Comparison Patrols on Drifting Orders: Certified Rank Maintenance, Evolving Planar Maxima, and Selection under Drifting Fitness

Faruk Alpay; Levent Sarioglu

Home/Archive/arXiv

arXiv · 2606.15022

Comparison Patrols on Drifting Orders: Certified Rank Maintenance, Evolving Planar Maxima, and Selection under Drifting Fitness

Faruk Alpay·Levent Sarioglu

View original source ↗Read source document ↗Export metadata ↓

Abstract

Rank-based selection in dynamic environments acts on order information that becomes stale while it is being used. Tournaments, elitism, truncation, and Pareto selection may therefore consume rankings that no longer match the current fitness order, while full re-evaluation competes with search for the same budget. This paper formulates the missing information layer as a data-structure problem. A hidden total order on $n$ items drifts by adjacent transpositions, while a maintainer receives one truthful pairwise comparison per step and must answer rank queries continuously. We introduce the comparison patrol, a constant-time maintained-order structure using $3n+O(1)$ words, one comparison per update, deterministic verification-age bounds, and per-item displacement certificates. We prove lower bounds showing that oblivious and location-oblivious maintainers incur expected Kendall error $\Omega(\min(\alpha,1)n)$, and show that the patrol operates at the same order. A bump invariant yields exact self-stabilization after drift-free corruption: if the maximum rank overstatement is $L$, recovery takes at most $L$ aligned cycles and cannot finish before $L-1$. This gives a deterministic shock-recovery calculus and a crossover with full rebuild near $L\approx \log_2 n$. The maintained order is then transferred to evolving planar maxima and to evolutionary selection rules, giving deterministic bounds for truncation, tournament, elitist, and two-objective Pareto decisions under drifting fitness. Experiments up to $n=65{,}536$ audit the certificates, recovery laws, equilibrium behavior, and equal-budget dynamic evolutionary loops, identifying when certified local rank maintenance outperforms global re-evaluation and when it should hand over.

Explore related subjects

cs.DS cs.NE

Keep this discovery

BibTeX RIS

Faruk Alpay, Levent Sarioglu. 2026-06-12. Comparison Patrols on Drifting Orders: Certified Rank Maintenance, Evolving Planar Maxima, and Selection under Drifting Fitness. https://arxiv.org/abs/2606.15022

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

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