SPI Height-relaxed AVL rebalancing: A uniied, ne-grained approach to concurrent dictionaries Height-relaxed AVL rebalancing: A uniied, ne-grained approach to concurrent dictionaries

Luc Boug, Joaquim Gabarrr, Xavier Messeguer, Nicolas Schabanel, Luc Boug, Joaquim Gabarrr, Xavier Messeguer, Nicolas Schabanel, Luc Boug, Joaquim Gabarrr, Xavier Messeguer, Nicolas Schabanel
1998 unpublished
We address the concurrent rebalancing of almost balanced binary search trees (AVL trees). Such a rebalancing may for instance be necessary after successive insertions and deletions of keys. We show that this problem can be studied through the self-reorganization of distributed systems of nodes controlled by l o c a l e v olution rules in the line of the approach of Dijkstra and Scholten. This yields a much simpler algorithm that the ones previously known. Based on the basic rebalancing
more » ... ebalancing framework, we describe algorithms to manage concurrent insertion and deletion of keys. Finally, this approach is used to emulate other well known concurrent A VL algorithms. As a by-product, this solves in a very general setting an old question raised by H.T. Kung and P.L. Lehman: where should rotations take place to rebalance arbitrary search trees? Ce rapport pr esente un algorithme concurrent pour la gestion dynamique d'un arbre binaire de recherche equilibr e (arbres AVL). Une s erie d'insertions et de suppressions de cl es dans un tel arbre peut lui donner une forme arbitraire. Nous montrons dans ce papier que le r e equilibrage de la structure peut ^ etre vu comme une auto-r eorganisation d'un syst eme distribu e form e par les noeuds, dirig ee par quelques r egles d' evolutions locales. Cette approche m ene a u n a l-gorithme bien plus simple que les solutions pr ec edentes connues. Des r egles compl ementaires permettent de plus de g erer les insertions et suppressions concurrentes. Ce r esultat permet en particulier de r epondre a la question pos ee par H.T. Kung et P.L.Lehman : \Peut-on eeectuer les rotations dans un ordre quelconque pour r e equilibrer un arbre arbitraire ?". La r eponse est : \Oui". Ce papier a et e soumis pour publication a A cta Informatica. Abstract We address the concurrent rebalancing of almost balanced binary search trees (AVL trees). Such a rebalancing may for instance be necessary after successive insertions and deletions of keys. We show that this problem can be studied through the self-reorganization of distributed systems of nodes controlled by l o c a l e v olution rules in the line of the approach of Dijkstra and Scholten. This yields a much simpler algorithm that the ones previously known. Based on the basic rebalancing framework, we describe algorithms to manage concurrent insertion and deletion of keys. Finally, this approach i s u s e d t o e m ulate other well known concurrent A VL algorithms. A s a b y-product, this solves in a very general setting an old question raised by H.T. Kung and P.L. Lehman: where should rotations take place to rebalance arbitrary search t r e e s ?
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