Algorithms and theory
Google’s mission presents many exciting algorithmic and optimization challenges across different product areas including Search, Ads, Social, and Google Infrastructure. These include optimizing internal systems such as scheduling the machines that power the numerous computations done each day, as well as optimizations that affect core products and users, from online allocation of ads to page-views to automatic management of ad campaigns, and from clustering large-scale graphs to finding best paths in transportation networks. Other than employing new algorithmic ideas to impact millions of users, Google researchers contribute to the state-of-the-art research in these areas by publishing in top conferences and journals.
Recent Publications
A simple and efficient implementation of strong call by need by an abstract machine
Małgorzata Biernacka
Witold Charatonik
Journal of Functional Programming, Volume 36 (2026)
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We present an abstract machine for a strong call-by-need strategy in the lambda calculus. The machine has been derived automatically from a higher-order evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an off-the-shelf transformation tool implementing the "functional correspondence" between higher-order interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak call-by-need strategy, and that it simulates the normal-order strategy in bilinear number of steps.
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Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of nonzero entries). A crucial property in applications is \emph{composability} of the sketching map, meaning that the sketch of a union of sets can be computed from individual sketches. Existing designs provide strong statistical guarantees, ensuring that a randomly sampled sketching map is accurate with high probability for a number of queries that is exponential in the sketch size $k$. However, these guarantees degrade to quadratic in $k$ when queries are adaptive, meaning they depend on previous responses.
Prior works on statistical queries (Steinke and Ullman, 2015) and specific MinHash cardinality sketches (Ahmadian and Cohen, 2024) established that this is tight in that they can be compromised using $\tilde{O}(k^2)$ adaptive queries. In this work, we develop a unified attack framework that applies to broad classes of cardinality sketches. We show that any union-composable sketching map can be compromised with $\tilde{O}(k^4)$ adaptive queries. Moreover, this improves to a tight bound of $\tilde{O}(k^2)$ for monotone composable maps (special cases include MinHash, statistical queries, Boolean linear maps), for any linear map over the reals $\mathbb{R}$ and finite fields $\mathbb{F}_p$, and for any linear map over the integers $\mathbb{Z}$ but when the estimator may only use the nonzero structure of the sketch (as in Cormode et al., 2003). Our work is the first to apply to general composable maps and establishes and builds on fundamental properties of these structures. Specifically for linear sketches, we are the first to establish tight quadratic bounds, to any subclass, and our bounds strengthen weaker polynomial bounds recently established by Gribelyuk et al. (2024).
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Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates
Shengjie Zhu
Xiaoming Liu
Vincent Chu
International Conference on 3D Vision (2026)
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Structure-from-Motion (SfM) is a classical 3D vision task for recovering camera parameters and scene geometry from multi-view images. Recent advances in deep learning enable accurate monocular depth estimation (MDE) that infers structure from a single image without depending on camera motion. But integrating MDE into SfM remains challenging. Unlike classical triangulated sparse pointclouds, MDE produces dense depthmaps with significantly higher error variance. Inspired by modern RANSAC estimators, we propose a Marginalized Bundle Adjustment (MBA) to accommodate MDE error variance with its density. With MBA, we show that MDE depthmaps are sufficiently accurate to support SoTA or competitive results in Structure-from-Motion and camera relocalization. Our benchmark demonstrates consistent remarkable results from two-view, few-frames small multiview, to thousands-frames large multiview system. Our method highlights the significant potential of MDE on multi-view 3D vision tasks.
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In large-scale distributed enterprises, traditional Knowledge Management (KM) systems face a critical failure mode: static documentation cannot keep pace with evolving operational realities and regional nuances. This "knowledge latency" forces employees out of self-service workflows and into costly support ticketing queues. This paper introduces SENTINEL, a geo-contextual AI framework designed to shift enterprise support from reactive retrieval to proactive interception. The architecture employs a novel dual-engine system integrated into an omni-present interface. The first engine utilizes Large Language Models (LLMs) to conduct pre-emptive, historical case-grounded audits of documentation, generating a "Contextual Density" score that identifies friction zones. The second engine is an autonomous Retrieval-Augmented Generation (RAG) agent that surfaces in-situ via a location-intelligent assistant window, resolving queries in real-time. By functioning as a strategic "defensive barrier" at the point of origin, SENTINEL demonstrates how a proactive AI assistant can drive high-fidelity, in-situ case deflection.
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Surviving the perfect storm: how hardware PMs can beat the AI tax and trade tariffs
Mind The Product (2026)
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This piece analyzes how hardware product managers can navigate the financial pressure of AI-related costs and trade tariffs. It presents a practical framework for deploying the Joint Development Model (JDM) as a product development strategy to balance innovation with cost efficiency, enabling sustainable growth for next-generation AI-native consumer devices.
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Regular-polygon geometry is tightly linked to cyclotomic arithmetic: Poonen and Rubinstein’s treatment of three-diagonal concurrence, for example, turns a geometric incidence condition into a short vanishing sum of roots of unity.
We prove an analogous rigidity result for areas. Two congruent crossing diagonals divide a regular n-gon into four regions. For the four regions cut out by the two congruent crossing diagonals V0Vm and VkVn−m+k of a regular n-gon, we completely classify, for all parameters (n, k, m), which sums of the normalized areas a0, . . . , a3 are rational. The classification has a sharp finite–infinite contrast: a0 is rational in only five configurations, whereas the rational cases for a2 and adjacent two-region sums form infinite families. Rationality is delicately sensitive to the parameters: for the configuration (14, 3, 5), no nontrivial subset sum is rational, while the neighboring cut (14, 4, 5) gives a2 = 5/7.
The proof reduces each rationality condition to trigonometric relations at rational multiples of π and combines cyclotomic norm arguments with the classification theorems of Conway–Jones and Poonen–Rubinstein.
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