The Las-Vegas Processor Identity Problem (How and When to Be Unique)
Identifieur interne : 009E16 ( Main/Exploration ); précédent : 009E15; suivant : 009E17The Las-Vegas Processor Identity Problem (How and When to Be Unique)
Auteurs : Shay Kutten [Israël] ; Rafail Ostrovsky [Colombie] ; Boaz Patt-Shamir [Israël]Source :
- Journal of Algorithms [ 0196-6774 ] ; 2000.
English descriptors
- Teeft :
- Academic press, Active processes, Adaptive, Adaptive adversaries, Adaptive adversary, Adaptive schedule, Additional time units, Adversary, Algorithm, Algorithm halts, Annual symposium, Asynchronous, Children subroutine, Colliding, Colliding processes, Complete iteration, Computer science, Correct value, Corresponding values, Counter value, Current value, Deterministic protocol, Different values, Dirty memory model, Dynamic algorithm, Dynamic model, Fair schedule, First access, First tree, Global, Global state, Global states, High probability, Impossibility, Impossibility result, Impossibility results, Inductive step, Initial contents, Initial state, Initialized, Ious schedule, Iteration, Kutten, Last process, Lemma, Local image, Local memory, Local state, Local states, Long time, Markov, Markov chain, Markov chains, Markov graph, Memory access, Memory model, Monte carlo, Morgan kaufmann, Negative results, Next state, Next step, Node, Oblivious adversary, Ostrovsky, Other process, Other processes, Other words, Positive probability, Primitive elements, Probabilistic function, Process claims, Process proceeds, Processor, Processor identity problem, Protocol, Random choices, Randomized protocols, Registers model, Same output value, Same state, Second tree, Simple fact, Simple property, Single process, Single step, Source node, Space requirement, Summation tree, Terminal component, Termination, Termination detection, Termination detection algorithm, Time unit, Time units, Total number, Transition function, Transition specification, Unbounded registers, Unique values, Uniqueness requirement.
Abstract
Abstract: We study the classical problem of assigning unique identifiers to identical concurrent processes. In this paper, we consider the asynchronous shared memory model, and the correctness requirement is that upon termination of the algorithm, the processes must have unique IDs always. Our results include tight characterization of the problem in several respects. We call a protocol solving this task Las Vegas if it has finite expected termination time. Our main positive result is the first Las-Vegas protocol that solves the problem. The protocol terminates in O(logn) expected asychronous rounds, using O(n) shared memory space, where n is the number of participating processes. The new protocol improves on all previous solutions simultaneously in running time (exponentially), probability of termination (to 1), and space requirement. The protocol works under the assumption that the asynchronous schedule is oblivious, i.e., independent of the actual unfolding execution. On the negative side, we show that there is no finite-state Las-Vegas protocol for the problem if the schedule may depend on the history of the shared memory (an adaptive schedule). We also show that any Las-Vegas protocol must know n in advance (which implies that crash faults cannot be tolerated) and that the running time is Ω(logn). For the case of an arbitrary (nonoblivious) adversarial schedule, we present a Las-Vegas protocol that uses O(n) unbounded registers. For the read-modify-write model, we present a constant-space deterministic algorithm.
Url:
DOI: 10.1006/jagm.2000.1110
Affiliations:
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In this paper, we consider the asynchronous shared memory model, and the correctness requirement is that upon termination of the algorithm, the processes must have unique IDs always. Our results include tight characterization of the problem in several respects. We call a protocol solving this task Las Vegas if it has finite expected termination time. Our main positive result is the first Las-Vegas protocol that solves the problem. The protocol terminates in O(logn) expected asychronous rounds, using O(n) shared memory space, where n is the number of participating processes. The new protocol improves on all previous solutions simultaneously in running time (exponentially), probability of termination (to 1), and space requirement. The protocol works under the assumption that the asynchronous schedule is oblivious, i.e., independent of the actual unfolding execution. On the negative side, we show that there is no finite-state Las-Vegas protocol for the problem if the schedule may depend on the history of the shared memory (an adaptive schedule). We also show that any Las-Vegas protocol must know n in advance (which implies that crash faults cannot be tolerated) and that the running time is Ω(logn). For the case of an arbitrary (nonoblivious) adversarial schedule, we present a Las-Vegas protocol that uses O(n) unbounded registers. For the read-modify-write model, we present a constant-space deterministic algorithm.</div></front></TEI><affiliations><list><country><li>Colombie</li><li>Israël</li></country></list><tree><country name="Israël"><noRegion><name sortKey="Kutten, Shay" sort="Kutten, Shay" uniqKey="Kutten S" first="Shay" last="Kutten">Shay Kutten</name></noRegion><name sortKey="Patt Shamir, Boaz" sort="Patt Shamir, Boaz" uniqKey="Patt Shamir B" first="Boaz" last="Patt-Shamir">Boaz Patt-Shamir</name></country><country name="Colombie"><noRegion><name sortKey="Ostrovsky, Rafail" sort="Ostrovsky, Rafail" uniqKey="Ostrovsky R" first="Rafail" last="Ostrovsky">Rafail Ostrovsky</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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