arXiv subjects

Pooja Kulkarni

Publications and source records attributed to Pooja Kulkarni.

16 recordsLinked to original sources

arXiv2026

Sidewall-Poled Nanophotonic Lithium Niobate with Bidirectional Characterization

Accurate characterization of integrated nonlinear photonic devices is often limited by unknown facet-coupling losses and fabrication-induced non-uniformities, leading to systematic over- or underestimation of the intrinsic on-chip performance. Here, we present and demonstrate a unified bidirectional characterization framework that exploits nonlinear interactions under forward and backward propagation to independently extract facet-specific coupling efficiencies, intrinsic nonlinear conversion efficiency, and the longitudinal quasi-phase-matching profile using only classical power measurements. We experimentally validate the method using sidewall-poled thin-film lithium niobate waveguides, obtaining a normalized second-harmonic generation efficiency of $(1850 \pm 20)~\%\mathrm{W}^{-1}$ while simultaneously demonstrating broadband non-degenerate optical parametric amplification and parametric generation spanning more than $10~\mathrm{THz}$. Our framework is non-destructive, relies solely on classical power measurements, requires neither time-intensive microscopy nor calibrated internal references, and is compatible with wafer-scale testing, providing a general route to rigorous benchmarking and high-throughput characterization of photonic devices across material platforms.

physics.optics↗

arXiv2026

Ultra-broadband, Low-loss Wavelength Combiners and Filters: Novel Designs and Experiments in Thin-film Lithium Niobate

Thin-film lithium niobate (TFLN) has emerged as a leading platform for large-scale programmable photonic circuits for quantum and classical applications. As circuits scale in complexity, low-loss routing of broadband pump and signal fields becomes essential. Here, we present closed-form analytical models and experimentally demonstrate compact, fast-quasi-adiabatic driving-optimized wavelength combiners and filters operating at the fundamental harmonic (FH, 1550 nm) and second-harmonic (SH, 775 nm) wavelengths. Our designs achieve ultra-low loss below 0.06 dB across a 90 nm bandwidth at FH, while maintaining extinction ratios exceeding 25 dB. At SH, the loss remains below 0.12 dB over a 45 nm bandwidth with extinction ratios greater than 19 dB. Devices fabricated on a 300-nm TFLN platform exhibit added loss below 0.1 dB across 1550 - 1600 nm, with minimum values of 0.04 dB around 1580 nm and 0.021 dB at 775 nm. Combined with recent advances in on-chip quantum state generation, low-loss interferometers, and detection, these results enable high-fidelity quantum photonic circuits on the TFLN platform.

physics.optics↗

arXiv2025

Cycle Cancellation for Submodular Fractional Allocations and Applications

We consider discrete allocation problem where $m$ indivisible goods are to be divided among $n$ agents. When agents' valuations are additive, the well-known cycle cancelling lemma by Lenstra, Shmoys, and Tardos plays a key role in design and analysis of rounding algorithms. In this paper, we prove an analogous lemma for the case of submodular valuations. Our algorithm removes cycles in the support graph of a fractional allocation while guaranteeing that each agent's value, measured using the multilinear extension, does not decrease. We demonstrate applications of the cycle-canceling algorithm, along with other ideas, to obtain new algorithms and results for three well-studied allocation objectives: max-min (Santa Claus problem), Nash social welfare (NSW), and maximin-share (MMS). For the submodular NSW problem, we obtain a $\frac{1}{5}$-approximation; for the MMS problem, we obtain a $\frac{1}{2}(1-1/e)$-approximation through new simple algorithms. For various special cases where the goods are "small" valued or the number of agents is constant, we obtain tight/best-known approximation algorithms. All our results are in the value-oracle model.

cs.GT↗

arXiv2025

Online Fair Division With Subsidy: When Do Envy-Free Allocations Exist, and at What Cost?

