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arXiv · 2610.33864

Efficiency--Complexity Tradeoff and Constrained Percolation

Yuliy Baryshnikov·Efe Onaran
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Abstract

We study the efficiency--complexity tradeoff for resource-limited agents through directed first-passage percolation. Nonnegative i.i.d. edge weights represent physical energy expenditure, while the logarithmic size of a constrained path family measures representational complexity. For translation-invariant families, a path-joining property yields deterministic large-distance costs in rational directions and joint convexity in constraint parameter and direction, under suitable moment and feasibility assumptions. Our main result concerns the limiting cost parameterized by path-family entropy. Using techniques from analytic combinatorics in several variables (ACSV), we establish its almost-sure existence and joint continuity in entropy and direction for nested families satisfying additional generating-function conditions, on the corresponding entropy range. Path-count asymptotics supply the change of parameter linking this cost to the constraint-parameterized cost. Two planar examples constrain the number of turns or the number of East-runs of length at least two.

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Yuliy Baryshnikov, Efe Onaran. 2026-10-24. Efficiency--Complexity Tradeoff and Constrained Percolation. https://arxiv.org/abs/2610.33864

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