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Anupam Gupta

Publications and source records attributed to Anupam Gupta.

At least 19 recordsLinked to original sources
arXiv2026

Better Late Than Never: Online Flow Time Scheduling with Online Estimates

In the classical online flow-time scheduling problem on a single machine, jobs arrive over time and must be processed to minimize the total time they spend in the system: for over fifty years, we have known that SRPT is an optimal online algorithm. But this algorithm requires exactness in two different ways: (a) job sizes must be known exactly, and (b) they must be revealed as soon as the job arrives. Recent work relaxed each of these assumptions separately: there are algorithms based on knowing approximate sizes (given when the job arrives), or based on knowing (exact) sizes at some point before the remaining size gets too small. Nonetheless, prior to this work, there was no known approach to relax both assumptions simultaneously. In this work, we consider a model that demands much less: When we process a job, at some point in time between when we complete an $\varepsilon$-fraction and a $(1-\varepsilon)$-fraction of its unknown processing requirement, we are informed that the job is ``somewhere in the middle''. Finally, when the job has received its desired amount of processing, we are informed of its completion. No other information is shared about the job. We give an $O(1/\varepsilon^2)$-competitive algorithm for this model. Slightly more generally, we assume that an algorithm receives a $\mu$-approximate estimate of each job's processing time at some time before we complete a $(1-\varepsilon)$-fraction of its processing. Our algorithm is $O(\mu/\varepsilon)$-competitive, and we show that this is asymptotically optimal. It is a surprisingly natural variant of the multilevel feedback algorithm (MLF) and it is parameter-oblivious: it does not need to know $\mu$ or $\varepsilon$ upfront. The core analytical contribution is to robustify the dual-fitting framework for this problem to handle jobs for which we have not yet received estimates.

cs.DS↗
arXiv2026

Length scale of cellular activity determines signatures of epithelial remodeling

Cellular activity drives epithelial fluidization --- a widespread phenomenon observed during tissue development, remodeling, and repair both in vivo and in vitro. Yet the physical origins and spatial organization of active forces vary widely across biological systems and are often represented by a single generic mechanism in theoretical models. Here, using an active vertex model, we systematically compare four modes of epithelial activity spanning subcellular to tissue scales: apolar motility, polar motility, fluctuating contractility, and mechanochemical regulation. Although all four mechanisms drive the same global transition from a solid-like rectangular tissue to a fluid-like circular morphology, they reach this state through distinct pathways --- differing in the rates and topology of junctional rearrangements, cell elimination, and collective motion and leave distinguishable signatures in tissue architecture, cell dynamics, and mechanical relaxation. Among these observables, spatial velocity correlations directly capture the spatial organization of activity: their correlation length and functional form together resolve all four mechanisms. The robustness of these signatures across activity strengths suggests that spatial velocity correlations offer an experimentally accessible means of identifying the physical origin of epithelial activity from live-cell imaging alone.

physics.bio-ph↗
arXiv2026

Distributed Load Balancing on Unrelated Machines

We study the well-known load balancing problem in the distributed CONGEST model of computation. We consider the unrelated machines setting, where each job $j$ specifies a size $s_{ij}$ for every machine $i$. We want to find an assignment $\varphi: J \to M$ minimizing the maximum machine load, where the load of a machine $i$ is the total size of the jobs assigned to it. In the CONGEST model, the state-of-the-art is an algorithm that runs in polylog rounds and returns a $(1+\varepsilon)$-approximate fractional solution from Ahmadian, Liu, Peng, and Zadimoghaddam (2021). However, this algorithm, as well as all previous CONGEST algorithms only solve a special case of load balancing, where each job has the same size on each machine. Our main contribution is an algorithm for general sizes $s_{ij}$. The algorithm computes a $(1+\varepsilon)$-approximate fractional solution or a $(2+\varepsilon)$-approximate integral solution in polylog rounds. The problem structure changes significantly once we allow arbitrary edge-sizes, so our techniques are very different from those used in previous algorithms for distributed load balancing. One ingredient of our result is a black-box tool of independent interest: a $(1+\varepsilon)$-approximation algorithm to arbitrary mixed packing-covering linear programs in the CONGEST model in polylog rounds. such algorithms were known in the more powerful parallel model, but previous polylog-round algorithms in the distributed CONGEST model only solved pure packing or pure covering problems. We improve upon a recent $O(D\,\mathrm{polylog})$-round CONGEST algorithm for mixed packing-covering, where $D$ is the diameter of the communication graph.

