|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
18 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Revisionist Simulations: A New Approach to Proving Space Lower Bounds | | Faith Ellen
; Rati Gelashvili
; Leqi Zhu
; | | Date: |
7 Nov 2017 | | Abstract: | Determining the space complexity of $x$-obstruction-free $k$-set agreement
for $xleq k$ is an open problem. 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 number of registers needed to solve this
problem among $n>k$ processes is $n-k+x$ registers. No general lower bound
better than $2$ was known.
We prove that any $x$-obstruction-free protocol solving $k$-set agreement
among $n>k$ processes uses at least $lfloor(n-x)/(k+1-x)
floor+1$ registers.
Our main tool is a simulation that serves as a reduction from the impossibility
of deterministic wait-free $k$-set agreement: if a protocol uses fewer
registers, then it is possible for $k+1$ processes to simulate the protocol and
deterministically solve $k$-set agreement in a wait-free manner, which is
impossible. A critical component of the simulation is the ability of simulating
processes to revise the past of simulated processes. We introduce a new
augmented snapshot object, which facilitates this.
We also prove that any space lower bound on the number of registers used by
obstruction-free protocols applies to protocols that satisfy nondeterministic
solo termination. Hence, our lower bound of $lfloor(n-1)/k
floor+1$ for the
obstruction-free ($x=1$) case also holds for randomized wait-free free
protocols. In particular, this gives a tight lower bound of exactly $n$
registers for solving obstruction-free and randomized wait-free consensus.
Finally, our new techniques can be applied to get a space lower of $lfloor
n/2
floor+1$ for $epsilon$-approximate agreement, for sufficiently small
$epsilon$. It requires participating processes to return values within
$epsilon$ of each other. The best known upper bounds are
$lceillog(1/epsilon)
ceil$ and $n$, while no general lower bounds were
known. | | Source: | arXiv, 1711.2455 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER