hertz Alain / Ries Bernard

    Yugoslav Journal of Operations Research, Vol 24, Iss 2, Pp 293-

    2014  Volume 298

    Abstract: A graph G = (V;E) is r-equitably k-colorable if there exists a partition of V into k independent sets V1, V2,. Vk such that ||Vi|- |Vj|| ≤ r for all i,j  {1,2. k}. In this note, we show that if two trees T1 and T2 of order at least two are r-equitably k- ...

    Abstract A graph G = (V;E) is r-equitably k-colorable if there exists a partition of V into k independent sets V1, V2,. Vk such that ||Vi|- |Vj|| ≤ r for all i,j  {1,2. k}. In this note, we show that if two trees T1 and T2 of order at least two are r-equitably k-colorable for r ≥ 1 and k ≥ 3, then all trees obtained by adding an arbitrary edge between T1 and T2 are also r-equitably k-colorable.
    Keywords trees ; equitable coloring ; independent sets ; Mathematics ; QA1-939 ; Science ; Q
    Language English
    Publishing date 2014-01-01T00:00:00Z
    Publisher University of Belgrade
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  7. Article ; Online: Tabu Search for the RNA Partial Degradation Problem

    Rybarczyk Agnieszka / Hertz Alain / Kasprzak Marta / Blazewicz Jacek

    International Journal of Applied Mathematics and Computer Science, Vol 27, Iss 2, Pp 401-

    2017  Volume 415

    Abstract: In recent years, a growing interest has been observed in research on RNA (ribonucleic acid), primarily due to the discovery of the role of RNA molecules in biological systems. They not only serve as templates in protein synthesis or as adapters in the ... ...

    Abstract In recent years, a growing interest has been observed in research on RNA (ribonucleic acid), primarily due to the discovery of the role of RNA molecules in biological systems. They not only serve as templates in protein synthesis or as adapters in the translation process, but also influence and are involved in the regulation of gene expression. The RNA degradation process is now heavily studied as a potential source of such riboregulators. In this paper, we consider the so-called RNA partial degradation problem (RNA PDP). By solving this combinatorial problem, one can reconstruct a given RNA molecule, having as input the results of the biochemical analysis of its degradation, which possibly contain errors (false negatives or false positives). From the computational point of view the RNA PDP is strongly NP-hard. Hence, there is a need for developing algorithms that construct good suboptimal solutions. We propose a heuristic approach, in which two tabu search algorithms cooperate, in order to reconstruct an RNA molecule. Computational tests clearly demonstrate that the proposed approach fits well the biological problem and allows to achieve near-optimal results. The algorithm is freely available at http://www.cs.put.poznan.pl/arybarczyk/tabusearch.php.
    Keywords rna degradation ; tabu search ; bioinformatics ; Mathematics ; QA1-939 ; Electronic computers. Computer science ; QA75.5-76.95
    Subject code 006
    Language English
    Publishing date 2017-06-01T00:00:00Z
    Publisher Sciendo
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Book ; Online: Der Graf der Graphen

    Hertz, Alain

    Kriminalistische Verwicklungen mit mathematischer Pointe

    2012  

    Author's details von Alain Hertz
    Keywords Mathematics
    Language German
    Size Online-Ressource (VIII, 192 S.)
    Publisher Vieweg+Teubner Verlag / Springer Fachmedien Wiesbaden GmbH, Wiesbaden
    Publishing place Wiesbaden
    Document type Book ; Online
    ISBN 9783834818140 ; 9783834886057 ; 3834818143 ; 383488605X
    DOI 10.1007/978-3-8348-8605-7
    Database Library catalogue of the German National Library of Science and Technology (TIB), Hannover

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  9. Book ; Online: Der Graf der Graphen

    Hertz, Alain

    Kriminalistische Verwicklungen mit mathematischer Pointe

    2012  

    Author's details von Alain Hertz
    Keywords Mathematics
    Language German
    Size Online-Ressource (VIII, 192 S.)
    Publisher Vieweg+Teubner Verlag / Springer Fachmedien Wiesbaden GmbH, Wiesbaden
    Publishing place Wiesbaden
    Document type Book ; Online
    ISBN 9783834818140 ; 9783834886057 ; 3834818143 ; 383488605X
    DOI 10.1007/978-3-8348-8605-7
    Database Former special subject collection: coastal and deep sea fishing

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  10. Article: Online algorithms for the maximum k-colorable subgraph problem

    Hertz, Alain / Gagnon, François / Montagné, Romain

    Computers & operations research : and their applications to problems of world concern : an international journal Vol. 91 , p. 209-224

    2018  Volume 91, Page(s) 209–224

    Author's details Alain Hertz, Romain Montagné, François Gagnon
    Keywords Online algorithms ; Maximum k-colorable subgraph ; Sequential vertex coloring ; Competitive analysis
    Language English
    Publisher Elsevier
    Publishing place Oxford [u.a.]
    Document type Article
    ZDB-ID 194012-0 ; 752014-1
    ISSN 0305-0548 ; 0163-0547
    ISSN 0305-0548 ; 0163-0547
    Database ECONomics Information System

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