cs.DS↗
arXiv2026

Asymmetric Trading Prophets

The "Trading Prophet" problem challenges an online trader to maximize its profit by buying and selling assets under stochastic prices and capacity constraints, competing against an offline prophet with full foresight. In previous work, each arriving asset was assumed to have a single price $p_t$, and the trader was allowed to either buy a copy at this price (subject to having available capacity), or sell a copy (if it already held at least one copy in hand). However, this abstraction can fail to capture the structural asymmetry of decentralized dealer-based markets, where buying and selling opportunities could be distinct, and driven by individual preferences. To address this, we introduce the Asymmetric Trading Prophets problem, where at each timestep the trader observes a price tuple $(b_t, s_t)$ -- representing the cost to buy, and the revenue from selling at this timestep. Importantly, the $(b_t,s_t)$ tuple could be potentially arbitrarily correlated. We provide the first competitive analysis for this asymmetric trading prophets problem, characterizing the achievable profit based on the trader's capacity $B$ and initial inventory $B_0$. For the unit-capacity case of $B=1$, we design online algorithms that achieve constant competitive ratios for both i.i.d. and non-i.i.d. distributions on the price tuples, when the trader has one initial copy ($B_0=1$). For the general capacity case where $B$ can be large, we give algorithms for i.i.d. distributions that achieve a competitive ratio of $1 - \Theta(\log B_0/\sqrt{B_0})$. Finally, for the symmetric case (where the price tuple satisfies $b_t=s_t$), we improve this to get a competitive ratio of $1 - O(\log B/\sqrt{B})$, demonstrating that the performance approaches optimality as the capacity increases. We show that both ratios are tight up to a logarithmic factor.

cs.DS↗
arXiv2026

Online Convex Optimization with Sublinear Noisy Probes

We study Online Convex Optimization (OCO) over a convex set $K\subseteq \mathbb R^d$, where in each round $t$ the learner selects $x_t\in K$ and then observes a convex loss $f_t:K\to[0,1]$, with the goal of minimizing regret to the best fixed decision in hindsight. We introduce a unified probing model that generalizes two recent lines of work: sublinear best-expert queries in the experts setting, and pairwise (comparison-based) feedback available every round in OCO. In our framework, the learner has a budget of $k\le T$ pairwise probes; on a probed round it may query two points and learn which one has smaller loss. Our main result shows that even a sublinear and noisy probe budget can provably improve worst-case regret in the full feedback OCO regime. With $k$ $\delta$-noisy pairwise probes, we obtain: $ \text{Reg}_T \le O\left(\min\left\{\sqrt{dT\ln T},\; \frac{dT\ln T}{k|1-2\delta|}\right\}\right) $, which is tight (up to logarithmic factors in $T$) across $T$, $k$ and $\delta$. Specifically regarding the noise parameter $\delta \in [0,1]$, the regret guarantee smoothly degrades as the oracle response approaches a coin flip, i.e., $\delta$ is close to $\frac{1}{2}$. When applying the same techniques to a finite $K$ for the prediction with $d$ experts setting, the resulting rates are instead completely tight in all parameters, including $d$. Our analysis gives a streamlined treatment of pairwise probing in OCO by quantifying the benefit of probing via a variance reduction effect, combined with a second-order (variance-based) analysis of Continuous Exponential Weights.

cs.LG↗
arXiv2026

Bayesian Probing on Graphs

We introduce a stochastic probing problem with correlated items. In our model, which we call Bayesian Probing, the correlations are modeled by an underlying graph $G$. Each vertex is independently active with a known probability. Each item corresponds to an edge in the graph. Probing an edge has some cost, gives some reward if both endpoints are active, and also reveals the state of its endpoints. Hence a probe induces a Bayesian update on the remaining edges. The goal is to adaptively probe items/edges subject to a knapsack constraint to maximize the expected total reward obtained from the probed edges. Bayesian Probing generalizes stochastic knapsack and stochastic probing by allowing correlations between items. Moreover, it gives a tractable model for the Bayesian Active Search problem, a popular problem considered in the machine learning community. In Bayesian Active Search, the goal is to find items in a particular class by adaptively probing at most, say $k$, items. Given a prior distribution over items, we want to compute a Bayesian policy to maximize the number of such items found. For this general problem with arbitrary priors, there are strong lower bounds on efficiently computing good policies. In this paper, we design efficient approximation algorithms for Bayesian Probing. These results give the first efficient approximation algorithms for Bayesian Active Search, for a class of practically-relevant prior distributions.

