Related papers: A divide-and-conquer sumcheck protocol
Delegated quantum computing enables a client with weak computational power to delegate quantum computing to a remote quantum server in such a way that the integrity of the server can be efficiently verified by the client. Recently, a new…
This paper studies three types of functions arising separately in the analysis of algorithms that we analyze exactly using similar Mellin transform techniques. The first is the solution to a Multidimensional Divide-and-Conquer (MDC)…
With the increasing popularity of continuous integration, algorithms for selecting the minimal test-suite to cover a given set of changes are in order. This paper reports on how polymorphism can handle false negatives in a previous…
We construct efficient data structures that are resilient against a constant fraction of adversarial noise. Our model requires that the decoder answers most queries correctly with high probability and for the remaining queries, the decoder…
We consider certificates of positivity for univariate polynomials with rational coefficients that are positive over (an interval of)~$\mathbb{R}$. Such certificates take the form of weighted sums of squares (SOS) of polynomials with…
This article introduces a novel communication scheme, termed coded compressed sensing, for unsourced multiple-access communication. The proposed divide-and-conquer approach leverages recent advances in compressed sensing and forward error…
We propose a refinement to the well known, and widely used, proof-of-work scheme of zeroing a cryptographic hash. Our refinement allows multiple autonomous users to cooperate on the proof-of-work for their own transactions in order to bring…
Regardless of their variations, blockchains require a consensus mechanism to validate transactions, supervise added blocks, maintain network security, synchronize the network state, and distribute incentives. Proof-of-Work (PoW), one of the…
We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or…
Several software systems are polyglot; that is, they comprise programs implemented in a combination of programming languages. Verifiers that directly run on mainstream programming languages are currently customized for single languages.…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
With the increasing availability of parallel computing power, there is a growing focus on parallelizing algorithms for important automated reasoning problems such as Boolean satisfiability (SAT). Divide-and-Conquer (D&C) is a popular…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
Mining dense subgraphs on multi-layer graphs is an interesting problem, which has witnessed lots of applications in practice. To overcome the limitations of the quasi-clique-based approach, we propose d-coherent core (d-CC), a new notion of…
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…
We introduce $\mathcal{V}$-polyhedral disjunctive cuts (VPCs) for generating valid inequalities from general disjunctions. Cuts are critical to integer programming solvers, but the benefit from many families is only realized when the cuts…
Inclusive deep inelastic scattering factorization combines two features that are often treated separately: an asymptotic reconstruction of the current-current matrix element from hard and long-distance data, and an invariance under finite…
In this work, we propose a new way to (non-interactively, verifiably) demonstrate quantum advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) constant degree multivariate…
We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results we give an algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be…
Selecting high-quality candidates from large datasets is critical in applications such as drug discovery, precision medicine, and alignment of large language models (LLMs). While Conformal Selection (CS) provides rigorous uncertainty…