The Tree Inclusion Problem: In Linear Space and Faster

Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML databases. Kilpel\"ainen and Mannila [\emph{SIAM J. Comput. 1995}] presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when $P$ and $T$ have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let $n_S$, $l_S$, and $d_S$ denote the number of nodes, the number of leaves, and the %maximum depth of a tree $S \in \{P, T\}$. In this paper we show that the tree inclusion problem can be solved in space $O(n_T)$ and time: O(\min(l_Pn_T, l_Pl_T\log \log n_T + n_T, \frac{n_Pn_T}{\log n_T} + n_{T}\log n_{T})). This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.Comment: Minor updates from last tim

Monographie du Permo-Carbonifère de Wardak (Afghanistan central)

In central Afghanistan, the Upper Paleozoic (Uppermost Carboniferous and Permian) provided a sequence of fossiliferous levels almost unique in South-Asia. Comparable but not similar to those of Salt Range and Kashmir, this series is, for Carboniferous, of gondwan affinities (contrary to the province north of Hindou Kouch) and, for Permian, tethyan. Such a duality, mostly climatic, makes it easier to give precise datations, even for levels without any microfauna.En Afghanistan central, le Paléozoïque supérieur (Carbonifère terminal et Permien) de Wardak a fourni une succession de niveaux fossilifères presque unique dans les régions sud-asiatiques. Comparable mais non identique à celle de la Sait Range et du Kashmir, cette série est, pour le Carbonifère, d'affinités gondwanes, ce qui l'oppose à la province située au Nord de l'Hindou Kouch, et pour le Permien, téthysienne. Cette dualité, en grande partie d'ordre climatique, rend plus aisées des datations assez précises, même pour les niveaux d'où sont absentes les microfaunes.Termier Geneviève, Termier Henri, de Lapparent A.F., Marin P. Monographie du Permo-Carbonifère de Wardak (Afghanistan central). In: Documents des Laboratoires de Géologie de la Faculté des Sciences de Lyon. Hors série n°2, 1974. Monographie du Permo-Carbonifère de Wardak (Afghanistan central) pp. 1-78

Towards a better understanding of the Oulmes hydrogeological system (Mid-Atlas, Morocco)

Located in the Mid-Atlas (Morocco), the Oulmes plateau is famous for its mineral water springs “Sidi Ali” and “Lalla Haya” commercialised by the company “Les Eaux minérales d’Oulmès S.A”. Additionally, groundwater of the Oulmes plateau is intensively exploited for irrigation. The objective of this study, essentially performed from data collected during isotopic (summer 2004) and piezometric and hydrogeochemical field campaigns (spring 2007), is to improve the understanding of the Oulmes hydrogeological system. Analyses and interpretation of these data lead to the statement that this system is constituted by a main deep aquifer of large extension and by minor aquifers in a perched position. However, these aquifers interact enough to be in total equilibrium during the cold and wet period. As highlighted by isotopes, the origin of groundwater is mainly infiltration water except a small part of old groundwater with dissolved gas rising up from the granite through the schists