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arxiv: 1907.10671 · v1 · pith:35CRRHZFnew · submitted 2019-07-23 · 📡 eess.SY · cs.SY

Distributed Average Consensus under Quantized Communication via Event-Triggered Mass Splitting

Apostolos I. Rikos , Christoforos N. Hadjicostis This is my paper

Pith reviewed 2026-05-24 17:25 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords distributed average consensusquantized communicationevent-triggered controlmulti-agent systemsdirected graphsfinite-time convergencemass splitting
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The pith

A new event-triggered protocol lets multi-agent systems reach exact quantized average consensus in finite time over directed graphs using only quantized exchanges.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a distributed averaging method for agents connected by directed links where all stored, processed, and transmitted values must be uniformly quantized. Updates occur only when an event condition is met, which limits communication. On any fixed strongly connected digraph the method drives every agent to the same value that equals the quantized average of the initial states, and this occurs after a finite number of steps. The result matters because many real networks use directed links and face strict limits on data precision and transmission frequency. The authors also supply an example and comparisons that show how the method behaves relative to earlier quantized consensus schemes.

Core claim

The authors present an event-triggered distributed averaging algorithm based on mass splitting that operates solely with quantized information. On any time-invariant strongly connected digraph, the algorithm guarantees that all agents reach a common consensus value equal to the quantized average in finite time.

What carries the argument

Event-Triggered Mass Splitting protocol, in which each agent maintains quantized mass and transfers portions to neighbors only when an event trigger fires, thereby driving the system toward the quantized average.

If this is right

  • All agents obtain exactly the quantized average after finitely many event-triggered steps.
  • No continuous communication or real-valued arithmetic is required.
  • The same protocol works on any time-invariant strongly connected directed graph.
  • Event triggering reduces the number of transmissions compared with periodic quantized schemes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The finite-time guarantee may simplify verification of safety properties in networked control systems.
  • The mass-splitting idea could be adapted to other quantized coordination tasks such as formation control or load balancing.
  • If the strong-connectivity assumption is relaxed, the protocol might still reach a quantized consensus value within each strongly connected component.

Load-bearing premise

The communication graph is fixed and strongly connected, and every stored or exchanged number is produced by deterministic uniform quantization.

What would settle it

Execute the algorithm on a three-node directed cycle with initial values 0, 1, 0; if the agents never all hold the same quantized average value after any finite number of steps, the finite-time consensus claim is false.

Figures

Figures reproduced from arXiv: 1907.10671 by Apostolos I. Rikos, Christoforos N. Hadjicostis.

Figure 1
Figure 1. Figure 1: Example of digraph for probabilistic quantized averaging. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Node state variables plotted against the number of iterations for [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example of digraph for simulation of Algorithm 1. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Node state variables plotted against the number of iterations for [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between Algorithm 1, the distributed averaging algorithm with quantized communication in [29], the quantized gossip algorithm [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. The goal of distributed average consensus is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this paper, we present and analyze a distributed averaging algorithm which operates exclusively with quantized values (specifically, the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and rely on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed distributed averaging protocol, illustrate its operation with an example, and show that its execution, on any timeinvariant and strongly connected digraph, will allow all agents to reach, in finite time, a common consensus value that is equal to the quantized average. We conclude with comparisons against existing quantized average consensus algorithms that illustrate the performance and potential advantages of the proposed algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript proposes and analyzes a distributed averaging algorithm for multi-agent systems on directed graphs that operates exclusively under deterministic uniform quantization of stored, processed, and exchanged values. Updates are event-triggered via a mass-splitting mechanism. The central claim is that, on any time-invariant strongly connected digraph, the protocol drives all agents to a common consensus value equal to the quantized average of the initial states in finite time.

Significance. If the finite-time convergence result is rigorously established, the work would contribute to quantized consensus literature by combining event-triggering with mass splitting to achieve exact quantized-average consensus while potentially lowering communication load. The abstract's mention of comparisons to prior quantized algorithms suggests the approach may offer measurable efficiency gains under the stated graph and quantization assumptions.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'quantized average' is invoked without an inline definition or reference to its precise computation from the initial vector under uniform quantization; a one-sentence clarification would improve accessibility.
  2. The manuscript states that an example is used to illustrate operation, yet no figure or table caption details are visible in the provided material; ensuring the example clearly labels initial values, quantization levels, and convergence time would strengthen the presentation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation of minor revision. The referee's summary accurately captures the contribution. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an event-triggered mass-splitting algorithm for quantized average consensus and proves finite-time convergence to the quantized average on any time-invariant strongly connected digraph under deterministic uniform quantization. The central claim is established by direct analysis of the algorithm's state evolution under the stated graph and quantization assumptions; no parameter is fitted to data and then re-used as a prediction, no self-citation is invoked as a load-bearing uniqueness theorem, and no ansatz or renaming reduces the result to its own inputs by construction. The derivation therefore remains self-contained against the external graph-theoretic and quantization conditions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard domain assumption that the underlying digraph is time-invariant and strongly connected together with the model of deterministic uniform quantization; no free parameters or invented entities are introduced.

axioms (2)
  • domain assumption The communication graph is time-invariant and strongly connected.
    This condition is explicitly required for the finite-time convergence result stated in the abstract.
  • domain assumption Quantization is deterministic and uniform.
    The abstract specifies that all stored, processed, and exchanged information is subject to deterministic uniform quantization.

pith-pipeline@v0.9.0 · 5714 in / 1221 out tokens · 35007 ms · 2026-05-24T17:25:38.712144+00:00 · methodology

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