arXiv subjects

Amit Kumar

Publications and source records attributed to Amit Kumar.

At least 199 records · Page 11Linked to original sources

arXiv2021

The Signatures of Self-Interacting Dark Matter and Subhalo Disruption on Cluster Substructure

The abundance, distribution and inner structure of satellites of galaxy clusters can be sensitive probes of the properties of dark matter. We run 30 cosmological zoom-in simulations with self-interacting dark matter (SIDM), with a velocity-dependent cross-section, to study the properties of subhalos within cluster-mass hosts. We find that the abundance of subhalos that survive in the SIDM simulations are suppressed relative to their cold dark matter (CDM) counterparts. Once the population of disrupted subhalos -- which may host orphan galaxies -- are taken into account, satellite galaxy populations in CDM and SIDM models can be reconciled. However, even in this case, the inner structure of subhalos are significantly different in the two dark matter models. We study the feasibility of using the weak lensing signal from the subhalo density profiles to distinguish between the cold and self-interacting dark matter while accounting for the potential contribution of orphan galaxies. We find that the effects of self-interactions on the density profile of subhalos can appear degenerate with subhalo disruption in CDM, when orphans are accounted for. With current error bars from the Subaru Hyper Suprime-Cam Strategic Program, we find that subhalos in the outskirts of clusters (where disruption is less prevalent) can be used to constrain dark matter physics. In the future, the Vera C. Rubin Observatory Legacy Survey of Space and Time will give precise measurements of the weak lensing profile and can be used to constrain $σ_T/m$ at the $\sim 1$ cm$^2$ g$^{-1}$ level at $v\sim 2000$ km s$^{-1}$.

astro-ph.CO↗

arXiv2021

GRB 140102A: Insight into Prompt Spectral Evolution and Early Optical Afterglow Emission

We present and perform a detailed analysis of multi-wavelength observations of \thisgrb, an optical bright GRB with an observed reverse shock (RS) signature. Observations of this GRB were acquired with the BOOTES-4 robotic telescope, the \fermi, and the \swift missions. Time-resolved spectroscopy of the prompt emission shows that changes to the peak energy (\Ep) tracks intensity and the low-energy spectral index seems to follow the intensity for the first episode, whereas this tracking behavior is less clear during the second episode. The fit to the afterglow light curves shows that the early optical afterglow can be described with RS emission and is consistent with the thin shell scenario of the constant ambient medium. The late time afterglow decay is also consistent with the prediction of the external forward shock (FS) model. We determine the properties of the shocks, Lorentz factor, magnetization parameters, and ambient density of \thisgrb, and compare these parameters with another 12 GRBs, consistent with having RS produced by thin shells in an ISM-like medium. The value of the magnetization parameter ($R_{\rm B} \approx 18$) indicates a moderately magnetized baryonic dominant jet composition for \thisgrb. We also report the host galaxy photometric observations of \thisgrb obtained with 10.4m GTC, 3.5m CAHA, and 3.6m DOT telescopes and find the host (photo $z$ = $2.8^{+0.7}_{-0.9}$) to be a high mass, star-forming galaxy with a star formation rate of $20 \pm 10 \msun$ $\rm yr^{-1}$.

astro-ph.HE↗

arXiv2021

Progenitor mass constraints for the type Ib intermediate-luminosity SN 2015ap and the highly extinguished SN 2016bau

Photometric and spectroscopic analyses of the intermediate-luminosity Type Ib supernova (SN) 2015ap and of the heavily reddened Type Ib SN~2016bau are discussed. Photometric properties of the two SNe, such as colour evolution, bolometric luminosity, photospheric radius, temperature, and velocity evolution, are also constrained. The ejecta mass, synthesised nickel mass, and kinetic energy of the ejecta are calculated from their light-curve analysis. We also model and compare the spectra of SN~2015ap and SN~2016bau at various stages of their evolution. The P~Cygni profiles of various lines present in the spectra are used to determine the velocity evolution of the ejecta. To account for the observed photometric and spectroscopic properties of the two SNe, we have computed 12\,$M_\odot$ zero-age main sequence (ZAMS) star models and evolved them until the onset of core collapse using the publicly available stellar-evolution code {\tt MESA}. Synthetic explosions were produced using the public version of {\tt STELLA} and another publicly available code, {\tt SNEC}, utilising the {\tt MESA} models. {\tt SNEC} and {\tt STELLA} provide various observable properties such as the bolometric luminosity and velocity evolution. The parameters produced by {\tt SNEC}/{\tt STELLA} and our observations show close agreement with each other, thus supporting a 12\,$M_\odot$ ZAMS star as the possible progenitor for SN~2015ap, while the progenitor of SN~2016bau is slightly less massive, being close to the boundary between SN and non-SN as the final product.

