Skip Trees, an Alternative Data Structure to Skip Lists in a Concurrent Approach

We present a new type of search trees, called Skip trees, which are a generalization of Skip lists. To be precise, there is a one-to-one mapping between the two data types which commutes with the sequential update algorithms. A Skip list is a data structure used to manage data bases which stores values in a sorted way and in which it is insured that the form of the Skip list is independent of the order of updates by using randomization techniques. Skip trees inherit all the properties of Skip lists, including the time bounds of sequential algorithms. The algorithmic improvement of the Skip tree type is that a concurrent algorithm on the y approach can be designed. Among other advantages, this algorithm is more compressive than the one designed by Pugh for Skip lists and accepts a higher degree of concurrence because it is based on a set of local updates. From a practical point of view, although the Skip list should be in the main memory, Skip trees can be registered into a secondary or external storage. Therefore we analyse the ability of Skip trees to manage data bases in comparison with B-trees. Nous presentons un nouveau type d'arbres, que nous appellons Skip trees, les quels sont une g en eralisation des Skip lists. Concr etement, il existe un isomorphisme entre eux qui commute avec les algorithmes s equentiels. Une Skip list est une structure de donn ees ordonn ees qui sert pour manager des base de donn ees. Une propri et e int eressante est que la connguration des Skip lists ne r esulte pas de l'ordre d'introduction des donnes parce qu'on utilise des techniques al eatoires. Des Skip trees h eritent toutes les propri et es des Skip lists, surtout les bornes des algorithmes s equentiels. Mieux encore, l'utilisation des Skip trees nous permet de construire un algorithme concurrent on the y. Cette solution oore de grands avantages: l'algorithme est plus compr ehensible que celui construit par Pugh pour les Skip lists, et il accepte plus de concurrence parce que les transformations sont locales. D'un point de vue pratique, malgr e que les Skip lists doivent ^ etre enregistr ees en m emoire centrale, les Skip trees peuvent ^ etre stock es sur un support secondaire. En level header NIL 1 2 3 4 Figure 1: Skip list cons equence, nous etudions l'habilit e des Skip trees …