arXiv subjects

Shengzhe Wang

Publications and source records attributed to Shengzhe Wang.

At least 19 recordsLinked to original sources

arXiv2026

Chandra Lensing-cluster Ultradeep Extragalactic Survey (CLUES) I: A 2 Ms Point-Source Catalog of the Abell 2744 Field

In the first paper of the Chandra Lensing-cluster Ultradeep Extragalactic Survey (CLUES), we present an ultradeep 2 Ms X-ray survey of the Abell 2744 field constructed from 101 archival Chandra ACIS-I observations. With an exposure comparable to the Chandra Deep Fields and further boosted by strong-lensing magnification from the Abell 2744 cluster at $z=0.3$, this field represents the third deepest extragalactic X-ray survey of the sky and also has rich synergy with extensive coverage by the Hubble Space Telescope and James Webb Space Telescope. We present the Chandra data reduction and detect sources in the soft (0.5-2 keV), hard (2-7 keV), and full (0.5-7 keV) bands over a total area of $369~\mathrm{arcmin^2}$. We perform dedicated image fitting with Chandra point spread functions to optimize point-source detections and improve X-ray positions and further screen the detections to address the impact of the central bright, structured intracluster medium. A total of 327 X-ray point sources are detected and cataloged, including their X-ray photometry and basic spectral properties. Detailed simulations are also conducted, based on which the expected 50% flux completeness reaches $6.3\times10^{-16}$, $2.8\times10^{-16}$, and $4.9\times10^{-16}~\mathrm{erg~cm^{-2}~s^{-1}}$ in the full, soft, and hard bands, respectively. The source number density as a function of flux is consistent with those in blank-field surveys within a factor of $\approx2$, with a slight excess above $\approx10^{-14}~\mathrm{erg~cm^{-2}~s^{-1}}$. All X-ray data products are publicly released, including the catalog, X-ray images, exposure maps, background maps, and sensitivity maps.

astro-ph.GA↗

arXiv2026

OneLA: Scaling Linear-Attention Decoding to Large Beams in Generative Recommendation

Generative recommendation (GR) relies on large-beam decoding to generate hundreds of candidate items, creating a new scaling challenge for recurrent linear attention. Existing linear attention serving systems either materialize a full recurrent state for every beam or repeatedly replay shared history, incurring substantial memory and traffic overhead. To address this, we present OneLA, a linear-attention decoding framework that exploits the shared prompt and short divergent suffixes of GR workloads. Specifically, OneLA represents all beam states using a single shared prompt-derived state and compact, append-only records of their divergent transitions. Using this representation, OneLA computes only the state information required at each decoding step, without reconstructing a full recurrent state for every beam. Furthermore, OneLA uses a lightweight ancestry index to track the transition records that make up each beam's history, allowing beams to be updated without moving or copying existing records. A fused GPU kernel further reuses the shared state across beams. Our analysis shows that OneLA achieves 1.54-2.46x end-to-end decode speedups while substantially reducing recurrent-state memory use and data movement.

cs.AI↗

arXiv2026

Pandora cluster Lensing, AGN, and Transient Exploration (PLATE) from JWST Multi-Epoch Imaging. I. Discovery of a type II supernova candidate in a spiral galaxy at $z=0.7$

We report the discovery and multi-wavelength analysis of a $z\sim0.7$ transient PLATE-23a in the Abell 2744 field, as the first results of the Pandora Lensing, AGN, and Transient Exploration (PLATE) project. Using multi-epoch JWST NIRCam imaging spanning from 2022 to 2025, we detect PLATE-23a in 12 filters. Difference-imaging analysis reveals its rising and declining phases. The host galaxy of PLATE-23a is a barred spiral at $z=0.688$ with a stellar mass of $\sim 10^{10.4}M_{\odot}$ and a star formation rate of $\sim5.1M_{\odot}~\rm yr^{-1}$, placing it on the star-forming main sequence. Bayesian light-curve classification strongly favors a type IIP supernova (SN) origin. It lies $\sim 13\rm kpc$ (after lensing correction) from the galaxy center in a region of low local star formation, suggesting the progenitor may have migrated from a distant star-forming clump. Physical properties derived from blackbody modeling indicate a temperature decreasing from $\sim8010\rm K$ to $\sim6100\rm K$ at around 65 days after the explosion; the late-time SED is consistent with entering the radioactive decay phase at about one rest-frame year. This work demonstrates the power of deep, multi-epoch JWST observations for studying transients at cosmological distances.