astro-ph.SR↗

arXiv2021

SN 2020ank: a bright and fast-evolving H-deficient superluminous supernova

We investigate the observational properties of a hydrogen-deficient superluminous supernova (SLSN) SN 2020ank (at z = 0.2485), with the help of early phase observations carried out between $-$21 and +52 d since $g$-band maximum. Photometrically, SN 2020ank is one of the brightest SLSN ($M_{g,peak}$ $\sim$ $-$21.84 $\pm$ 0.10 mag), having fast pre-peak rising and post-peak decaying rates. The bolometric light curve of SN 2020ank exhibits a higher peak luminosity ($L_{max}$) of $\sim$(3.9 $\pm$ 0.7) $\times$ 10$^{44}$ erg s$^{-1}$ and appears to be symmetric around the peak with $L^{rise}_{max}$/e $\approx$ $L^{fall}_{max}$/e $\approx$ 15 d. The semi-analytical light-curve modelling using the MINIM code suggests a spin down millisecond magnetar with $P_i$ $\sim$2.2 $\pm$ 0.5 ms and $B$ $\sim$(2.9 $\pm$ 0.1) $\times$ $10^{14}$ G as a possible powering source for SN 2020ank. The possible magnetar origin and excess ultraviolet flux at early epochs indicate a central-engine based powering source for SN 2020ank. Near-peak spectra of SN 2020ank are enriched with the W-shaped O II features but with the weaker signatures of C II and Fe III. Using the estimated rise time of $\sim$27.9 d and the photospheric velocity of $\sim$12050 km s$^{-1}$, we constrain the ejecta mass to $\sim$7.2 $M_{\odot}$ and the kinetic energy of $\sim$6.3 $\times$ 10$^{51}$ erg. The near-peak spectrum of SN 2020ank exhibits a close spectral resemblance with that of fast-evolving SN 2010gx. The absorption features of SN 2020ank are blueshifted compared to Gaia16apd, suggesting a higher expansion velocity. The spectral similarity with SN 2010gx and comparatively faster spectral evolution than PTF12dam (a slow-evolving SLSN) indicate the fast-evolving behavior of SN 2020ank.

astro-ph.HE↗

arXiv2020

Algorithms for finding $k$ in $k$-means

$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find $k$ from data ? This paper provides the first affirmative answers to both these questions. As common in the literature, we assume that the data admits an unknown Ground Truth (GT) clustering with cluster centers separated. This assumption alone is not sufficient to answer Yes to (i). We assume a novel, but natural second constraint called no tight sub-cluster (NTSC) which stipulates that no substantially large subset of a GT cluster can be "tighter" (in a sense we define) than the cluster. Our yes answer to (i) and (ii) are under these two deterministic assumptions. We also give polynomial time algorithm to identify $k$. Our algorithm relies on NTSC to peel off one cluster at a time by identifying points which are tightly packed. We are also able to show that our algorithm(s) apply to data generated by mixtures of Gaussians and more generally to mixtures of sub-Gaussian pdf's and hence are able to find the number of components of the mixture from data. To our knowledge, previous results for these specialized settings as well, assume generally that $k$ is given besides the data.

cs.DS↗

arXiv2020

EVRNet: Efficient Video Restoration on Edge Devices

Video transmission applications (e.g., conferencing) are gaining momentum, especially in times of global health pandemic. Video signals are transmitted over lossy channels, resulting in low-quality received signals. To restore videos on recipient edge devices in real-time, we introduce an efficient video restoration network, EVRNet. EVRNet efficiently allocates parameters inside the network using alignment, differential, and fusion modules. With extensive experiments on video restoration tasks (deblocking, denoising, and super-resolution), we demonstrate that EVRNet delivers competitive performance to existing methods with significantly fewer parameters and MACs. For example, EVRNet has 260 times fewer parameters and 958 times fewer MACs than enhanced deformable convolution-based video restoration network (EDVR) for 4 times video super-resolution while its SSIM score is 0.018 less than EDVR. We also evaluated the performance of EVRNet under multiple distortions on unseen dataset to demonstrate its ability in modeling variable-length sequences under both camera and object motion.

