arXiv subjects

Abhinav Srivastav

Publications and source records attributed to Abhinav Srivastav.

6 recordsLinked to original sources

arXiv2026

Efficient calculation of exclusive diffractive cross sections at the EIC and LHeC with the Sartre event generator

We present a new version of the Sartre event generator for exclusive diffraction at small xP in the colour dipole model, for $ep$ and $e$A scattering at the EIC and the LHeC as well as ultra-peripheral $pp$, $p$A, and AA collisions at RHIC and the LHC. Sartre stores the first and second moment of the interaction amplitudes in lookup tables which are then used for efficient event generation. There are many possible combinations of processes in Sartre, with different initial state nuclear targets and different final state vector mesons or real photons. We also want to implement different versions of the dipole model: with and without non-linear saturation effects, with and without nucleon hotspot substructure. A long-standing bottleneck for simulating all possible exclusive processes has been the production of lookup tables, which take a few CPU-year for each combination, necessitating the use of computing farms. The calculation also involves integrations of rapidly fluctuating integrands, which may cause numerical glitches which takes much effort to smoothen out. In this paper we present a solution to these issues, by presenting a new numerical calculation which improves the efficiency in the table production by 3-4 orders of magnitudes. This enables us to produce lookup tables for any process that we may be interested in, in a few hours. The new calculation does also not exhibit numerical glitches. We provide novel predictions for the EIC and the LHeC using the new version of Sartre.

hep-ph↗

arXiv2020

Online Non-Monotone DR-submodular Maximization

In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a subclass of non-convex optimization that provides both theoretical and practical guarantees. Here, we focus on minimizing regret for online arriving non-monotone DR-submodular functions over different types of convex sets: hypercube, down-closed and general convex sets. First, we present an online algorithm that achieves a $1/e$-approximation ratio with the regret of $O(T^{2/3})$ for maximizing DR-submodular functions over any down-closed convex set. Note that, the approximation ratio of $1/e$ matches the best-known guarantee for the offline version of the problem. Moreover, when the convex set is the hypercube, we propose a tight 1/2-approximation algorithm with regret bound of $O(\sqrt{T})$. Next, we give an online algorithm that achieves an approximation guarantee (depending on the search space) for the problem of maximizing non-monotone continuous DR-submodular functions over a \emph{general} convex set (not necessarily down-closed). To best of our knowledge, no prior algorithm with approximation guarantee was known for non-monotone DR-submodular maximization in the online setting. Finally we run experiments to verify the performance of our algorithms on problems arising in machine learning domain with the real-world datasets.

cs.LG↗

arXiv2019

Non-monotone DR-submodular Maximization: Approximation and Regret Guarantees

Diminishing-returns (DR) submodular optimization is an important field with many real-world applications in machine learning, economics and communication systems. It captures a subclass of non-convex optimization that provides both practical and theoretical guarantees. In this paper, we study the fundamental problem of maximizing non-monotone DR-submodular functions over down-closed and general convex sets in both offline and online settings. First, we show that for offline maximizing non-monotone DR-submodular functions over a general convex set, the Frank-Wolfe algorithm achieves an approximation guarantee which depends on the convex set. Next, we show that the Stochastic Gradient Ascent algorithm achieves a 1/4-approximation ratio with the regret of $O(1/\sqrt{T})$ for the problem of maximizing non-monotone DR-submodular functions over down-closed convex sets. These are the first approximation guarantees in the corresponding settings. Finally we benchmark these algorithms on problems arising in machine learning domain with the real-world datasets.

cs.LG↗

arXiv2018

Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines

In this paper, we consider the online problem of scheduling independent jobs \emph{non-preemptively} so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. %Using the speed augmentation model, Anand et al. showed that the greedy algorithm is $O\left(\frac{1}ε\right)$-competitive in the preemptive setting. In the non-preemptive setting, Lucarelli et al. showed that there exists a strong lower bound for minimizing weighted flow-time even on a single machine. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a $O\left(\frac{1}{ε^2}\right)$-competitive ratio when the algorithm is allowed to reject $ε$-fraction of total weight of jobs and $ε$-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights. In this paper, we affirmatively answer this question. Specifically, we show that there exists a $O\left(\frac{1}{ε^3}\right)$-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most $O(ε)$-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms.

cs.DS↗

arXiv2018

Online Non-preemptive Scheduling on Unrelated Machines with Rejections

When a computer system schedules jobs there is typically a significant cost associated with preempting a job during execution. This cost can be from the expensive task of saving the memory's state and loading data into and out of memory. It is desirable to schedule jobs non-preemptively to avoid the costs of preemption. There is a need for non-preemptive system schedulers on desktops, servers and data centers. Despite this need, there is a gap between theory and practice. Indeed, few non-preemptive \emph{online} schedulers are known to have strong foundational guarantees. This gap is likely due to strong lower bounds on any online algorithm for popular objectives. Indeed, typical worst case analysis approaches, and even resource augmented approaches such as speed augmentation, result in all algorithms having poor performance guarantees. This paper considers on-line non-preemptive scheduling problems in the worst-case rejection model where the algorithm is allowed to reject a small fraction of jobs. By rejecting only a few jobs, this paper shows that the strong lower bounds can be circumvented. This approach can be used to discover algorithmic scheduling policies with desirable worst-case guarantees. Specifically, the paper presents algorithms for the following two objectives: minimizing the total flow-time and minimizing the total weighted flow-time plus energy under the speed-scaling mechanism. The algorithms have a small constant competitive ratio while rejecting only a constant fraction of jobs. Beyond specific results, the paper asserts that alternative models beyond speed augmentation should be explored to aid in the discovery of good schedulers in the face of the requirement of being online and non-preemptive.

cs.DS↗

arXiv2014

Total stretch minimization on single and identical parallel machines

We consider the classical problem of scheduling $n$ jobs with release dates on both single and identical parallel machines. We measure the quality of service provided to each job by its stretch, which is defined as the ratio of its response time to processing time. Our objective is to schedule these jobs non-preemptively so as to minimize sum stretch. So far, there have been very few results for sum stretch minimization especially for the non-preemptive case. For the preemptive version, the Shortest remaining processing time (SRPT) algorithm is known to give $2$-competitive for sum stretch on single machine while its is $13$-competitive on identical parallel machines. Leonardi and Kellerer provided the strong lower bound for the more general problem of \textit{sum (weighted) flow time} in single machine and identical parallel machines, respectively . Therefore, we study this problem with some additional assumptions and present two new competitive ratio for existing algorithms. We show that the Shortest processing time (SPT) algorithm is $Δ- \frac{1}Δ+1$-competitive for non-preemptive sum stretch minimization on single machine and it is $Δ- \frac{1}Δ+ \frac{3}{2} -\frac{1}{2m}$ on $m$ identical parallel machines, where $Δ$ is the upper bound on the ratio between the maximum and the minimum processing time of the jobs.

cs.DS↗