This paper addresses the properties and design of long-lived adaptive algorithms in the read/write shared memory model. In particular we present adaptive and long-lived algorithms that adapt to the point contention of an operation while using only a bounded amount of memory. We believe the techniques and building blocks developed here to be of further use in the design of adaptive and long-lived algorithms. We use the renaming problem as a test-case to demonstrate the new techniques and properties. Three new implementations of adaptive, wait-free, and long-lived renaming in the read/write shared memory model are presented. Unlike previous algorithms [1] the three algorithms require a bounded number of registers and adapt to the point contention of an operation. The two previous algorithms presented in [1] either adapt to the point contention or use a bounded size memory...

this paper. Motivated by their first work Moir and Anderson developed renaming algorithms, in the read/write model, when such a bound on the maximum number of processes is known in advance. This led to a sequence of works on the renaming problem in this model [MA95, MG96, BGHM95] that lead to a long-lived (2K \Gamma 1)-renaming algorithm with O(K ) step complexity and O(K space complexity [Moi98]. These works employed various variants of the splitter building block which is a descendant of Lamport's adaptive mutual exclusion algorithm, however the last one [Moi98] depends on an additional work which is the first long-lived renaming algorithm by Burns and Peterson [BP89]

ACKNOWLEDGEMENTS The generous financial help of Technion is gratefully acknowledged First of all, I thank Prof. Hagit Attiya for her excellent guidance, for knowledge, experience and time that she has given me throughout all stages of the work. Thanks to Prof. Yehuda Afek, Dr. Dan Touitou and Dr. Gideon Stupp for their friendship, help and support, particularly during the PODC98 conference. I would like to thank Prof. Eli Gafni for his insight and for very helpful discussions. I owe a depth of gratitude to Rabbi Yosef Brook who encouraged me to continue studies towards Ph.D. degree, and to Rabbi Nachum Diamont for his wise advise and help.

Two implementations of an adaptive, wait-free, and long-lived renaming task in the read/write shared memory model are presented. Implementations of longlived and adaptive objects were previously known only in the much stronger model of load-linked and store-conditional (i.e., read-modify-write) shared memory. In read/write shared-memory only one-shot adaptive objects are known. Presented here are two algorithms that assign a new unique id in the range 1, ..., O(k²) to any process whose initial unique name is taken from a set of size N , for an arbitrary N and where k is the number of processors that actually take steps or hold a name while the new name is being acquired. The step complexity of acquiring a new name is respectively O(k²) and O(k² log k), while the step complexity of releasing a name is 1. The main differences between the two algorithms are in the prec...