We study the problem of fairly allocating $m$ indivisible items arriving online, among $n$ (offline) agents. Although envy-freeness has emerged as the archetypal fairness notion, envy-free (EF) allocations need not exist with indivisible items. To bypass this, a prominent line of research demonstrates that there exist allocations that can be made envy-free by allowing a subsidy. Extensive work in the offline setting has focused on finding such envy-freeable allocations with bounded subsidy. We extend this literature to an online setting where items arrive one at a time and must be immediately and irrevocably allocated. Our contributions are two-fold: 1. Maintaining EF Online: We show that envy-freeability cannot always be preserved online when the valuations are submodular or supermodular, even with binary marginals. In contrast, we design online algorithms that maintain envy-freeability at every step for the class of additive valuations, and for its superclasses including $k$-demand and SPLC valuations. 2. Ensuring Low Subsidy: We investigate the quantity of subsidy required to guarantee envy-freeness online. Surprisingly, even for additive valuations, the minimum subsidy may be as large as $\Omega(mn)$, in contrast to the offline setting, where the bound is $O(n)$. On the positive side, we identify valuation classes where the minimum subsidy is small (i.e., does not depend on $m$), including $k$-valued, rank-one, restricted additive, and identical valuations, and we obtain (mostly) tight subsidy bounds for these classes.

cs.GT↗

arXiv2025

On the Existence and Complexity of Core-Stable Data Exchanges

The rapid growth of data-driven technologies and the emergence of various data-sharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents -- or groups of agents -- from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data. The net utility of an agent is payoff minus the cost. We adapt the classical notion of core-stability from cooperative game theory to data exchange. A data exchange is core-stable if no subset of agents has any incentive to deviate to a different exchange. We show that a core-stable data exchange is guaranteed to exist when agents have concave payoff functions and convex cost functions -- a setting typical in domains like PAC learning and random discovery models. We show that relaxing either of the foregoing conditions may result in the nonexistence of core-stable data exchanges. Then, we prove that finding a core-stable exchange is PPAD-hard, even when the potential blocking coalitions are restricted to constant size. To the best of our knowledge, this provides the first known PPAD-hardness result for core-like guarantees in data economics. Finally, we show that data exchange can be modelled as a balanced $n$-person game. This immediately gives a pivoting algorithm via Scarf's theorem \cite{Scarf1967core}. We show that the pivoting algorithm works well in practice through our empirical results.

cs.GT↗

arXiv2025

Covering a Few Submodular Constraints and Applications

We consider the problem of covering multiple submodular constraints. Given a finite ground set $N$, a cost function $c: N \rightarrow \mathbb{R}_+$, $r$ monotone submodular functions $f_1,f_2,\ldots,f_r$ over $N$ and requirements $b_1,b_2,\ldots,b_r$ the goal is to find a minimum cost subset $S \subseteq N$ such that $f_i(S) \ge b_i$ for $1 \le i \le r$. When $r=1$ this is the well-known Submodular Set Cover problem. Previous work \cite{chekuri2022covering} considered the setting when $r$ is large and developed bi-criteria approximation algorithms, and approximation algorithms for the important special case when each $f_i$ is a weighted coverage function. These are fairly general models and capture several concrete and interesting problems as special cases. The approximation ratios for these problem are at least $\Omega(\log r)$ which is unavoidable when $r$ is part of the input. In this paper, motivated by some recent applications, we consider the problem when $r$ is a \emph{fixed constant} and obtain two main results. For covering multiple submodular constraints we obtain a randomized bi-criteria approximation algorithm that for any given integer $\alpha \ge 1$ outputs a set $S$ such that $f_i(S) \ge$ $(1-1/e^\alpha -\epsilon)b_i$ for each $i \in [r]$ and $\mathbb{E}[c(S)] \le (1+\epsilon)\alpha \cdot \sf{OPT}$. Second, when the $f_i$ are weighted coverage functions from a deletion-closed set system we obtain a $(1+\epsilon)$ $(\frac{e}{e-1})$ $(1+\beta)$-approximation where $\beta$ is the approximation ratio for the underlying set cover instances via the natural LP. These results show that one can obtain nearly as good an approximation for any fixed $r$ as what one would achieve for $r=1$. We mention some applications that follow easily from these general results and anticipate more in the future.