cs.CV↗

arXiv2020

Manufacturing Process Optimization using Statistical Methodologies

Response Surface Methodology (RSM) introduced in the paper (Box & Wilson, 1951) explores the relationships between explanatory and response variables in complex settings and provides a framework to identify correct settings for the explanatory variables to yield the desired response. RSM involves setting up sequential experimental designs followed by application of elementary optimization methods to identify direction of improvement in response. In this paper, an application of RSM using a two-factor two-level Central Composite Design (CCD) is explained for a diesel engine nozzle manufacturing sub-process. The analysis shows that one of the factors has a significant influence in improving desired values of the response. The implementation of RSM is done using the DoE plug-in available in R software.

stat.ME↗

arXiv2020

Online Carpooling using Expander Decompositions

We consider the online carpooling problem: given $n$ vertices, a sequence of edges arrive over time. When an edge $e_t = (u_t, v_t)$ arrives at time step $t$, the algorithm must orient the edge either as $v_t \rightarrow u_t$ or $u_t \rightarrow v_t$, with the objective of minimizing the maximum discrepancy of any vertex, i.e., the absolute difference between its in-degree and out-degree. Edges correspond to pairs of persons wanting to ride together, and orienting denotes designating the driver. The discrepancy objective then corresponds to every person driving close to their fair share of rides they participate in. In this paper, we design efficient algorithms which can maintain polylog$(n,T)$ maximum discrepancy (w.h.p) over any sequence of $T$ arrivals, when the arriving edges are sampled independently and uniformly from any given graph $G$. This provides the first polylogarithmic bounds for the online (stochastic) carpooling problem. Prior to this work, the best known bounds were $O(\sqrt{n \log n})$-discrepancy for any adversarial sequence of arrivals, or $O(\log\!\log n)$-discrepancy bounds for the stochastic arrivals when $G$ is the complete graph. The technical crux of our paper is in showing that the simple greedy algorithm, which has provably good discrepancy bounds when the arriving edges are drawn uniformly at random from the complete graph, also has polylog discrepancy when $G$ is an expander graph. We then combine this with known expander-decomposition results to design our overall algorithm.

cs.DS↗

arXiv2020

Controlling the macroscopic electrical properties of reduced graphene oxide by nanoscale writing of electronic channels

The allure of all carbon electronics stems from the spread in physical properties, across all its allotropes. The scheme also harbours unique challenges, like tunability of band-gap, variability of doping and defect control. Here, we explore the technique of scanning probe tip induced nanoscale reduction of graphene oxide (GO), which nucleates conducting, sp2 rich graphitic regions on the insulating GO background. Flexibility of direct writing is supplemented with control over degree of reduction and tunability of bandgap, through macroscopic control parameters. The fabricated reduced - GO channels and ensuing devices are investigated via spectroscopic, and temperature and bias dependent electrical transport and correlated with spatially resolved electronic properties, using surface potentiometry. Presence of carrier localization effects, induced by the phase-separated sp2/sp3 domains, and large local electric field fluctuations are reflected in the non-linear transport across the channels. Together the results indicate a complex transport phenomena which may be variously dominated by tunnelling, variable range hopping or activated depending on the electronic state of the material.

cond-mat.mes-hall↗

arXiv2020

Lattice calculation of transport coefficient $\hat{q}$ in pure gluon plasma and (2+1)-flavor QCD plasma

The transport coefficient $\hat{q}$ is a leading coefficient that controls the modification of the hard parton traversing QGP, and hence, responsible for the suppression of the high transverse momentum (transverse to the beam direction) charged-hadrons in heavy-ion collisions. In this article, we present the first unquenched lattice QCD calculation of $\hat{q}$. The calculation is carried out using (2+1)-flavor of quarks, using the highly improved staggered quark action (HISQ) and tree-level Symanzik improved gauge action. The calculation is performed in a wide range of temperatures, ranging from 200 MeV $<T<$ 800 MeV using MILC code package. We considered a leading-order process where a hard parton scatters off the glue field of a thermal QCD medium by exchanging a Glauber gluon (whose transverse momentum is larger than its longitudinal components). The hard scale associated with the jet parton allows the coupling of the gluon to that parton to be treated in perturbation theory. The coupling of the gluon to the medium is treated non-perturbatively. This non-perturbative part is expressed in terms of a non-local (two-point) field-strength-field-strength operator product which can be Taylor expanded after analytic continuation to the deep Euclidean region. Such an expansion allows us to write $\hat{q}$ in terms of a series of local operators, which are suppressed by factors of the hard parton energy. The calculated $\hat{q}$ and its temperature dependence demonstrates reasonable agreement with the phenomenological extraction carried out by the JET collaboration.

