{"id":18035,"date":"2023-02-17T23:42:27","date_gmt":"2023-02-17T22:42:27","guid":{"rendered":"https:\/\/www.ummto.dz\/fs\/?p=18035"},"modified":"2023-02-17T23:44:27","modified_gmt":"2023-02-17T22:44:27","slug":"avis-de-soutenance-de-doctorat-en-mathematiques-de-mr-talem-djamel","status":"publish","type":"post","link":"https:\/\/www.ummto.dz\/fs\/avis-de-soutenance-de-doctorat-en-mathematiques-de-mr-talem-djamel\/","title":{"rendered":"Avis de soutenance de Doctorat en Math\u00e9matiques de Mr. TALEM Djamel"},"content":{"rendered":"

[et_pb_section fb_built=\u00a0\u00bb1″ theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb custom_padding=\u00a0\u00bb|144px||||\u00a0\u00bb custom_margin=\u00a0\u00bb|-105px||||\u00a0\u00bb][et_pb_row _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb custom_margin=\u00a0\u00bb|-496px||71px||\u00a0\u00bb hover_enabled=\u00a0\u00bb0″ sticky_enabled=\u00a0\u00bb0″ custom_padding=\u00a0\u00bb|0px||||\u00a0\u00bb width=\u00a0\u00bb100%\u00a0\u00bb max_width=\u00a0\u00bb2524px\u00a0\u00bb][et_pb_column _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb type=\u00a0\u00bb4_4″ theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb][et_pb_accordion _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb hover_enabled=\u00a0\u00bb0″ sticky_enabled=\u00a0\u00bb0″ width=\u00a0\u00bb100%\u00a0\u00bb toggle_text_color=\u00a0\u00bb#E02B20″ toggle_font=\u00a0\u00bbAdamina|700|||||||\u00a0\u00bb toggle_text_align=\u00a0\u00bbjustify\u00a0\u00bb toggle_font_size=\u00a0\u00bb23px\u00a0\u00bb][et_pb_accordion_item title=\u00a0\u00bbAvis de Soutenance de Doctorat en Sciences en Math\u00e9matiques de Monsieur TALEM Djamel\u00a0\u00bb _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb open=\u00a0\u00bboff\u00a0\u00bb theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb hover_enabled=\u00a0\u00bb0″ sticky_enabled=\u00a0\u00bb0″ toggle_font_size=\u00a0\u00bb19px\u00a0\u00bb]<\/p>\n

du Le candidat Monsieur Djamel TALEM<\/span>\u00a0<\/span><\/strong>soutiendra sa th\u00e8se de Doctorat en Sciences\u00a0 en Math\u00e9matiques,\u00a0\u00a0<\/span><\/strong>sp\u00e9cialit\u00e9:\u00a0<\/span>Recherche Op\u00e9rationnelle<\/span>,\u00a0<\/span><\/strong>le 18<\/strong><\/span>\u00a0f\u00e9vrier 2023<\/span>\u00a0<\/strong><\/span>\u00e0 09<\/strong><\/span>h<\/strong><\/span>.<\/span><\/p>\n