cs.DS↗

arXiv2025

Online Fair Division: Towards Ex-Post Constant MMS Guarantees

We investigate the problem of fairly allocating $m$ indivisible items among $n$ sequentially arriving agents with additive valuations, under the sought-after fairness notion of maximin share (MMS). We first observe a strong impossibility: without appropriate knowledge about the valuation functions of the incoming agents, no online algorithm can ensure any non-trivial MMS approximation, even when there are only two agents. Motivated by this impossibility, we introduce OnlineKTypeFD (online $k$-type fair division), a model that balances theoretical tractability with real-world applicability. In this model, each arriving agent belongs to one of $k$ types, with all agents of a given type sharing the same known valuation function. We do not constrain $k$ to be a constant. Upon arrival, an agent reveals her type, receives an irrevocable allocation, and departs. We study the ex-post MMS guarantees of online algorithms under two arrival models: 1- Adversarial arrivals: In this model, an adversary determines the type of each arriving agent. We design a $\frac{1}{k}$-MMS competitive algorithm and complement it with a lower bound, ruling out any $\Omega(\frac{1}{\sqrt{k}})$-MMS-competitive algorithm, even for binary valuations. 2- Stochastic arrivals: In this model, the type of each arriving agent is independently drawn from an underlying, possibly unknown distribution. Unlike the adversarial setting where the dependence on $k$ is unavoidable, we surprisingly show that in the stochastic setting, an asymptotic, arbitrarily close-to-$\frac{1}{2}$-MMS competitive guarantee is achievable under mild distributional assumptions. Our results extend naturally to a learning-augmented framework; when given access to predictions about valuation functions, we show that the competitive ratios of our algorithms degrade gracefully with multiplicative prediction errors.

cs.GT↗

arXiv2023

1/2 Approximate MMS Allocation for Separable Piecewise Linear Concave Valuations

We study fair distribution of a collection of m indivisible goods among a group of n agents, using the widely recognized fairness principles of Maximin Share (MMS) and Any Price Share (APS). These principles have undergone thorough investigation within the context of additive valuations. We explore these notions for valuations that extend beyond additivity. First, we study approximate MMS under the separable (piecewise-linear) concave (SPLC) valuations, an important class generalizing additive, where the best known factor was 1/3-MMS. We show that 1/2-MMS allocation exists and can be computed in polynomial time, significantly improving the state-of-the-art. We note that SPLC valuations introduce an elevated level of intricacy in contrast to additive. For instance, the MMS value of an agent can be as high as her value for the entire set of items. Further, the equilibrium computation problem, which is polynomial-time for additive valuations, becomes intractable for SPLC. We use a relax-and-round paradigm that goes through competitive equilibrium and LP relaxation. Our result extends to give (symmetric) 1/2-APS, a stronger guarantee than MMS. APS is a stronger notion that generalizes MMS by allowing agents with arbitrary entitlements. We study the approximation of APS under submodular valuation functions. We design and analyze a simple greedy algorithm using concave extensions of submodular functions. We prove that the algorithm gives a 1/3-APS allocation which matches the current best-known factor. Concave extensions are hard to compute in polynomial time and are, therefore, generally not used in approximation algorithms. Our approach shows a way to utilize it within analysis (while bypassing its computation), and might be of independent interest.

cs.GT↗

arXiv2023

Approximating APS under Submodular and XOS valuations with Binary Marginals

We study the problem of fairly dividing indivisible goods among a set of agents under the fairness notion of Any Price Share (APS). APS is known to dominate the widely studied Maximin share (MMS). Since an exact APS allocation may not exist, the focus has traditionally been on the computation of approximate APS allocations. Babaioff et al. studied the problem under additive valuations, and asked (i) how large can the APS value be compared to the MMS value? and (ii) what guarantees can one achieve beyond additive functions. We partly answer these questions by considering valuations beyond additive, namely submodular and XOS functions, with binary marginals. For the submodular functions with binary marginals, also known as matroid rank functions (MRFs), we show that APS is exactly equal to MMS. Consequently, we get that an exact APS allocation exists and can be computed efficiently while maximizing the social welfare. Complementing this result, we show that it is NP-hard to compute the APS value within a factor of 5/6 for submodular valuations with three distinct marginals of {0, 1/2, 1}. We then consider binary XOS functions, which are immediate generalizations of binary submodular functions in the complement free hierarchy. In contrast to the MRFs setting, MMS and APS values are not equal under this case. Nevertheless, we show that under binary XOS valuations, $MMS \leq APS \leq 2 \cdot MMS + 1$. Further, we show that this is almost the tightest bound we can get using MMS, by giving an instance where $APS \geq 2 \cdot MMS$. The upper bound on APS, implies a ~0.1222-approximation for APS under binary XOS valuations. And the lower bound implies the non-existence of better than 0.5-APS even when agents have identical valuations, which is in sharp contrast to the guaranteed existence of exact MMS allocation when agent valuations are identical.