nucl-th↗

arXiv2020

FPT Approximation for Constrained Metric $k$-Median/Means

The Metric $k$-median problem over a metric space $(\mathcal{X}, d)$ is defined as follows: given a set $L \subseteq \mathcal{X}$ of facility locations and a set $C \subseteq \mathcal{X}$ of clients, open a set $F \subseteq L$ of $k$ facilities such that the total service cost, defined as $Φ(F, C) \equiv \sum_{x \in C} \min_{f \in F} d(x, f)$, is minimised. The metric $k$-means problem is defined similarly using squared distances. In many applications there are additional constraints that any solution needs to satisfy. This gives rise to different constrained versions of the problem such as $r$-gather, fault-tolerant, outlier $k$-means/$k$-median problem. Surprisingly, for many of these constrained problems, no constant-approximation algorithm is known. We give FPT algorithms with constant approximation guarantee for a range of constrained $k$-median/means problems. For some of the constrained problems, ours is the first constant factor approximation algorithm whereas for others, we improve or match the approximation guarantee of previous works. We work within the unified framework of Ding and Xu that allows us to simultaneously obtain algorithms for a range of constrained problems. In particular, we obtain a $(3+\varepsilon)$-approximation and $(9+\varepsilon)$-approximation for the constrained versions of the $k$-median and $k$-means problem respectively in FPT time. In many practical settings of the $k$-median/means problem, one is allowed to open a facility at any client location, i.e., $C \subseteq L$. For this special case, our algorithm gives a $(2+\varepsilon)$-approximation and $(4+\varepsilon)$-approximation for the constrained versions of $k$-median and $k$-means problem respectively in FPT time. Since our algorithm is based on simple sampling technique, it can also be converted to a constant-pass log-space streaming algorithm.

cs.DS↗

arXiv2020

Probing low temperature non-equilibrium magnetic state in Co$_{2.75}$Fe$_{0.25}$O$_{4+δ}$ spinel oxide using dc magnetization, ac susceptibility and neutron diffraction experiments

The low temperature lattice structure and magnetic properties of Co$_{2.75}$Fe$_{0.25}$O$_4$ ferrite have been investigated using experimental results from synchrotron x-ray diffraction (SXRD), dc magnetization, ac susceptibility, neutron diffraction and neutron depolarization techniques. The samples have been prepared by chemical co-precipitation of the Fe and Co nitrates solution in high alkaline medium and subsequent thermal annealing of the precipitates in the temperature range of 200- 900 $^\circ$C. Rietveld refinement of the SXRD patterns at room temperature indicated two-phased cubic spinel structure for the samples annealed at temperatures 200-600 $^\circ$C. The samples annealed at temperatures 700 $^\circ$C and 900 $^\circ$C (CF90) have been best fitted with single phased lattice structure. Refinement of the neutron diffraction patterns in the temperature range of 5-300 K confirmed antiferromagnetic (AFM) Co$_3$O$_4$ and ferrimagnetic (FIM) Co$_{2.75}$Fe$_{0.25}$O$_4$ phases for the sample annealed at 600 $^\circ$C and single FIM phase of Co$_{2.75}$Fe$_{0.25}$O$_4$ for the CF90 sample. Magnetic measurements have shown a non-equilibrium magnetic structure, consisting of the high temperature FIM phase and low temperature AFM phase. The magnetic phases are sensitive to magnetic fields, where high temperature phase is suppressed at higher magnetic fields by enhancing the low temperature AFM phase, irrespective of annealing temperature of the samples.