cs.DS↗
arXiv2026

DNA Replication under Thermal, Chemical, and Genotoxic Stress

Eukaryotic DNA replication must remain robust under thermal, chemical, and genotoxic stress despite large fluctuations in replication dynamics. Here, we develop a lattice-based stochastic Monte Carlo framework for whole-genome replication in Saccharomyces cerevisiae at single base-pair resolution, incorporating probabilistic origin firing, replication fork-speed distributions, and a time-dependent limiting factor that governs the availability of cellular replication resources. The model is benchmarked quantitatively against experimental replication profiles before being applied to stress conditions, and reproduces diverse replication stress responses using only two effective parameters. Importantly, the analysis reveals that replication fork-speed heterogeneity underlies the emergence of Erlang-distributed S-phase durations and rare, anomalously prolonged replication events observed experimentally in Escherichia coli and human cell lines, while predicting similar behavior in S. cerevisiae. The framework further predicts non-monotonic thermal behavior, power-law scaling under hydroxyurea stress, and total replication-time dynamics under diverse genotoxic conditions.

physics.bio-ph↗
arXiv2026

FPT Approximation Schemes for Min-Sum Radii and Min-Sum Diameters Clustering

In the classical Min-Sum Radii problem (MSR) we are given a set $X$ of $n$ points in a metric space and a positive integer $k\in [n]$. Our goal is to partition $X$ into $k$ subsets (the clusters) so as to minimize the sum of the radii of these clusters. The Min-Sum Diameters problem (MSD) is defined analogously, where instead of the radii of the clusters we consider their diameters. For both problems we present FPT approximation schemes for the natural parameter $k$. Specifically, given $\epsilon>0$, we show how to compute $(1+\epsilon)$-approximations for both MSD and MSR in time $(1/\epsilon)^kn^{O(1)}$ and $(1/\epsilon)^{O(k/\epsilon \log 1/\epsilon)}n^{poly(1/\epsilon)}$ respectively. The previous best FPT approximation algorithms for these problems have approximation factors $4+\epsilon$ and $2+\epsilon$, respectively, and finding an FPT approximation scheme for both these problems had been outstanding open problems.

cs.DS↗
arXiv2026

Improved Online Hitting Set Algorithms for Structured and Geometric Set Systems

In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive ratio $O(\log n \log m)$ for the (general) online hitting set and set cover problems for $m$ sets and $n$ elements; this is known to be tight for efficient online algorithms. Given this barrier for general set systems, we ask: can we break this double-logarithmic phenomenon for online hitting set/set cover on structured and geometric set systems? We provide an $O(\log n \log\log n)$-competitive algorithm for the weighted online hitting set problem on set systems with linear shallow-cell complexity, replacing the double-logarithmic factor in the general result by effectively a single logarithmic term. As a consequence of our results we obtain the first bounds for weighted online hitting set for natural geometric set families, thereby answering open questions regarding the gap between general and geometric weighted online hitting set problems.

cs.DS↗
arXiv2026

Contextual Online Bilateral Trade

We study repeated bilateral trade when the valuations of the sellers and the buyers are contextual. More precisely, the agents' valuations are given by the inner product of a context vector with two unknown $d$-dimensional vectors -- one for the buyers and one for the sellers. At each time step $t$, the learner receives a context and posts two prices, one for the seller and one for the buyer, and the trade happens if both agents accept their price. We study two objectives for this problem, gain from trade and profit, proving no-regret with respect to a surprisingly strong benchmark: the best omniscient dynamic strategy. In the natural scenario where the learner observes \emph{separately} whether the agents accept their price -- the so-called \emph{two-bit} feedback -- we design algorithms that achieve $O(d\log d)$ regret for gain from trade, and $O(d \log\log T + d\log d)$ regret for profit maximization. Both results are tight, up to the $\log(d)$ factor, and implement per-step budget balance, meaning that the learner never incurs negative profit. In the less informative \emph{one-bit} feedback model, the learner only observes whether a trade happens or not. For this scenario, we show that the tight two-bit regret regimes are still attainable, at the cost of allowing the learner to possibly incur a small negative profit of order $O(d\log d)$, which is notably independent of the time horizon. As a final set of results, we investigate the combination of one-bit feedback and per-step budget balance. There, we design an algorithm for gain from trade that suffers regret independent of the time horizon, but \emph{exponential} in the dimension $d$. For profit maximization, we maintain this exponential dependence on the dimension, which gets multiplied by a $\log T$ factor.

