Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2602.15921

Latent Objective Induction and Diversity-Constrained Selection: Algorithms for Multi-Locale Retrieval Pipelines

Faruk Alpay·Levent Sarioglu
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present three algorithms with formal correctness guarantees and complexity bounds for the problem of selecting a diverse, multi-locale set of sources from ranked search results. First, we formulate weighted locale allocation as a constrained integer partition problem and give an $O(n \log n)$ algorithm that simultaneously satisfies minimum-representation, budget-exhaustion, and proportionality-bound constraints; we prove all three hold with a tight deviation bound of $< 1$. Second, we define a cascaded country-code inference function as a deterministic priority chain over heterogeneous signals (TLD structure, model-inferred metadata, language fallback) and prove it satisfies both determinism and graceful degradation. Third, we introduce a $κ$-domain diversity constraint for source selection and give an $O(|K| \cdot R)$ algorithm that maintains the invariant via hash-map lookup, eliminating the aggregator monopolization pathology present in URL-level deduplication. We further formalize Latent Objective Induction (LOI), an environment-shaping operator over prompt spaces that steers downstream model behavior without restricting the feasible output set, and prove its convergence under mild assumptions. Applied to a multi-locale retrieval pipeline, these algorithms yield 62% improvement in first-party source ratio and 89% reduction in same-domain duplication across 120 multilingual queries.

Explore related subjects

cs.DScs.IR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Faruk Alpay, Levent Sarioglu. 2026-02-17. Latent Objective Induction and Diversity-Constrained Selection: Algorithms for Multi-Locale Retrieval Pipelines. https://arxiv.org/abs/2602.15921

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

KEEP EXPLORING

Related papers

arXiv2026

Beyond Kruskal: Polynomial-Time Tensor Decomposition under the Lovitz-Petrov Condition

Identifiability criteria certify that a given tensor decomposition is a unique rank decomposition. Kruskal's classical condition is one of the best-known deterministic criteria for identifiability. However, no polynomial-time decomposition algorithm is known under the Kruskal condition, and verifying the condition itself is NP-hard. Lovitz and Petrov introduced a strictly more general identifiability condition which, in contrast, is polynomial-time verifiable, but no polynomial-time decomposition algorithm was previously known under this condition. We give a polynomial-time algorithm for tensor decomposition under the Lovitz--Petrov condition. Moreover, combining our algorithm with polynomial-time verification of the Lovitz--Petrov condition yields an efficient end-to-end certification procedure: after computing a decomposition, one can deterministically certify in polynomial time that it is unique and therefore of minimum rank. This contrasts with an arbitrary tensor decomposition, which certifies only an upper bound on the tensor rank, while determining tensor rank is NP-hard in general.

cs.DS↗
arXiv2026

Poisson Exchange Beyond Submodularity: Effective Approximation Algorithms for Offline and Online Subset Selection over Matroids

Over the past decade, a growing body of research has shown that $γ$-weak submodularity broadly arises in numerous subset selection tasks, including feature selection, neural network pruning, and video summarization. Despite its prevalence, maximizing a $γ$-weakly submodular function subject to a general matroid constraint remains challenging. To date, the only known approximation guarantee is the conservative $(1+1/γ)^{-2}$ factor established by \citet{chen2018weakly}. To improve upon this result, this paper proposes a novel algorithm called \MGPE, which repeatedly performs maximum-gain local exchanges through careful control of a non-homogeneous Poisson clock, and proves that this \MGPE\ can attain an approximation ratio arbitrarily close to $ρ_γ=1-\left(γ/(2-γ)\right)^{ \frac{γ^2}{2(1-γ)} }$. In sharp contrast to the previous guarantee, our obtained factor $ρ_γ$ not only strictly improves upon $(1+1/γ)^{-2}$ for every $γ\in(0,1]$, but also can asymptotically approach the optimal $(1-1/e)$-approximation for submodular maximization as $γ\to1$. Furthermore, we surprisingly find that when the matroid constraint reduces to a cardinality or the objective satisfies the stronger notion of $α$-weak DR-submodularity, \MGPE\ can automatically recover the tight approximation ratios of $1-e^{-γ}$ and $1-e^{-α}$, respectively. Here, $α\in(0,1]$ denotes the DR ratio.

cs.DS↗
arXiv2026

Linear-Query Deterministic Approximation for Non-monotone Submodular Maximization under a Knapsack Constraint

Submodular maximization under a knapsack constraint (SMK) is a fundamental combinatorial optimization problem with broad applications across machine learning and data mining. Motivated by large-scale applications where query efficiency is paramount, we study non-monotone SMK and focus on deterministic algorithms with linear query complexity. Prior deterministic linear-query algorithms achieve at best a $1/5-\varepsilon$ approximation, falling short of the $1/4-\varepsilon$ ratio attainable by randomized algorithms. We close this gap by presenting a deterministic $(1/4-\varepsilon)$-approximation with $O(n\log^2(1/\varepsilon)/\varepsilon^2)$ queries. Our approach partitions the analysis based on the cost of the largest optimal element $r$: when the cost of $r$ is moderate, we refine the threshold-twin-greedy framework via residual-budget enumeration to tighten the analysis; when the cost of $r$ is large, we reduce the problem to bicriteria submodular maximization. As a secondary contribution, we obtain a $(1/2-\varepsilon, O(1/\varepsilon))$-bicriteria approximation with $O(n\log(1/\varepsilon)/\varepsilon^2)$ queries, improving over the previous $O(n^2/\varepsilon)$ query bound.

cs.DS↗