Multi-Agent Distributed and Decentralized Geometric Task Allocation

Michael Amir, Yigal Koifman, Yakov Bloch, Ariel Barel, Alfred M. Bruckstein

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Section 3.1.1 derives the attraction–repulsion gradient form by splitting the gradient into three terms, nulling the baseline term, reducing pairwise integrals via symmetry/rotation, and defining a radial kernel F with compact support; it also shows locality (F(r)=0 for r≥2V) and uses a normalized discrete-time gradient step. The candidate solution reproduces the same derivation with the same sign/direction conventions and adds a rigorous justification for differentiating under the integral (dominated convergence) and for the vanishing of the baseline term. Thus, both are correct and essentially the same proof, with the model providing slightly more analytic detail.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The core derivation from the squared-error objective to attraction–repulsion dynamics is correct and clearly motivated, and the locality result is well stated and useful for decentralized implementation. The paper would benefit from stating minimal regularity assumptions and a brief dominated-convergence justification for differentiating under the integral; these are straightforward additions that would make the argument fully rigorous without changing the results.