cs.GT↗

arXiv2023

Approximation Algorithms for Envy-Free Cake Division with Connected Pieces

Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece of the cake, we develop approximation algorithms for finding envy-free (fair) cake divisions. In particular, this work improves the state-of-the-art additive approximation bound for this fundamental problem. Our results hold for general cake division instances in which the agents' valuations satisfy basic assumptions and are normalized (to have value $1$ for the cake). Furthermore, the developed algorithms execute in polynomial time under the standard Robertson-Webb query model. Prior work has shown that one can efficiently compute a cake division (with connected pieces) in which the additive envy of any agent is at most $1/3$. An efficient algorithm is also known for finding connected cake divisions that are (almost) $1/2$-multiplicatively envy-free. Improving the additive approximation guarantee and maintaining the multiplicative one, we develop a polynomial-time algorithm that computes a connected cake division that is both $\left(\frac{1}{4} +o(1) \right)$-additively envy-free and $\left(\frac{1}{2} - o(1) \right)$-multiplicatively envy-free. Our algorithm is based on the ideas of interval growing and envy-cycle-elimination. In addition, we study cake division instances in which the number of distinct valuations across the agents is parametrically bounded. We show that such cake division instances admit a fully polynomial-time approximation scheme for connected envy-free cake division.

cs.GT↗

arXiv2022

Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations

We study the problem of allocating indivisible goods among $n$ agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents' valuations and, hence, it strikes a balance between the extremes of social welfare (arithmetic mean) and egalitarian welfare (max-min value). Nash social welfare has been extensively studied in recent years for various valuation classes. In particular, a notable negative result is known when the agents' valuations are complement-free and are specified via value queries: for XOS valuations, one necessarily requires exponentially many value queries to find any sublinear (in $n$) approximation for NSW. Indeed, this lower bound implies that stronger query models are needed for finding better approximations. Towards this, we utilize demand oracles and XOS oracles; both of these query models are standard and have been used in prior work on social welfare maximization with XOS valuations. We develop the first sublinear approximation algorithm for maximizing Nash social welfare under XOS valuations, specified via demand and XOS oracles. Hence, this work breaks the $O(n)$-approximation barrier for NSW maximization under XOS valuations. We obtain this result by developing a novel connection between NSW and social welfare under a capped version of the agents' valuations. In addition to this insight, which might be of independent interest, this work relies on an intricate combination of multiple technical ideas, including the use of repeated matchings and the discrete moving knife method. In addition, we partially complement the algorithmic result by showing that, under XOS valuations, an exponential number of demand and XOS queries are necessarily required to approximate NSW within a factor of $\left(1 - \frac{1}{e}\right)$.

cs.GT↗

arXiv2021

On Fair and Efficient Allocations of Indivisible Public Goods

We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select $k \leq m$ goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), $1/n$ approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop.

cs.GT↗

arXiv2021

Memory Leak Detection Algorithms in the Cloud-based Infrastructure

A memory leak in an application deployed on the cloud can affect the availability and reliability of the application. Therefore, identifying and ultimately resolve it quickly is highly important. However, in the production environment running on the cloud, memory leak detection is a challenge without the knowledge of the application or its internal object allocation details. This paper addresses this challenge of detection of memory leaks in cloud-based infrastructure without having any internal knowledge by introducing two novel machine learning-based algorithms: Linear Backward Regression (LBR) and Precog and, their two variants: Linear Backward Regression with Change Points Detection (LBRCPD) and Precog with Maximum Filteration (PrecogMF). These algorithms only use one metric i.e the system's memory utilization on which the application is deployed for detection of a memory leak. The developed algorithm's accuracy was tested on 60 virtual machines manually labeled memory utilization data and it was found that the proposed PrecogMF algorithm achieves the highest accuracy score of 85%. The same algorithm also achieves this by decreasing the overall compute time by 80% when compared to LBR's compute time. The paper also presents the different memory leak patterns found in the various memory leak applications and are further classified into different classes based on their visual representation.

