Wait-free approximate agreement on graphs

@inproceedings{Alistarh2021WaitfreeAA,
  title={Wait-free approximate agreement on graphs},
  author={Dan Alistarh and Faith Ellen and Joel Rybicki},
  booktitle={SIROCCO},
  year={2021}
}
Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that – all the outputs are within distance 1 of one another, and – each output value… Expand

Figures and Tables from this paper

Brief Announcement: Variants of Approximate Agreement on Graphs and Simplicial Complexes
TLDR
This work shows that both tasks of approximate agreement on graphs, edge agreement and clique agreement arise as special cases of a more general, higher-dimensional, approximate agreement task, where the processes must agree on the vertices of a simplex in a given simplicial complex. Expand
Reductions and Extension-Based Proofs
TLDR
It is proved that, if T reduces to S, and T has an augmented extension-based proof that it is impossible to solve in the NIS model, then so does S. Expand
Why extension-based proofs fail
TLDR
This work introduces extension-based proofs, a class of impossibility proofs that are modelled as an interaction between a prover and a protocol and that include valency arguments. Expand

References

SHOWING 1-10 OF 58 REFERENCES
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
TLDR
It is shown that for any k < n, there is no deterministic wait-free protocol for n processors that solves the k-set agreement problem and this structure reveals a close analogy between the impossibility ofWait-free k- set agreement and the Brouwer fixed point theorem for thek-dimensional ball. Expand
Convergence and covering on graphs for wait-free robots
TLDR
This article studies the case where the space is uni-dimensional, modeled as a graph G, and considers a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Expand
Generalized FLP impossibility result for t-resilient asynchronous computations
TLDR
This paper generalizes FLP to multiple faults and establishes that k-set consensus proposed by Chaudhuri is impossible, if the protocol is to tolerate k failures, while there exists a protocol that tolerates k – 1 failures. Expand
The asynchronous computability theorem for t-resilient tasks
TLDR
The main theorem characterizes computability y in terms of the topological properties of a simplicial complex so that a given task is computable only if it can be associated with a complex that is simply connected with trivial homology groups. Expand
Byzantine Approximate Agreement on Graphs
TLDR
This work gives the first Byzantine-tolerant algorithm for a variant of lattice agreement and shows tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures. Expand
Optimal Resilience Asynchronous Approximate Agreement
TLDR
This paper presents a deterministic optimal resilience approximate agreement algorithm that can tolerate any t Byzantine faults while requiring only 3t+1 processes. Expand
On processor coordination using asynchronous hardware
TLDR
It is shown that the coordination problem cannot be solved by means of a deterministic protocol even if the system consists of only two processors, and the impossibility result holds for the most powerful type of shared atomic registers and does not assume symmetric protocols. Expand
Are wait-free algorithms fast?
TLDR
An O(log <italic>n</italic>) time wait-free approximate agreement algorithm is presented; the complexity of this algorithm is within a small constant of the lower bound. Expand
Tight bounds for k-set agreement
TLDR
The proof of this result is interesting because it is the first to apply topological techniques to the synchronous model and proves tight bounds on the time needed to solve k-set agreement. Expand
Easy impossibility proofs for distributed consensus problems
Easy proofs are given, of the impossibility of solving several consensus problems (Byzantine agreement, weak agreement, Byzantine firing squad, approximate agreement and clock synchronization) inExpand
...
1
2
3
4
5
...