astro-ph.GA↗

arXiv2026

An emerging baryon cycle in a galaxy 500 million years after the Big Bang

The emergence of stellar feedback as a regulator of galaxy growth marks a fundamental transition in cosmic history. At early times, rapid gas accretion and collapse may induce intense star formation before feedback becomes effective, producing feedback-free starbursts. When and how such bursts subsequently develop into self-regulated baryon cycles remain observationally unknown. Here we show that Gz9p3, a merging galaxy at $z=9.311$, is caught in this transition only 500 million years after the Big Bang. Deep JWST spectroscopy reveals a substantial neutral-gas reservoir along its merger-driven tidal structure and a multiphase outflow. Fine-structure absorption provides the first direct measurement of the electron density of the cool outflowing gas at high redshift ($\approx\,17\,{\rm cm^{-3}}$), yielding a mass-loading factor among the highest yet measured for galaxies of comparable stellar mass. The emergence of such efficient feedback after an intense burst is consistent with the delayed onset of feedback expected in feedback-free starburst models. The cool outflowing gas is unlikely to escape the host halo, implying that much of this metal-enriched material may remain available for future recycling through the circumgalactic medium. Gz9p3 therefore provides an early view of a baryon cycle being established through the interplay of merger-driven gas redistribution, bursty star formation and stellar feedback, suggesting that feedback-regulated recycling was already shaping galaxy growth during the epoch of reionization.

astro-ph.GA↗

arXiv2026

Improved Space-Time Tradeoffs for Permutation Problems via Extremal Combinatorics

We provide improved space-time tradeoffs for permutation problems over additively idempotent semi-rings. In particular, there is an algorithm for the Traveling Salesperson Problem that solves $N$-vertex instances using space $S$ and time $T$ where $S\cdot T \leq 3.1861^{N}$. This improves a previous work by Koivisto and Parviainen [SODA'10] where $S\cdot T \leq 3.9271^N$, and overcomes a barrier they identified, as their bound was shown to be optimal within their framework. To get our results, we introduce a new parameter of a set system that we call the chain efficiency. This relates the number of maximal chains contained in the set system with the cardinality of the system. We show that set systems of high efficiency imply efficient space-time tradeoffs for permutation problems, and give constructions of set systems with high chain efficiency, disproving a conjecture by Johnson, Leader and Russel [Comb. Probab. Comput.'15].

cs.DS↗

arXiv2026

Confirmation and Refutation of Lyman Continuum Leakers at $z\sim3$ with JWST NIRSpec/IFU

Our understanding of the physical mechanisms and environments conducive to the escape of Lyman-continuum (LyC) radiation within the first 2 Gyr of cosmic history remains limited. Here we present a detailed analysis of JWST/NIRSpec medium-resolution IFU observations of two LyC-leaker candidates, LACES-94460 and LACES-104037 at z = 3.1, selected from deep HST/WFC3 F336W imaging and supported by ground-based spectroscopy. We first rule out LACES-94460 as a genuine LyC leaker, demonstrating that its apparent F336W signal originates from a nearby low-redshift interloper at z = 1.6, unambiguously identified through IFU spectroscopy. In contrast, for LACES-104037 we spectroscopically confirm bona fide LyC emission arising from a tidal-tail structure during the early stage of a galaxy merger, dubbed LACES104037-LyC. LACES104037-LyC exhibits extremely low rest-frame optical emission-line equivalent widths together with an exceptionally strong LyC flux. Within a picket-fence model framework, we reproduce its observed spectral and photometric properties with a young stellar population of age $\sim5$ Myr and a LyC escape fraction of $f_{\mathrm{esc}} \sim 99\%$. Our identification and detailed modeling of LACES104037-LyC provide one of the first compelling observational demonstrations for merger-driven LyC escape, indicating that galaxy mergers may represent an important and previously underappreciated contributor to the ionizing photon budget relevant for cosmic reionization. Furthermore, our analysis highlights the critical role of sub-kiloparsec resolution spectroscopy in securely identifying LyC leakers, removing contamination from closely projected low-redshift interlopers, and pinpointing the physical regions responsible for LyC leakage.