cond-mat.str-el↗

arXiv2020

Caching with Time Windows and Delays

We consider two generalizations of the classical weighted paging problem that incorporate the notion of delayed service of page requests. The first is the (weighted) Paging with Time Windows (PageTW) problem, which is like the classical weighted paging problem except that each page request only needs to be served before a given deadline. This problem arises in many practical applications of online caching, such as the "deadline" I/O scheduler in the Linux kernel and video-on-demand streaming. The second, and more general, problem is the (weighted) Paging with Delay (PageD) problem, where the delay in serving a page request results in a penalty being assessed to the objective. This problem generalizes the caching problem to allow delayed service, a line of work that has recently gained traction in online algorithms (e.g., Emek et al. STOC '16, Azar et al. STOC '17, Azar and Touitou FOCS '19). We give $O(\log k\log n)$-competitive algorithms for both the PageTW and PageD problems on $n$ pages with a cache of size $k$. This significantly improves on the previous best bounds of $O(k)$ for both problems (Azar et al. STOC '17). We also consider the offline PageTW and PageD problems, for which we give $O(1)$ approximation algorithms and prove APX-hardness. These are the first results for the offline problems; even NP-hardness was not known before our work. At the heart of our algorithms is a novel "hitting-set" LP relaxation of the PageTW problem that overcomes the $Ω(k)$ integrality gap of the natural LP for the problem. To the best of our knowledge, this is the first example of an LP-based algorithm for an online algorithm with delays/deadlines.

cs.DS↗

arXiv2020

Testing Rotating Regular Metrics as Candidates for Astrophysical Black Holes

The Event Horizon Telescope, a global submillimeter wavelength very long baseline interferometry array, produced the first image of supermassive black hole M87* showing a ring of diameter $θ_d= 42\pm 3\,μ$as, inferred a black hole mass of $M=(6.5 \pm 0.7) \times 10^9 M_\odot $ and allowed us to investigate the nature of strong-field gravity. The observed image is consistent with the shadow of a Kerr black hole, which according to the Kerr hypothesis describes the background spacetimes of all astrophysical black holes. The hypothesis, a strong-field prediction of general relativity, may be violated in the modified theories of gravity that admit non-Kerr black holes. Here, we use the black hole shadow to investigate the constraints when rotating regular black holes (non-Kerr) can be considered as astrophysical black hole candidates, paying attention to three leading regular black hole models with additional parameters $g$ related to nonlinear electrodynamics charge. Our interesting results based on the systematic bias analysis are that rotating regular black holes shadows may or may not capture Kerr black hole shadows, depending on the values of the parameter $g$. Indeed, the shadows of Bardeen black holes ($g\lesssim 0.26 M$), Hayward black holes ($g\lesssim 0.65 M$), and non-singular black holes ($g\lesssim 0.25 M$) are indistinguishable from Kerr black hole shadows within the current observational uncertainties, and thereby they can be strong viable candidates for the astrophysical black holes. Whereas Bardeen black holes ( $g\leq 0.30182M$), Hayward black holes ($g\leq 0.73627M$), and non-singular black holes ($g\leq 0.30461M$), within the $1σ$ region for $θ_d= 39\, μ$as, are consistent with the observed angular diameter of M87*.

gr-qc↗

arXiv2020

Peculiar prompt emission and afterglow in H.E.S.S. detected GRB 190829A

We present the results of a detailed investigation of the prompt and afterglow emission in the HESS detected GRB 190829A. Swift and Fermi observations of the prompt phase of this GRB reveal two isolated sub-bursts or episodes, separated by a quiescent phase. The energetic and the spectral properties of the first episode are in stark contrast to the second. The first episode, which has a higher spectral peak of $\sim 120\:\text{keV}$ and a low isotropic energy $\sim 10^{50}\:\text{erg}$ is an outlier to the Amati correlation and marginally satisfies the Yonetoku correlation. However, the energetically dominant second episode has lower peak energy and is consistent with the above correlations. We compared this GRB to other low luminosity GRBs (LLGRBs). Prompt emission of LLGRBs also indicates a relativistic shock breakout origin of the radiation. For GRB 190829A, some of the properties of a shock breakout origin are satisfied. However, the absence of an accompanying thermal component and energy above the shock breakout critical limit precludes a shock breakout origin. In the afterglow, an unusual long-lasting late time flare of duration $\sim 10^4\:\text{s}$ is observed. We also analyzed the late-time \fermi-LAT emission that encapsulates the H.E.S.S. detection. Some of the LAT photons are likely to be associated with the source. All the above observational facts suggest GRB 190829A is a peculiar low luminosity GRB that is not powered by a shock breakout, and with an unusual rebrightening due to a patchy emission or a refreshed shock during the afterglow. Furthermore, our results show that TeV energy photons seem common in both high luminosity GRBs and LLGRBs.

