Related papers: Every Bit Counts in Consensus
The problem of electing a leader from among $n$ contenders is one of the fundamental questions in distributed computing. In its simplest formulation, the task is as follows: given $n$ processors, all participants must eventually return a…
In this paper we present an open source, fully asynchronous, leaderless algorithm for reaching consensus in the presence of Byzantine faults in an asynchronous network. We prove the algorithm's correctness provided that less than a third of…
Agreement protocols are crucial in various emerging applications, spanning from distributed (blockchains) oracles to fault-tolerant cyber-physical systems. In scenarios where sensor/oracle nodes measure a common source, maintaining output…
We present the first provably almost-optimal gossip-based algorithms for aggregate computation that are both time optimal and message-optimal. Given a $n$-node network, our algorithms guarantee that all the nodes can compute the common…
Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…
In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate…
We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…
We prove that longest common prefix (LCP) information can be stored in much less space than previously known. More precisely, we show that in the presence of the text and the suffix array, o(n) additional bits are sufficient to answer…
In recent decades, the RAFT distributed consensus algorithm has become a main pillar of the distributed systems ecosystem, ensuring data consistency and fault tolerance across multiple nodes. Although the fact that RAFT is well known for…
Efficient computation of shortest cycles which form a homology basis under $\mathbb{Z}_2$-additions in a given simplicial complex $\mathcal{K}$ has been researched actively in recent years. When the complex $\mathcal{K}$ is a weighted graph…
An average-case variant of the $k$-SUM conjecture asserts that finding $k$ numbers that sum to 0 in a list of $r$ random numbers, each of the order $r^k$, cannot be done in much less than $r^{\lceil k/2 \rceil}$ time. On the other hand, in…
Cascade systems route computational requests to smaller models when possible and defer to larger models only when necessary, offering a promising approach to balance cost and quality in LLM deployment. However, they face a fundamental…
Various networks are broadly and deeply applied in real-life applications. Reliability is the most important index for measuring the performance of all network types. Among the various algorithms, only implicit enumeration algorithms, such…
Sparse principal component analysis (PCA) improves interpretability of the classic PCA by introducing sparsity into the dimension-reduction process. Optimization models for sparse PCA, however, are generally non-convex, non-smooth and more…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
Layer-2 protocols can assist Ethereum's limited throughput, but globally broadcasting layer-2 data limits their scalability. The Danksharding evolution of Ethereum aims to support the selective distribution of layer-2 data, whose…
We take a systematic look at the problem of storing whole files in a cache with limited capacity in the context of optimistic learning, where the caching policy has access to a prediction oracle (provided by, e.g., a Neural Network). The…
Proof-of-stake blockchains require consensus protocols that support Dynamic Availability and Reconfiguration (so-called DAR setting), where the former means that the consensus protocol should remain live even if a large number of nodes…
Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts…
We show a tight lower bound of $\Omega(N \log\log N)$ on the number of transmissions required to compute the parity of $N$ input bits with constant error in a noisy communication network of $N$ randomly placed sensors, each having one input…