cs.GT↗
arXiv2026

Learning Markov Decision Processes under Fully Bandit Feedback

A standard assumption in Reinforcement Learning is that the agent observes every visited state-action pair in the associated Markov Decision Process (MDP), along with the per-step rewards. Strong theoretical results are known in this setting, achieving nearly-tight $\Theta(\sqrt{T})$-regret bounds. However, such detailed feedback can be unrealistic, and recent research has investigated more restricted settings such as trajectory feedback, where the agent observes all the visited state-action pairs, but only a single \emph{aggregate} reward. In this paper, we consider a far more restrictive ``fully bandit'' feedback model for episodic MDPs, where the agent does not even observe the visited state-action pairs -- it only learns the aggregate reward. We provide the first efficient bandit learning algorithm for episodic MDPs with $\widetilde{O}(\sqrt{T})$ regret. Our regret has an exponential dependence on the horizon length $\H$, which we show is necessary. We also obtain improved nearly-tight regret bounds for ``ordered'' MDPs; these can be used to model classical stochastic optimization problems such as $k$-item prophet inequality and sequential posted pricing. Finally, we evaluate the empirical performance of our algorithm for the setting of $k$-item prophet inequalities; despite the highly restricted feedback, our algorithm's performance is comparable to that of a state-of-art learning algorithm (UCB-VI) with detailed state-action feedback.

cs.LG↗
arXiv2025

Modeling complex motility patterns for autophoretic microswimmers

Symmetry breaking is essential for biological microswimmers to achieve locomotion in viscous environments. Such asymmetry in the swimming mechanism enables the generation of directional forces that overcome fluid resistance, leading to efficient motion and complex interactions. As synthetic analogues, autophoretic microswimmers including isotropic active colloids and active droplets exhibit spontaneous symmetry breaking of a chemical field, which generates interfacial flows and drives persistent self-propulsion. Modeling these systems is challenging because the chemical concentration and flow fields are strongly coupled through nonlinear advective transport of the chemical species. In this work, we propose a new numerical framework for modeling isotropic autophoretic microswimmers whose propulsion arises solely from self-generated chemical gradients, without any imposed geometric or chemical anisotropy. The framework employs a high-accuracy pseudospectral method to solve the fully coupled advection diffusion Stokes equations, without prescribing any slip velocity model.Slip velocities emerge self-consistently from instantaneous concentration gradients at the particle surface, driving propulsion and inducing flow disturbances through a stresslet representation of force and torque free swimmers. This approach naturally captures nonlinear advection, chemo-hydrodynamic feedback, and many-particle interactions within a unified framework. We demonstrate that the model reproduces complex emergent behaviors observed in experiments, including disordered swimming at higher fluid viscosities and chemotactically guided pairwise interactions. At each stage, numerical predictions are quantitatively compared with independent experiments on active droplets, validating the proposed framework as a robust tool for studying autophoretic microswimmers.

physics.flu-dyn↗
arXiv2025

Complexity of Local Search for CSPs Parameterized by Constraint Difference

In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset $S$ of a universe $U$, the new input consists of a current solution $P$ (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution $S^*$, the goal is to find a feasible solution as good as $S^*$ in parameterized time $f(k) \cdot n^{O(1)}$, where $k$ denotes the distance $|P\Delta S^*|$. This model generalizes numerous classical parameterized optimization problems whose parameter $k$ is the minimum number of elements removed from $U$ to make it feasible, which corresponds to the case $P = U$. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where $U$ is the set of constraints, and a subset $U'$ of constraints is feasible if there is an assignment to the variables satisfying all constraints in $U'$. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate's acceptance depends on the number of true literals.

cs.DS↗
arXiv2025

Steiner Forest: A Simplified Better-Than-2 Approximation

In the Steiner Forest problem, we are given a graph with edge lengths, and a collection of demand pairs; the goal is to find a subgraph of least total length such that each demand pair is connected in this subgraph. For over twenty years, the best approximation ratio known for the problem was a $2$-approximation due to Agrawal, Klein, and Ravi (STOC 1991), despite many attempts to surpass this bound. Finally, in a recent breakthrough, Ahmadi, Gholami, Hajiaghayi, Jabbarzade, and Mahdavi (FOCS 2025) gave a $2-\varepsilon$-approximation, where $\varepsilon \approx 10^{-11}$. In this work, we show how to simplify and extend the work of Ahmadi et al. to obtain an improved $1.994$-approximation. We combine some ideas from their work (e.g., an extended run of the moat-growing primal-dual algorithm, and identifying autarkic pairs) with other ideas -- submodular maximization to find components to contract, as in the relative greedy algorithms for Steiner tree, and the use of autarkic triples. We hope that our cleaner abstraction will open the way for further improvements.