astro-ph.HE↗

arXiv2020

Integrating Acting, Planning and Learning in Hierarchical Operational Models

We present new planning and learning algorithms for RAE, the Refinement Acting Engine. RAE uses hierarchical operational models to perform tasks in dynamically changing environments. Our planning procedure, UPOM, does a UCT-like search in the space of operational models in order to find a near-optimal method to use for the task and context at hand. Our learning strategies acquire, from online acting experiences and/or simulated planning results, a mapping from decision contexts to method instances as well as a heuristic function to guide UPOM. Our experimental results show that UPOM and our learning strategies significantly improve RAE's performance in four test domains using two different metrics: efficiency and success ratio.

cs.AI↗

arXiv2020

SN 2010kd: Photometric and Spectroscopic Analysis of a Slow-Decaying Superluminous Supernova

This paper presents data and analysis of SN 2010kd, a low-redshift ($z = 0.101$) H-deficient superluminous supernova (SLSN), based on ultraviolet/optical photometry and optical spectroscopy spanning between $-$28 and +194 days relative to $\mathit{B}$ band maximum light. The $\mathit{B}$ band light curve comparison of SN 2010kd with a subset of well-studied SLSNe I at comparable redshifts indicates that it is a slow-decaying PTF12dam like SLSN. Analytical light-curve modeling using the $\mathtt{Minim}$ code suggests that the bolometric light curve of SN 2010kd favors circumstellar matter interaction for the powering mechanism. $\mathtt{SYNAPPS}$ modeling of the early-phase spectra does not identify broad H or He lines, whereas the photospheric-phase spectra are dominated by O I, O II, C II, C IV and Si II, particularly, presence of both low and high-velocity components of O II and Si II lines. The nebular-phase spectra of SN 2010kd are dominated by O I and Ca II emission lines similar to those seen in other SLSNe I. The line velocities in SN 2010kd exhibit flatter evolution curves similar to SN 2015bn but with comparatively higher values. SN 2010kd shows a higher single-zone local thermodynamic equilibrium temperature in comparison to PTF12dam and SN 2015bn, and it has an upper O I ejected mass limit of $\sim 10~M_\odot$. The host of SN 2010kd is a dwarf galaxy with a high star-formation rate ($\sim 0.18 \pm 0.04~M_\odot$ yr$^{-1}$) and extreme emission lines.

astro-ph.HE↗

arXiv2020

Streaming PTAS for Constrained k-Means

We generalise the results of Bhattacharya et al. (Journal of Computing Systems, 62(1):93-115, 2018) for the list-$k$-means problem defined as -- for a (unknown) partition $X_1, ..., X_k$ of the dataset $X \subseteq \mathbb{R}^d$, find a list of $k$-center sets (each element in the list is a set of $k$ centers) such that at least one of $k$-center sets $\{c_1, ..., c_k\}$ in the list gives an $(1+\varepsilon)$-approximation with respect to the cost function $\min_{\textrm{permutation } π} \left[ \sum_{i=1}^{k} \sum_{x \in X_i} ||x - c_{π(i)}||^2 \right]$. The list-$k$-means problem is important for the constrained $k$-means problem since algorithms for the former can be converted to PTAS for various versions of the latter. Following are the consequences of our generalisations: - Streaming algorithm: Our $D^2$-sampling based algorithm running in a single iteration allows us to design a 2-pass, logspace streaming algorithm for the list-$k$-means problem. This can be converted to a 4-pass, logspace streaming PTAS for various constrained versions of the $k$-means problem. - Faster PTAS under stability: Our generalisation is also useful in $k$-means clustering scenarios where finding good centers becomes easy once good centers for a few "bad" clusters have been chosen. One such scenario is clustering under stability where the number of such bad clusters is a constant. Using the above idea, we significantly improve the running time of the known algorithm from $O(dn^3) (k \log{n})^{poly(\frac{1}β, \frac{1}{\varepsilon})}$ to $O \left(dn^3 k^{\tilde{O}_{β\varepsilon}(\frac{1}{β\varepsilon})} \right)$.

cs.DS↗