astro-ph.GA↗

arXiv2026

Atom Optics for Multidimensional Raman Interferometry

The coherent control of atomic wave packets in multiple momentum dimensions is a central challenge in Raman atom optics and a key requirement for multidimensional atom interferometry. In this paper, a momentum-basis theoretical framework is developed for two-dimensional Raman interactions. We formulate the atom-laser interaction for two-dimensional Raman beams and obtain the effective two-level ground-state Hamiltonian after adiabatic elimination of the excited states. The resulted Hamiltonian is constructed on the reachable momentum-state lattice and includes AC Stark shifts, intra-dimensional Raman couplings, and cross-dimensional Raman coupling terms, thereby describing multidimensional Raman dynamics beyond a simple superposition of independent single-dimensional models. The framework is used to analyze the principles and operating conditions of two-dimensional atom interferometry. Cross-dimensional Raman coupling and sequential reverse Raman transitions are identified as the main mechanisms that redistribute atoms into non-target momentum states and reduce the contrast of atomic interferometer fringe. Experimentally, Ramsey fringes are observed in a cold-atom fountain interferometer, with a contrast of $14.8\%$ at an interrogation time of $T=10~{\rm ms}$, in good agreement with the theoretical calculation. The conditions required for velocity-sensitive multidimensional atom interferometry are further clarified, including detuning control, velocity-class selection, and suppression of undesired inter-dimensional transitions. This work provides a theoretical and experimental basis for multidimensional Raman atom interferometry.

physics.atom-ph↗

arXiv2026

The Structure and Evolution of LRDs: Insights from JWST NIRSpec Medium and High Resolution Spectroscopy at $z\sim4$

We present an analysis of medium/high-resolution JWST/NIRSpec spectra for 11 LRDs at $z \sim 4$. By decomposing the broad and narrow components of the Balmer emission lines, we investigate the connection between line emission and UV/optical continua for the LRD population. We find that the broad H$α$ luminosity strongly correlates with the optical continuum (but not with the UV), indicating a common AGN origin for both. In contrast, the [O III] line strength is correlated with the UV continuum rather than the optical. Using the width and luminosity of the broad H$α$ line, we estimate central black hole masses of $10^6-10^8 M_{\odot}$ accreting at high Eddington ratios, consistent with an early ($λ_{\rm Edd} \sim 0.6$), rapid-growth phase of AGN evolution. Assuming a constant mass accretion rate in the framework of slim-disk models, we infer growth timescales of $\sim 10^5-10^7\rm yr$, and suggest LRDs may evolve into narrow-line Seyfert 1 galaxies. Upper limits from our spectra indicate that LRDs exhibit intrinsically weak optical Fe II emission compared to typical AGN. To simultaneously account for the inferred broad-line region size and observed luminosity, we propose a "Clumpy Envelope" model in which the optical emission arises from an extended, clumpy gas with a characteristic radius of tens of light-days. The diversity in observed optical continuum shapes can be explained by radial temperature gradients and self-absorption effects within this structure. Our results demonstrate the power of JWST high-resolution spectroscopy in probing the central engines and physical nature of the LRD population.

astro-ph.GA↗

arXiv2026

A Spatially Resolved HI Survey of Seyfert Galaxies: the Role of AGN Feedback in Shaping Atomic Gas Reservoirs

Active galactic nucleus (AGN) feedback is a key ingredient in galaxy evolution, yet its impact on the cold atomic gas reservoir -- the neutral hydrogen (HI) phase -- remains poorly constrained. We present the most extensive spatially resolved HI 21-cm survey of Seyfert AGN hosts to date, based on observations with the Giant Metrewave Radio Telescope (GMRT). Our high-resolution HI maps of eight Seyfert galaxies reveal detailed kinematics and surface density distributions of their atomic gas disks. We find that AGN-host galaxies exhibit a slightly shallower HI mass-size relation than the canonical relation or the SIMBA simulation predictions; however, the measured slope remains consistent with the canonical value within $2σ$ uncertainties. This result suggests that AGN feedback does not significantly disrupt the global extent or large-scale structure of atomic gas reservoirs. To investigate the internal HI kinematics in greater detail, we perform a 3D kinematic forward modeling of the HI disk in UGC 4503. Our analysis reveals an elevated intrinsic velocity dispersion of $σ= 14.9^{+6.1}_{-3.8}$ km/s and a reduced level of rotational support, with $V/σ= 14.28_{-4.17}^{+4.97}$, compared to large-sample star-forming spirals. These kinematic signatures, together with localized residuals in the velocity field, indicate that AGN-driven outflows or jets may inject or indirectly affect the turbulence in the atomic gas disk, potentially regulating the cold gas reservoir. Future GMRT observations, combined with optical integral-field spectroscopy from MaNGA, will enable quantitative constraints on the role of AGN feedback in regulating star formation efficiency across a larger and more representative galaxy sample.

