Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2208.14229

Lower bound for constant-size local certification

Virgina Ardévol Martínez·Marco Caoduro·Laurent Feuilloley·Jonathan Narboni·Pegah Pournajafi·Jean-Florent Raymond
View original source ↗Read source document ↗Export metadata ↓

Abstract

Given a network property or a data structure, a local certification is a labeling that allows to efficiently check that the property is satisfied, or that the structure is correct. The quality of a certification is measured by the size of its labels: the smaller, the better.This notion plays a central role in self-stabilization, because the size of the certification is a lower bound (and often an upper bound) on the memory needed for silent self-stabilizing construction of distributed data structures. From the point of view of distributed computing in general, it is also a measure of the locality of a property (e.g. properties of the network itself, such as planarity). When it comes to the size of the certification labels, one can identify three important regimes: the properties for which the optimal size is polynomial in the number of vertices of the graph, the ones that require only polylogarithmic size, and the ones that can be certified with a constant number of bits. The first two regimes are well studied, with several upper and lower bounds, specific techniques, and active research questions. On the other hand, the constant regime has never been really explored, at least on the lower bound side. The main contribution of this paper is the first non-trivial lower bound for this low regime. More precisely, we show that by using certification on just one bit (a binary certification), one cannot certify $k$-colorability for $k\geq 3$. To do so, we develop a new technique, based on the notion of score, and both local symmetry arguments and a global parity argument. We hope that this technique will be useful for establishing stronger results. We complement this result by a discussion of the implication of lower bounds for this constant-size regime, and with an upper bound for a related problem, illustrating that in some cases one can do better than the natural upper bound.

Explore related subjects

cs.DCcs.DM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Virgina Ardévol Martínez, Marco Caoduro, Laurent Feuilloley, Jonathan Narboni, Pegah Pournajafi, Jean-Florent Raymond. 2022-08-30. Lower bound for constant-size local certification. https://doi.org/10.1016/j.tcs.2023.114068

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reforge: Low-Latency Distributed GNN Serving with Selective Embedding Recomputation

Graph Neural Networks (GNNs) have been widely adopted for their ability to compute expressive node representations in graph datasets. However, serving GNNs on large graphs is challenging due to the high communication, computation, and memory overheads of constructing and executing computation graphs, which represent information flow across large neighborhoods. Existing approximation techniques in training can mitigate the overheads but, in serving, still lead to high latency and/or accuracy loss. To this end, we propose Reforge, a system that enables low-latency GNN serving for large graphs with minimal accuracy loss through two key ideas. First, Reforge employs selective recomputation of precomputed embeddings, which allows for reusing precomputed computation subgraphs while selectively recomputing a small fraction to minimize accuracy loss. Second, we develop computation graph parallelism, which reduces communication overhead by parallelizing the creation and execution of computation graphs across machines. Our evaluation with large graph datasets and GNN models shows that Reforge significantly outperforms state-of-the-art techniques.

cs.DC↗
arXiv2026

Agentic AI Workload Characteristics

Agentic AI shifts LLM serving from isolated prompt-generation requests to stateful, multi-turn executions that repeatedly invoke the model, call tools, and grow context over time. This paper characterizes ReAct-style agents from both the LLM-serving and tool-execution perspectives using an end-to-end tracing infrastructure across reasoning and non-reasoning Gemma and Qwen configurations on five agentic benchmarks. Our study shows that agentic workloads are not simply long-prompt workloads: with effective context caching, most input tokens are reused across turns, making execution decode-dominated while increasing dependence on long-lived KV-cache state. We also find that tool use has a clear temporal structure, with agents shifting from read/explore behavior early in execution to execute/write behavior later. These results show that efficient agentic serving must jointly manage repeated model re-entry, persistent context state, and workload-dependent tool behavior.

cs.DC↗
arXiv2026

Byzantine Causal Reliable Broadcast (BCRB) with Constant-Size Message Metadata

Asynchronous Byzantine Reliable Broadcast (BRB) is a fundamental primitive that guarantees agreement and validity in distributed systems subject to Byzantine faults, but it lacks ordering guarantees. In this paper, we address Byzantine Causal Reliable Broadcast (BCRB), which builds on BRB to enforce causal message ordering. We present a novel BCRB protocol that decouples causal ordering from the BRB layer, achieving constant-size $\mathcal{O}(1)$ message metadata overhead and $\mathcal{O}(n^2)$ communication word complexity as against $\mathcal{O}(n^3)$ communication word complexity of existing protocols; here $n$ is the number of processes. We present two variants of our protocol: a cryptographic version using a threshold encryption scheme and sequence gating, and its non-cryptographic version. In the cryptographic version, senders broadcast ciphertexts immediately, and decryption shares are piggybacked on out-of-band ACKs, preventing early decryption and front-running. In both versions, causal safety is achieved probabilistically. We evaluate the probability of causal safety violations using a random variable path analysis under independent exponential link delay distributions. We show that both variants satisfy liveness and the probability of weak safety violation is bounded by $\mathcal{O}(f^{-3}\cdot\ln^3 f)$, where $f$ is the upper bound on the number of Byzantine processes, and $f < n/3$ and $f=\mathcal{O}(n)$. Further, for the crypto version, we show that the probability of strong safety violation is bounded by $\mathcal{O}(f^{-1} \cdot \ln^2 f)$. We also show how to modify our two protocols to guarantee 100\% weak safety keeping $\mathcal{O}(1)$ message space overhead but with $\mathcal{O}(n^3)$ messages and $\mathcal{O}(n^3)$ communication word complexity.

cs.DC↗