Lieu\u00a0: Salle de soutenance de la Facult\u00e9 des Sciences<\/p>\n

Intitul\u00e9\u00a0de la th\u00e8se\u00a0:<\/p>\n

Calcul d\u2019invariants dans les Graphes et Ordres<\/strong><\/span><\/p>\n

Devant le jury d\u2019examen compos\u00e9 de\u00a0:<\/p>\n\n\n\n\n\n\n\n\n
AIDENE Mohamed<\/td>\nProfesseur<\/td>\nUMMTO<\/td>\nPr\u00e9sident<\/td>\n<\/tr>\n
SADI Bachir<\/td>\nProfesseur<\/td>\nUMMTO<\/td>\nDirecteur de th\u00e8se<\/td>\n<\/tr>\n
AIDER Meziane<\/td>\nProfesseur<\/td>\nUSTHB<\/td>\nExaminateur<\/td>\n<\/tr>\n
BOUCHEMAKH Isma<\/td>\nProfesseur<\/td>\n\u00a0USTHB<\/td>\nExaminatrice<\/td>\n<\/tr>\n
OUKACHA Brahim<\/td>\nProfesseur<\/td>\n\u00a0UMMTO<\/td>\nExaminateur<\/td>\n<\/tr>\n
SLIMANI Hachem<\/td>\nProfesseur<\/td>\nUniv-Bejaia<\/td>\nExaminateur<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/strong><\/p>\n

Le public est cordialement invit\u00e9<\/strong><\/p>\n

R\u00e9f\u00a0:\u00a0D\u00e9cision de soutenance N\u00b005\/VRPGRS\/2023 du 30\/01\/2023<\/strong><\/span><\/p>\n

[\/et_pb_accordion_item][et_pb_accordion_item title=\u00a0\u00bbR\u00e9sum\u00e9\u00a0de la th\u00e8se en Fran\u00e7ais\u00a0\u00bb _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb hover_enabled=\u00a0\u00bb0″ sticky_enabled=\u00a0\u00bb0″ open=\u00a0\u00bbon\u00a0\u00bb text_orientation=\u00a0\u00bbjustified\u00a0\u00bb]<\/p>\n

Dans cette th\u00e8se, nous nous int\u00e9ressons au calcul des invariants suivants : d\u00e9compo-sition minimum d’un graphe biparti en bicliques<\/u>, chaine d\u00e9viation d’un ensemble partiellement ordonn\u00e9 (poset<\/u>) et P-couplage. Les invariants de graphes (resp<\/u>. \u00a0des ordres) sont des param\u00e8tres qui caract\u00e9risent les graphes (resp<\/u>. \u00a0les ordres) et dont la valeur est la m\u00eame pour tous les graphes (resp<\/u>. \u00a0les ordres) qui sont isomorphes. La formulation des probl\u00e8mes de calcul des invariants est souvent facile, mais leurs r\u00e9solution est, en g\u00e9n\u00e9rale, loin d’\u00eatre pareille. En effet, les situations o\u00f9 nous disposons d’algorithmes \u00ab efficaces \u00bb\u00a0 pour les r\u00e9soudre sont limit\u00e9es, dans les plus parts des cas un tel algorithme n’existe pas (ou du moins, la communaut\u00e9 scientifique s’accorde \u00e0 penser qu’il n’existe pas), c’est le cas pour les probl\u00e8mes du stable maximum, de la coloration minimum, de la dimension d’un poset<\/u>, de la couverture minimum des sommets et d’un ensemble dominant minimum, etc. Nos contributions sont r\u00e9sum\u00e9es comme suit:<\/p>\n

Le probl\u00e8me de la d\u00e9composition d’un graphe biparti en bicliques<\/u> est aussi connu pour \u00eatre difficile en g\u00e9n\u00e9rale. En utilisant le parcours en largeur lexicographique, nous proposons d’abord un algorithme lin\u00e9aire pour la reconnaissance de la classe des graphes biparti distance h\u00e9r\u00e9ditaire, nous proposons aussi des algorithmes lin\u00e9aires pour calculer une biclique<\/u> maximum, une partition minimum des ar\u00eates en biclique<\/u> et une couverture minimum des sommets en bicliques<\/u> pour la m\u00eame classe de graphes.<\/p>\n

