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
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Protecting user privacy in financial transactions is desirable, yet in the classical world it is effectively impossible without hardware assumptions. Most existing quantum money schemes also fail to guarantee anonymity. We introduce a construction of single-use quantum tokens that give users the ability to detect whether the issuing authority is tracking them, for which we prove unconditional security. Our tokens do not require quantum communication from the users themselves, making them relatively practical to deploy.
We discuss potential applications including one-time payment tokens, anonymous one-time pads and voting.
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Google has a long tradition of open-source software, which encompasses the field of operations research with OR-Tools. In development since 2008, it offers several solvers useful to many OR practitioners:
- PDLP, a revolutionary first-order linear solver that is reshaping the landscape of linear optimisation;
- CP-SAT, an award-winning constraint-programming solver;
- Glop, an accurate linear solver;
- Routing, a vehicle routing solver underpinning Google Maps Platform Route Optimization.
OR-Tools has long had its features accessible from other languages: the core algorithms are implemented in C++ for performance, but users can tap into them in Python, Java, C#, or Go.
It is recently available in Julia too, with a current focus on the linear and constraint solvers, either locally or remotely.
We provide a wrapper for our solvers that brings them to JuMP.jl through MathOptInterface.jl.
This tutorial will walk you through the features of OR-Tools and its solvers, then show examples of using OR-Tools from within Julia, either through JuMP or a lower-level interface.
We will also share our experience of C++-Julia interop.
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While prior works focused on the computational separation between Transformers and fully connected networks, here we focus on a purely statistical separation, and ask: What function class can Transformers learn with fewer samples compared to fully connected networks, even with infinite compute? We define a toy task---q-sparse token retrieval---and prove that the sample complexities of transformers that solve this task is smaller than those of feedforward and recurrent neural networks.
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Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we derive iterative auctions that maintain a single price path, eliminating the overhead and incentive problems associated with multiple price paths used solely for payment calculations. We demonstrate the versatility of our method by developing novel UCE auctions for multi-unit settings and deriving an iterative UCE variant of the Product-Mix auction. The resulting auctions combine the transparency of iterative price discovery with the efficiency and incentive properties of the VCG mechanism.
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This paper presents a novel framework for optimizing capacitor selection in electronic design using multi-objective linear and non-linear constrained optimization techniques. We demonstrate the effectiveness of this approach in minimizing cost and board area while meeting critical performance requirements.
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Julia's strength in mathematical computation and high performance makes it a popular choice across scientific fields, mostly due to its focus on mathematics in a broad sense and execution performance. It is a language of choice to implement new numerical algorithms, but it really shines in modelling for optimisation thanks to JuMP.jl and MathOptInterface.jl.
These libraries are, first and foremost, made for mathematical optimisation (linear, mixed-integer, conic, etc.), yet they are now generic enough to support more paradigms, such as constraint programming. This talk will introduce the basic principles behind the current implementation of JuMP.jl and explain why and how they are very good matches for modelling using constraint programming… and solving using any kind of mixed-integer-programming solver.
Constraint-programming solvers can also be implemented using linear programming, in a great collaboration between discrete and continuous optimisation. This talk will briefly explain the connection and its implementation in Google’s CP-SAT, a leading, award-winning constraint solver that uses linear programs in its solving process — a solver that will soon be available in Julia too.
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