cs.DS↗
arXiv2025

Combinatorial Optimization using Comparison Oracles

In linear combinatorial optimization, we aim to find $S^* = \arg\min_{S \in \mathcal{F}} \langle w,\mathbf{1}_S \rangle$ for a family $\mathcal{F} \subseteq 2^U$ over a ground set $U$ of $n$ elements. Traditionally, $w$ is known or accessible via a value oracle. Motivated by practical applications involving pairwise preferences, we study the weaker and more robust comparison oracle, which for any $S, T \in \mathcal{F}$ reveals only if $w(S) <, =, \text{ or } > w(T)$. We investigate the query complexity and computational efficiency of optimizing in this model. We present three main contributions. (1) Query Complexity: We establish that the query complexity over any arbitrary set system $\mathcal{F} \subseteq 2^U$ is $\tilde{O}(n^2)$. This demonstrates a fundamental separation between information and computational complexity, as the runtime may still be exponential for NP-hard problems. (2) Algorithmic Frameworks: We develop two general tools. First, a Dual Ellipsoid framework establishes an efficient reduction from optimization to certification. It shows that to optimize efficiently, it suffices to efficiently certify a candidate's optimality using only comparisons. Second, Global Subspace Learning (GSL) sorts all feasible sets using $O(nB \log(nB))$ queries for integer weights bounded by $B$. We efficiently implement GSL for linear matroids, yielding improved query complexities for problems like $k$-SUM, SUBSET-SUM, and $A+B$ sorting. (3) Combinatorial Applications: We give the first polynomial-time, low-query algorithms for classic problems, including minimum cuts, minimum weight spanning trees (and matroid bases), bipartite matching (and matroid intersection), and shortest $s$-$t$ paths. Our work provides the first general query complexity bounds and efficient algorithmic results for this fundamental model.

cs.DS↗
arXiv2025

A Learning Perspective on Random-Order Covering Problems

In the random-order online set cover problem, the instance with $m$ sets and $n$ elements is chosen in a worst-case fashion, but then the elements arrive in a uniformly random order. Can this random-order model allow us to circumvent the bound of $O(\log m \log n)$-competitiveness for the adversarial arrival order model? This long-standing question was recently resolved by Gupta et al. (2021), who gave an algorithm that achieved an $O(\log mn)$-competitive ratio. While their LearnOrCover was inspired by ideas in online learning (and specifically the multiplicative weights update method), the analysis proceeded by showing progress from first principles. In this work, we show a concrete connection between random-order set cover and stochastic mirror-descent/online convex optimization. In particular, we show how additive/multiplicative regret bounds for the latter translate into competitiveness for the former. Indeed, we give a clean recipe for this translation, allowing us to extend our results to covering integer programs, set multicover, and non-metric facility location in the random order model, matching (and giving simpler proofs of) the previous applications of the LearnOrCover framework.

cs.DS↗
arXiv2025

Motility-Driven Viscoelastic Control of Tissue Morphology in Presomitic Mesoderm

Embryonic tissues deform across broad spatial and temporal scales and relax stress through active rearrangements. A quantitative link between cell-scale activity, spatial forcing, and emergent tissue-scale mechanics remains incomplete. Here, we use a vertex-based tissue model with active force fluctuations to study how motility controls viscoelastic response. After validation against experimental presomitic mesoderm relaxation dynamics, we extract intrinsic mechanical timescales using stress relaxation and oscillatory shear. The model captures motility-dependent shifts between elastic and viscous behavior and the coexistence of fast relaxation with long-lived residual stress. When subjected to spatially patterned, temporally pulsed forcing, tissues behave as mechanical filters: long-wavelength inputs are accumulated, whereas short-wavelength, cell-scale perturbations are rapidly erased, largely independent of motility. Simulations with localized motility hotspots, motivated by spatially confined FGF signaling reported in vertebrate limb development, produce sustained protrusive tissue deformations consistent with experimentally observed early bud-like morphologies. Together, these results establish a minimal framework linking motility-driven activity to wavelength-selective mechanical memory and emergent tissue patterning.

physics.bio-ph↗