Le probl\u00e8me de la chaine d\u00e9viation d’un ensemble partiellement ordonn\u00e9, introduit par Kong<\/u> et Ribemboin<\/u> en 1984, est d\u00e9finit comme suit : pour un ensemble partiellement ordonn\u00e9 \u00ab\u00a0P\u00a0\u00bb, \u00ab\u00a0(D^i(P))i>0<\/sub>\u00a0\u00bb est une suite d\u2019ensembles partiellement ordonn\u00e9s\u00a0 d\u00e9finie \u00e0 partir de \u00ab\u00a0P\u00a0\u00bb d’une mani\u00e8re r\u00e9cursive, o\u00f9 \u00ab\u00a0P=D0<\/sup>(P)\u00a0\u00bb et pour\u00a0 \u00ab\u00a00<i, Di<\/sup>(P)\u00a0\u00bb est l’ordre strict sur les antichaines<\/u> maximales de l\u2019ordre Di-1 <\/sup>(P).\u00a0 Les m\u00eames auteurs ont montr\u00e9 que cette s\u00e9quence ainsi d\u00e9finie converge vers un ordre total apr\u00e8s un nombre fini d’it\u00e9rations. La notation \u00ab\u00a0cdev(P)\u00a0\u00bb d\u00e9signe le plus petit entier naturel pour lequel Dcdev(P) <\/sup>(P) est une chaine. Pour un ordre P qui n’est, ni antichaine<\/u> ni somme lin\u00e9aire d’autres ordres, nous montrons que la valeur du param\u00e8tre \u00ab\u00a0cdev(P)\u00a0\u00bb est la distance dans le graphe \u00ab\u00a0Inc(P)\u00a0\u00bb, graphe d’incomparabilit\u00e9 de \u00ab\u00a0P\u00a0\u00bb, entre deux sommets additionnels \u00ab\u00a00p\u00a0\u00bb et \u00ab\u00a01P<\/sub>\u00a0\u00bb, o\u00f9 \u00ab\u00a00P<\/sub>\u00a0\u00bb adjacent \u00e0 tous les \u00e9l\u00e9ments minimaux de \u00ab\u00a0P\u00a0\u00bb et \u00ab\u00a01P<\/sub>\u00a0\u00bb <\/sub>adjacent \u00e0 tous les \u00e9l\u00e9ments maximaux de \u00ab\u00a0P\u00a0\u00bb. Nous donnons aussi sa valeur pour les deux cas particuliers cit\u00e9s ci-dessus. Enfin, nous montrons que \u00ab\u00a0cdev\u00a0\u00bb est un invariant de comparabilit\u00e9, c’est-\u00e0-dire les posets<\/u> ayant un m\u00eame graphe de comparabilit\u00e9 ont le m\u00eame \u00ab\u00a0cdev\u00a0\u00bb.<\/p>\n

Quant au probl\u00e8me du \u00ab\u00a0P\u00a0\u2013couplage\u00a0\u00bb, il consiste en la g\u00e9n\u00e9ralisation de la notion du couplage comme suit: \u00e9tant donn\u00e9 un ordre<\/u> \u00ab\u00a0P=(E,_P)\u00a0\u00bb, un graphe biparti \u00ab\u00a0G=(X,Y,E’)\u00a0\u00bb tels que \u00ab\u00a0|E|=|E’|\u00a0\u00bb et une bijection \u00ab\u00a0f:E\u27f6 E’\u00a0\u00bb. Un \u00ab\u00a0P-couplage\u00a0\u00bb dans \u00ab\u00a0G\u00a0\u00bb est un ensemble d’ar\u00eates \u00ab\u00a0M\u00a0\u00bb v\u00e9rifiant \u00ab\u00a0f(A)\u2229 M\u00a0\u00bb est un couplage pour toute antichaine<\/u> de \u00ab\u00a0P\u00a0\u00bb. Le probl\u00e8me est de trouver un \u00ab\u00a0P-couplage\u00a0\u00bb avec un maximum d’ar\u00eates. La complexit\u00e9 de ce probl\u00e8me est inconnue \u00e0 l’heure actuelle. Nous donnons une condition n\u00e9cessaire et suffisante pour qu’un ensemble d’ar\u00eates soit un \u00ab\u00a0P-couplage\u00a0\u00bb, et nous montrons comment calculer efficacement un \u00ab\u00a0P-couplage\u00a0\u00bb maximum pour quelques classes de ordres<\/u> et de graphes tr\u00e8s particuli\u00e8res.<\/p>\n

