A Tight Lower Bound for k-Set Agreement
نویسندگان
چکیده
We prove tight bounds on the time needed to solve k-set agreement, a natural generalization of consensus. We analyze this problem in a synchronous, message-passing model where processors fail by crashing. We prove a lower bound of [f/k] + 1 rounds of communication for solutions to k-set agreement that tolerate f failures. This bound is tight, and shows that there is an inherent tradeoff between the running time, the degree of coordination required, and the number of faults tolerated, even in idealized models like the synchronous model. The proof of this result is interesting because it is a geometric combination of other well-known proof techniques.
منابع مشابه
The Complexity of Early Deciding Set Agreement
In the k-set agreement problem, each processor starts with a private input value and eventually decides on an output value. At most k distinct output values may be chosen, and every processor’s output value must be one of the proposed values. We consider a synchronous message passing system, and we prove a tight bound of f/k +2 rounds of communication for all processors to decide in every run i...
متن کاملA Tight Lower Bound for Processor Coordination
We prove a tight lower bound on the running time of oblivious solutions to k set agreement In k set agreement processors start with input values from a given set and choose output values from the same set In every execution the set of output values must be contained in the set of input values and the set of output values must have size at most k A solution is oblivious if it does not make use o...
متن کاملA bound for Feichtinger conjecture
In this paper, using the discrete Fourier transform in the finite-dimensional Hilbert space C^n, a class of nonRieszable equal norm tight frames is introduced and using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...
متن کاملRevisionist Simulations: A New Approach to Proving Space Lower Bounds
Determining the number of registers required for solving x-obstruction-free (or randomized wait-free) k-set agreement for x ≤ k is an open problem that highlights important gaps in our understanding of the space complexity of synchronization. In x-obstruction-free protocols, processes are required to return in executions where at most x processes take steps. The best known upper bound on the nu...
متن کاملA Note on Set Agreement with Omission Failures
This paper considers the k-set agreement problem in a synchronous distributed system model with send-omission failures in which at most f processes can fail by send-omission. We show that, in a system of n + 1 processes (n + 1 > f), no algorithm can solve k-set agreement in ⌊ f k ⌋ rounds. Our lower bound proof uses topological techniques to characterize subsets of executions of our model. The ...
متن کامل