astro-ph.GA↗

arXiv2026

New Parameterized and Exact Exponential Time Algorithms for Strongly Connected Steiner Subgraph

The Strongly Connected Steiner Subgraph (SCSS) problem is a well-studied network design problem that asks for a minimum subgraph that strongly connects a given set of terminals. In this paper, we present several new algorithmic and complexity results for SCSS. As our main result, we show that SCSS can be solved in time $17^{\mathrm{tw}} n^{O(1)}$ on directed graphs with $n$ vertices when a tree decomposition of the underlying graph of width $\mathrm{tw}$ is provided. This improves over a natural $\mathrm{tw}^{O(\mathrm{tw})}n^{O(1)}$ time algorithm, and is the first algorithm with this kind of running time for a problem involving strong connectivity. Second, we give an exact exponential-time algorithm that solves SCSS in $2^n n^{O(1)}$ time, improving the known bounds for general directed graphs. Finally, we investigate kernelization with respect to vertex cover. We prove that SCSS does not admit a polynomial kernel when parameterized by the size of a vertex cover, unless the polynomial hierarchy collapses. In contrast, we show that the closely related Strongly Connected Spanning Subgraph problem does admit a polynomial kernel under the same parameterization.

cs.DS↗

arXiv2026

Stronger Directed Low-Diameter Decompositions with Sub-Logarithmic Diameter and Separation

This paper significantly strengthens directed low-diameter decompositions in several ways. We define and give the first results for separated low-diameter decompositions in directed graphs, tighten and generalize probabilistic guarantees, and prove new independence results between (far away) edges. Our results are the first to give meaningful guarantees for decompositions with small diameters $D = Ω(\log\log n)$ in contrast to the state of the art that only applies to super-logarithmic diameters $D = ω(\log n)$. These results transfer several important and widely used aspects of undirected low-diameter decompositions to the directed setting. All our results are algorithmic -- small modifications to two existing directed low-diameter decompositions [BFHL25; Li25] can be used to sample decompositions with our new guarantees in near-linear time $\tilde{O}(m)$.

cs.DS↗

arXiv2026

The GLASS-JWST Early Release Science Program. V. H$α$ luminosity functions at $z\sim1.3$ and $z\sim2.0$

We present H$α$ luminosity function (LF) measurements at redshifts $z\sim1.3$ and $z\sim2.0$ using JWST NIRISS grism data from the GLASS-JWST survey. Based on emission lines spectroscopically identified in the F115W, F150W and F200W filters, we select 99 H$α$ emitters. Through detailed effective volume and completeness analysis for each source, we construct the H$α$ LF in two redshift bins. Thanks to the sensitivity of NIRISS WFSS and gravitational lensing magnification, our sample reaches intrinsic H$α$ luminosities $\sim$10 times deeper than previous grism surveys, down to $L_{\rm Hα}\sim10^{40.5}~\rm erg~s^{-1}$ at $z\sim1.3$ and $L_{\rm Hα}\sim10^{40.9}~\rm erg~s^{-1}$ at $z\sim2.0$ with completeness larger than 0.8, corresponding to star formation rates of 0.4 and 1.0 $M_{\odot}~\rm yr^{-1}$, respectively. We robustly constrain the faint-end slope of the H$α$ luminosity function to be $-1.50^{+0.14}_{-0.08}$ at $z\sim1.3$ and $-1.60^{+0.17}_{-0.09}$ at $z\sim2.0$ after considering the cosmic variance of $\sim 20\%$, consistent with previous estimations. The emission-line samples presented here will enable further detailed studies of galaxy properties including metallicities. We find a negligible contribution from bright active galactic nuclei in our sample. We estimate integrated cosmic star formation rate densities of $0.097^{+0.015}_{-0.016}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim1.3$ and $0.129^{+0.025}_{-0.030}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim2.0$. The methodology presented here can be readily applicable to other JWST slitless spectroscopic datasets and future wide-field slitless surveys, including those from Euclid, Roman, and the Chinese Space Station Telescope.

astro-ph.GA↗

arXiv2026

The faint end of the UV luminosity function at $0.4 < z < 0.7$ from the Hubble Frontier Fields