Mots Cl\u00e9s<\/strong> : <\/span>Ensemble partiellement ordonn\u00e9, D\u00e9composition d’un graphe biparti en bicliques<\/u>, Biclique<\/u> maximale, Chaine maximale, Antichaine<\/u> maximale.<\/p>\n

 <\/p>\n

[\/et_pb_accordion_item][et_pb_accordion_item title=\u00a0\u00bbR\u00e9sum\u00e9 de la th\u00e8se en Anglais\u00a0\u00bb _builder_version=\u00a0\u00bb4.19.5″ _module_preset=\u00a0\u00bbdefault\u00a0\u00bb theme_builder_area=\u00a0\u00bbpost_content\u00a0\u00bb hover_enabled=\u00a0\u00bb0″ sticky_enabled=\u00a0\u00bb0″ open=\u00a0\u00bboff\u00a0\u00bb body_text_align=\u00a0\u00bbjustify\u00a0\u00bb]<\/p>\n

Abstract\u00a0<\/strong>: In this thesis, we focus on the calculation of the following invariants: decomposition of a bipartite graph into bicliques, invariant computation in a poset and \u00ab\u00a0P-matching\u00a0\u00bb. Graph (resp. poset) invariants are parameters that characterize graphs (resp. posets) and whose value is the same for all graphs (resp. posets) that are isomorphic. The formulation of invariant calculation problems is often easy, but their resolution, in general, is far from the same. Situations where we have \u201cefficient\u201d algorithms to solve these problems are rare, in most cases such an algorithm does not exist (or at least the scientific community agrees that it does not exist), this is the case for the problems of maximum independent set, minimum coloring problem, dimension of a poset, etc. Our contributions are summarized as follows:<\/p>\n

The problem of decomposition of a bipartite graph into bicliques is also known to be difficult in general. Using the lexicographic width search algorithm, we first propose a linear algorithm for the recognition of the class of distance hereditary bipartite graphs ; we also propose linear algorithms to calculate a maximum biclique, a minimum biclique edge partition and a minimum biclique cover for the same graph classes.<\/p>\n

 <\/p>\n

Invariant computation in a poset is introduced by Kong and Rebimboin: let \u00ab\u00a0P\u00a0\u00bb be a poset. We define an order on \u00ab\u00a0D(P)\u00a0\u00bb, the set of maximal antichain of \u00ab\u00a0P\u00a0\u00bb, as follows: for \u00ab\u00a0A, B\\in D(P), A <_{D (P)} B\u00a0\u00bb if and only if\u00a0 \u00ab\u00a0\\forall a\\in A, \\exists b\\in B\u00a0\u00bb such that \u00ab\u00a0a <_P b\u00a0\u00bb. In the same way, we define an order\u00a0 on the set of\u00a0 maximal antichains of \u00ab\u00a0D (P)\u00a0\u00bb, and so on. At the end, we will have built a sequence of orders \u00ab\u00a0P, D(P), D^2 (P),\\ldots, D^i (P),\\ldots\u00a0\u00bb\u00a0 where \u00ab\u00a0D^i (P) = D (D^{i-1}(P))\u00a0\u00bb. They proved that for a finite poset $P$, the sequence so constructed\u00a0 converges to a chain, i.e. there exists a natural integer $i$ such that \u00ab\u00a0D^i (P)\u00a0\u00bb is a total order. For a finite poset \u00ab\u00a0P\u00a0\u00bb which is neither an antichain nor a linear sum, we show that the value of the smallest natural integer noted \u00ab\u00a0cdev(P)\u00a0\u00bb is given by the distance in the incomparability graph of \u00ab\u00a0P\u00a0\u00bb between two additional, artificial vertices \u00ab\u00a00_P\u00a0\u00bb and \u00ab\u00a01_P\u00a0\u00bb , where \u00ab\u00a00_P\u00a0\u00bb is adjacent to all minimal elements of \u00ab\u00a0P\u00a0\u00bb and \u00ab\u00a01_P\u00a0\u00bb is adjacent to all maximal elements of \u00ab\u00a0P\u00a0\u00bb. We also show how to handle the latter two particular cases. Finally, we show that \u00ab\u00a0cdev\u00a0\u00bb is a comparability invariant.<\/p>\n

