arXiv subjects

Yuhao Guo

Publications and source records attributed to Yuhao Guo.

7 recordsLinked to original sources

arXiv2026

A Simple Analysis of Quadratic Probing and Other Open Addressing Schemes

In open addressed hashing, quadratic probing is attractive for striking a nice balance between having a high locality of reference and a low number of probes per search. However, these are empirical observations, not theoretical guarantees. Indeed, until recently, it was not known whether quadratic probing had constant expected insertion cost under any positive load factor $\alpha > 0$, even with uniformly random hash functions. In a recent breakthrough---albeit a numerically understated breakthrough---Kuszmaul and Xi (2024) proved that any fixed offset sequence (including quadratic probing) does, in fact, have constant expected insertion cost for load factors $\alpha \leq 8.9\%$. This is well below what we would like to prove, that quadratic probing has constant insertion cost for any load factor $\alpha < 1-\epsilon$ bounded away from 1. In this paper, we prove that open addressed hashing with any fixed offset sequence has constant expected insertion cost for load factors up to $35.74\%$, and that for quadratic probing in particular, we can increase the load factor to $37.61\%$. Our main innovation is a new type of witness forest for recording collisions among the probe sequences.

cs.DS↗

arXiv2026

The Greedy Binary Search Tree is Non-trivially Competitive

We prove that the $\textsf{Greedy}$ binary search tree is $2^{O(\sqrt{\log\log n})}$-competitive. It is widely conjectured that $\textsf{Greedy}$ is $O(1)$-competitive, but before this work it was not known to be $f$-competitive, for any non-trivial $f(n)=o(\log n)$. Our analysis differs from prior analyses of binary search trees. It takes what might be called a "scaling" approach, where the cost at a refined scale is related to the cost at a coarser scale, and Wilber's interleave lower bound.

cs.DS↗

arXiv2026

$k$-Clustering via Iterative Randomized Rounding

In this work we propose a single rounding algorithm for the fractional solutions of the standard LP relaxation for $k$-clustering. As a starting point, we obtain an iterative rounding $(\frac{3^p + 1}{2})$-Lagrangian Multiplier-Perserving (LMP) approximation for the $k$-clustering problem with the cost function being the $p$-th power of the distance. Such an algorithm outputs a random solution that opens $k$ facilities \emph{in expectation}, whose cost in expectation is at most $\frac{3^p + 1}{2}$ times the optimum cost. Thus, we recover the $2$-LMP approximation for $k$-median by Jain et al.~[JACM'03], which played a central role in deriving the current best $2$ approximation for $k$-median. Unlike the result of Jain et al., our algorithm is based on LP rounding, and it can be easily adapted to the $L_p^p$-cost setting. For the Euclidean $k$-means problem, the LMP factor we obtain is $\frac{11}{3}$, which is better than the $5$ approximation given by this framework for general metrics. Then, we show how to convert the LMP-approximation algorithms to a true-approximation, with only a $(1+\varepsilon)$ factor loss in the approximation ratio. We obtain a ($\frac{3^p + 1}{2}+\varepsilon$)-approximation algorithm for $k$-clustering with cost function being the $p$-th power of the distance, for $p \geq 1$. This reproduces the best known ($2+\varepsilon$)-approximation for $k$-median by Cohen-Addad et al. [STOC'25], and improves the approximation factor for metric $k$-means from 5.83 by Charikar at al. [FOCS'25] to $5+\varepsilon$ in our framework. Moreover, the same algorithm, but with a specialized analysis, attains ($4+\varepsilon$)-approximation for Euclidean $k$-means matching the recent result by Charikar et al. [STOC'26].

cs.DS↗

arXiv2025

Ultralight Boson Ionization from Comparable-Mass Binaries

Detection of gravitational waves enables probes of environmental effects around compact binaries. Ultralight bosons, well motivated in particle physics and capable of forming core-like dark matter structures, induce environmental dynamics that differ qualitatively from those produced by stars or particle dark matter. For comparable-mass binaries, such bosons can form gravitationally bound states analogous to molecules once the binary separation falls below the characteristic wavelength of the bound states, with an inner region co-moving with the binary. We combine numerical simulations and a semi-analytic framework to characterize the structure and ionization of these gravitational molecules. We determine the extent of the co-moving region and compute the ionization flux driven by orbital motion over a range of eccentricities. Using these results, we estimate the backreaction on the binary orbital evolution and identify a new environmental effect: eccentricity-induced ionization of the co-moving component leads to efficient circularization. We further show that this molecular phase can be astrophysically viable and significantly modify the stochastic gravitational wave background from supermassive black hole binaries.

gr-qc↗

arXiv2024

Quasi-normal modes of slowly-rotating Johannsen black holes

The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations and of low values of the black hole spin parameter and deformation parameters. We find that the deformation parameter $\alpha_{13}$ has a stronger impact on the quasi-normal modes than the other leading order deformation parameters ($\alpha_{22}$, $\alpha_{52}$, and $\epsilon_{3}$). We derive a fitting formula for the fundamental modes with $l=2$ and $l=3$ for the deformation parameter $\alpha_{13}$ valid in the slow rotation approximation ($a_* < 0.4$). Finally, we constrain $\alpha_{13}$ from the event GW170104; within our analysis, we find that the data of GW170104 are consistent with the predictions of GR.

gr-qc↗

arXiv2023

Packet Header Recognition Utilizing an All-Optical Reservoir Based on Reinforcement-Learning-Optimized Double-Ring Resonator

Optical packet header recognition is an important signal processing task of optical communication networks. In this work, we propose an all-optical reservoir, consisting of integrated double-ring resonators (DRRs) as nodes, for fast and accurate optical packet header recognition. As the delay-bandwidth product (DBP) of the node is a key figure-of-merit in the reservoir, we adopt a deep reinforcement learning algorithm to maximize the DBPs for various types of DRRs, which has the advantage of full parameter space optimization and fast convergence speed. Intriguingly, the optimized DBPs of the DRRs in cascaded, parallel, and embedded configurations reach the same maximum value, which is believed to be the global maximum. Finally, 3-bit and 6-bit packet header recognition tasks are performed with the all-optical reservoir consisting of the optimized cascaded rings, which have greatly reduced chip size and the desired "flat-top" delay spectra. Using this optical computing scheme, word-error rates as low as 5*10-4 and 9*10-4 are achieved for 3-bit and 6-bit packet header recognition tasks, respectively, which are one order of magnitude better than the previously reported values.

eess.SP↗

arXiv2021

Deformation Control of a Deformable Object Based on Visual and Tactile Feedback

In this paper, we presented a new method for deformation control of deformable objects, which utilizes both visual and tactile feedback. At present, manipulation of deformable objects is basically formulated by assuming positional constraints. But in fact, in many situations manipulation has to be performed under actively applied force constraints. This scenario is considered in this research. In the proposed scheme a tactile feedback is integrated to ensure a stable contact between the robot end-effector and the soft object to be manipulated. The controlled contact force is also utilized to regulate the deformation of the soft object with its shape measured by a vision sensor. The effectiveness of the proposed method is demonstrated by a book page turning and shaping experiment.

cs.RO↗