cs.DC↗

arXiv2019

Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings

We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents' valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms have been designed using approaches customized for these specific settings, and they fail to extend to more general settings. Hence, no approximation algorithm with factor independent of m is known either for asymmetric agents with additive valuations or for symmetric agents beyond additive(-like) valuations. In this paper, we extend our understanding of the NSW problem to far more general settings. Our main contribution is two approximation algorithms for asymmetric agents with additive and submodular valuations respectively. Both algorithms are simple to understand and involve non-trivial modifications of a greedy repeated matchings approach. Allocations of high valued items are done separately by un-matching certain items and re-matching them, by processes that are different in both algorithms. We show that these approaches achieve approximation factors of O(n) and O(n log n) for additive and submodular case respectively, which is independent of the number of items. For additive valuations, our algorithm outputs an allocation that also achieves the fairness property of envy-free up to one item (EF1). Furthermore, we show that the NSW problem under submodular valuations is strictly harder than all currently known settings with an e/(e-1) factor of the hardness of approximation, even for constantly many agents. For this case, we provide a different approximation algorithm that achieves a factor of e/(e-1), hence resolving it completely.

cs.GT↗

arXiv2019

Fair Division of Indivisible Goods Among Strategic Agents

We study fair division of indivisible goods in a single-parameter environment. In particular, we develop truthful social welfare maximizing mechanisms for fairly allocating indivisible goods. Our fairness guarantees are in terms of solution concepts which are tailored to address allocation of indivisible goods and, hence, provide an appropriate framework for fair division of goods. This work specifically considers fairness in terms of envy freeness up to one good (EF1), maximin share guarantee (MMS), and Nash social welfare (NSW). Our first result shows that (in a single-parameter environment) the problem of maximizing welfare, subject to the constraint that the allocation of the indivisible goods is EF1, admits a polynomial-time, 1/2-approximate, truthful auction. We further prove that this problem is NP-Hard and, hence, an approximation is warranted. This hardness result also complements prior works which show that an arbitrary EF1 allocation can be computed efficiently. We also establish a bi-criteria approximation guarantee for the problem of maximizing social welfare under MMS constraints. In particular, we develop a truthful auction which efficiently finds an allocation wherein each agent gets a bundle of value at least $\left(1/2 - \varepsilon \right)$ times her maximin share and the welfare of the computed allocation is at least the optimal, here $\varepsilon >0$ is a fixed constant. We complement this result by showing that maximizing welfare is computationally hard even if one aims to only satisfy the MMS constraint approximately.

cs.GT↗

arXiv2018

Automatically Assessing Vulnerabilities Discovered by Compositional Analysis

Testing is the most widely employed method to find vulnerabilities in real-world software programs. Compositional analysis, based on symbolic execution, is an automated testing method to find vulnerabilities in medium- to large-scale programs consisting of many interacting components. However, existing compositional analysis frameworks do not assess the severity of reported vulnerabilities. In this paper, we present a framework to analyze vulnerabilities discovered by an existing compositional analysis tool and assign CVSS3 (Common Vulnerability Scoring System v3.0) scores to them, based on various heuristics such as interaction with related components, ease of reachability, complexity of design and likelihood of accepting unsanitized input. By analyzing vulnerabilities reported with CVSS3 scores in the past, we train simple machine learning models. By presenting our interactive framework to developers of popular open-source software and other security experts, we gather feedback on our trained models and further improve the features to increase the accuracy of our predictions. By providing qualitative (based on community feedback) and quantitative (based on prediction accuracy) evidence from 21 open-source programs, we show that our severity prediction framework can effectively assist developers with assessing vulnerabilities.

cs.SE↗