 <\/p>\n

The \u00ab\u00a0P-matching\u00a0\u00bb consists in generalization the concept of matching as follows: given a poset \u00ab\u00a0P=(E, \\leq_P)\u00a0\u00bb, a bipartite graph \u00ab\u00a0G=(X,Y,E’)\u00a0\u00bb \u00a0such that \u00ab\u00a0|E|=|E’|\u00a0\u00bb and a bijection \u00ab\u00a0f:E\u27f6 E’\u00a0\u00bb. A \u00ab\u00a0P-matching\u00a0\u00bb in \u00ab\u00a0G\u00a0\u00bb is a set of \u00ab\u00a0M\u00a0\u00bb edges verifying \u00ab\u00a0f(A)\u2229 M\u00a0\u00bb is a matching\u00a0 for any antichain of \u00ab\u00a0P\u00a0\u00bb. The problem is to find a maximum \u00ab\u00a0P-matching\u00a0\u00bb. The complexity of this problem is unknown. In this thesis, we give a necessary and sufficient condition for a set of edges to be a \u00ab\u00a0P\u00a0\u00bb-matching, and schow how to calculate a maximum \u00ab\u00a0P-matching\u00a0\u00bb for some very specific posets and graph classes.<\/p>\n

\u00a0Keywords<\/strong> :<\/span> Partially<\/u> ordered<\/u> set, Chain<\/u>, Antichain<\/u>, decomposition<\/u> of<\/u> bipartite graph into<\/u> bicliques<\/u>, maximal biclique<\/u><\/p>\n

[\/et_pb_accordion_item][\/et_pb_accordion][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

du Le candidat Monsieur Djamel TALEM\u00a0soutiendra sa th\u00e8se de Doctorat en Sciences\u00a0 en Math\u00e9matiques,\u00a0\u00a0sp\u00e9cialit\u00e9:\u00a0Recherche Op\u00e9rationnelle,\u00a0le 18\u00a0f\u00e9vrier 2023\u00a0\u00e0 09h. Lieu\u00a0: Salle de soutenance de la Facult\u00e9 des Sciences Intitul\u00e9\u00a0de la th\u00e8se\u00a0: Calcul d\u2019invariants dans les Graphes et Ordres Devant le jury d\u2019examen compos\u00e9 de\u00a0: AIDENE Mohamed Professeur UMMTO Pr\u00e9sident SADI Bachir Professeur UMMTO Directeur de th\u00e8se […]<\/p>\n","protected":false},"author":13,"featured_media":14680,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[1,9],"tags":[],"class_list":["post-18035","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe","category-new_dep_maths"],"yoast_head":"\nAvis de soutenance de Doctorat en Math\u00e9matiques de Mr. TALEM Djamel - Facult\u00e9 des Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.ummto.dz\/fs\/avis-de-soutenance-de-doctorat-en-mathematiques-de-mr-talem-djamel\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Avis de soutenance de Doctorat en Math\u00e9matiques de Mr. TALEM Djamel - Facult\u00e9 des Sciences\" \/>\n<meta property=\"og:description\" content=\"du Le candidat Monsieur Djamel TALEM\u00a0soutiendra sa th\u00e8se de Doctorat en Sciences\u00a0 en Math\u00e9matiques,\u00a0\u00a0sp\u00e9cialit\u00e9:\u00a0Recherche Op\u00e9rationnelle,\u00a0le 18\u00a0f\u00e9vrier 2023\u00a0\u00e0 09h. 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