By extending the Hubble Frontier Fields (HFF) observations to the F225W band using HST WFC3/UVIS, we measure the rest-frame UV luminosity function (LF) of galaxies at $0.4 < z < 0.7$, pushing into the low-luminosity galaxy regime. In this first paper of a series, we describe the HST Cycle-27 GO-15940 F225W observations and data reduction, and present a corresponding catalog for the Abell 2744 field, which is the most data-rich HFF cluster field. Combining deep Near-UV imaging and the high magnification from strong gravitational lensing of the foreground cluster, we identify 152 faint galaxies with $-19.5 < M_{UV} < -12.1$ at $0.4 < z < 0.7$ through hybrid photometric-spectroscopic redshift selection from the Abell 2744 F225W catalog. Using a sample defined by a $50\%$ completeness cut and applying the maximum likelihood estimation, we derive the best-fit Schechter parameters for the UV LF at $z \sim 0.55$ down to $M_\text{UV} < -13.5$ mag, including a faint-end slope of $α= -1.324^{+0.072}_{-0.074}$. We incorporate a curvature parameter $δ$ in parameter estimation to account for a possible turn-over at the faint end of the UV LF, leveraging the exceedingly low luminosities probed by our sample. Our results rule out a turn-over brighter than $M_{UV} = -15.5$ at the $3σ$ confidence level.

astro-ph.GA↗

arXiv2026

SMES: Towards Scalable Multi-Task Recommendation via Expert Sparsity

Industrial recommender systems typically rely on multi-task learning to estimate diverse user feedback signals and aggregate them for ranking. Recent advances in model scaling have shown promising gains in recommendation. However, naively increasing model capacity imposes prohibitive online inference costs and often yields diminishing returns for sparse tasks with skewed label distributions. This mismatch between uniform parameter scaling and heterogeneous task capacity demands poses a fundamental challenge for scalable multi-task recommendation. In this work, we investigate parameter sparsification as a principled scaling paradigm and identify two critical obstacles when applying sparse Mixture-of-Experts (MoE) to multi-task recommendation: exploded expert activation that undermines instance-level sparsity and expert load skew caused by independent task-wise routing. To address these challenges, we propose SMES, a scalable sparse MoE framework with progressive expert routing. SMES decomposes expert activation into a task-shared expert subset jointly selected across tasks and task-adaptive private experts, explicitly bounding per-instance expert execution while preserving task-specific capacity. In addition, SMES introduces a global multi-gate load-balancing regularizer that stabilizes training by regulating aggregated expert utilization across all tasks. SMES has been deployed in Kuaishou large-scale short-video services, supporting over 400 million daily active users. Extensive online experiments demonstrate stable improvements, with GAUC gain of 0.29% and a 0.31% uplift in user watch time.

cs.IR↗

arXiv2026

MAMMOTH-LyC: Investigating the Role of Galaxy Mergers in a Strong Lyman Continuum Leaker at $z=2.39$

The MAMMOTH-LyC survey is a cycle 30 Hubble Space Telescope (HST) medium program obtaining 18-orbit-deep WFC3/UVIS F225W imaging in two massive galaxy protocluster fields at $z\sim2.2$. We introduce this survey by reporting the discovery of J1244-LyC1, a strong Lyman continuum (LyC) leaker at $z = 2.39$, exhibiting clear merger signatures. J1244-LyC1 has a highly significant ($10σ$) LyC detection, corresponding to an absolute escape fraction of $f_{\mathrm{esc}} \! =\!36\%\pm4\%$ ($1σ$). The LyC emission is spatially resolved into multiple peaks that coincide with the system's disturbed morphology, confirming genuine multi-site LyC leakage. With a stellar mass of $10^{10.2}{M_\odot}$, J1244-LyC1 is both the first confirmed high-redshift LyC-leaking merger and the most massive LyC emitter known to date. We interpret J1244-LyC1 as a merger-driven starburst system in which tidal interactions have disrupted the interstellar medium, creating multiple low-column-density pathways that facilitate LyC escape. This discovery provides the first direct evidence of spatially resolved LyC escape in a merging system, offering new insight into the potential role of major mergers in driving the cosmic reionization.

astro-ph.GA↗

arXiv2026

Discovery of a gas-enshrouded broad-line AGN at z $\sim$ 7

The Lyman-alpha (Ly$α$) absorption profile in star-forming galaxies serves as a powerful tracer of the extended, dense neutral hydrogen in their surroundings during the Epoch of Reionization (EoR). We report a unique galaxy, A2744-z7DLA, at $z\approx 6.87$ gravitationally lensed by the foreground galaxy cluster Abell 2744, which exhibits both moderate Ly$α$ emission and damped Ly$α$ absorption, suggesting the presence of a dense neutral hydrogen environment. Our analysis suggests that the UV continuum turnover near Ly$α$ is more likely shaped by a damped Ly$α$ system rather than nebular continuum from two photon process. We analyze the physical properties of A2744-z7DLA with spectroscopic and photometric data from the JWST and the HST. The galaxy shows a compact morphology ($r_e \sim 0.3\ {\rm kpc}$) and a broadened H$α$ emission line, suggesting possible AGN activity. The broad component of H$α$ has a FWHM of $2721 \pm 200\ {\rm km\ s^{-1}}$, corresponding to a black hole mass of $M_{\rm BH}=2.90^{+2.35}_{-1.28}\times 10^7 M_\odot$ and a black hole-to-stellar mass ratio of $\log (M_{\rm BH}/M_{\rm stellar}) = -1.58^{+0.45}_{-0.34}$. The Balmer decrement ($\rm Hα/Hβ$) yields a dust attenuation of $\rm A_V \approx 1.15 \pm 0.23$, indicating that this system is less dust-rich than some "little red dots". Furthermore, we perform SED fitting using both stellar and AGN models. The results show that the UV and optical wavelengths are dominated by star-forming regions, while the AGN component contributes primarily at longer wavelengths. This work provides new insights into the interplay between star formation, neutral gas, and potential AGN activity in galaxies during the EoR.

astro-ph.GA↗

arXiv2025

OneRec-V2 Technical Report

Recent breakthroughs in generative AI have transformed recommender systems through end-to-end generation. OneRec reformulates recommendation as an autoregressive generation task, achieving high Model FLOPs Utilization. While OneRec-V1 has shown significant empirical success in real-world deployment, two critical challenges hinder its scalability and performance: (1) inefficient computational allocation where 97.66% of resources are consumed by sequence encoding rather than generation, and (2) limitations in reinforcement learning relying solely on reward models. To address these challenges, we propose OneRec-V2, featuring: (1) Lazy Decoder-Only Architecture: Eliminates encoder bottlenecks, reducing total computation by 94% and training resources by 90%, enabling successful scaling to 8B parameters. (2) Preference Alignment with Real-World User Interactions: Incorporates Duration-Aware Reward Shaping and Adaptive Ratio Clipping to better align with user preferences using real-world feedback. Extensive A/B tests on Kuaishou demonstrate OneRec-V2's effectiveness, improving App Stay Time by 0.467%/0.741% while balancing multi-objective recommendations. This work advances generative recommendation scalability and alignment with real-world feedback, representing a step forward in the development of end-to-end recommender systems.

cs.IR↗

arXiv2025

Parallel $(1+ε)$-Approximate Multi-Commodity Mincost Flow in Almost Optimal Depth and Work

We present a parallel algorithm for computing $(1+ε)$-approximate mincost flow on an undirected graph with $m$ edges, where capacities and costs are assigned to both edges and vertices. Our algorithm achieves $\hat{O}(m)$ work and $\hat{O}(1)$ depth when $ε> 1/\mathrm{polylog}(m)$, making both the work and depth almost optimal, up to a subpolynomial factor. Previous algorithms with $\hat{O}(m)$ work required $Ω(m)$ depth, even for special cases of mincost flow with only edge capacities or max flow with vertex capacities. Our result generalizes prior almost-optimal parallel $(1+ε)$-approximation algorithms for these special cases, including shortest paths [Li, STOC'20] [Andoni, Stein, Zhong, STOC'20] [Rozhen, Haeupler, Marinsson, Grunau, Zuzic, STOC'23] and max flow with only edge capacities [Agarwal, Khanna, Li, Patil, Wang, White, Zhong, SODA'24]. Our key technical contribution is the first construction of length-constrained flow shortcuts with $(1+ε)$ length slack, $\hat{O}(1)$ congestion slack, and $\hat{O}(1)$ step bound. This provides a strict generalization of the influential concept of $(\hat{O}(1),ε)$-hopsets [Cohen, JACM'00], allowing for additional control over congestion. Previous length-constrained flow shortcuts [Haeupler, Hershkowitz, Li, Roeyskoe, Saranurak, STOC'24] incur a large constant in the length slack, which would lead to a large approximation factor. To enable our flow algorithms to work under vertex capacities, we also develop a close-to-linear time algorithm for computing length-constrained vertex expander decomposition. Building on Cohen's idea of path-count flows [Cohen, SICOMP'95], we further extend our algorithm to solve $(1+ε)$-approximate $k$-commodity mincost flow problems with almost-optimal $\hat{O}(mk)$ work and $\hat{O}(1)$ depth, independent of the number of commodities $k$.

cs.DS↗