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Satyam Singh

Publications and source records attributed to Satyam Singh.

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IMBench: A Benchmark for Intuitive Robotic Manipulation

Humans combine reasoning and motor control to solve complex manipulation tasks under diverse constraints. They build an understanding of the physical world that helps them convert reasoning into actions and quickly adapt to new scenes, tasks, and rules. We refer to this capability as intuitive manipulation. Existing benchmarks fail to capture this integration: they evaluate physical reasoning in isolation from execution, or measure policy performance without requiring explicit reasoning. We introduce IMBENCH, a benchmark designed to evaluate intuitive manipulation as an integrated capability spanning perception, physical reasoning, action generation, and iterative execution. Our tasks require models to infer task-relevant physical structure and generate feasible action sequences under explicit constraints, including contact-rich manipulation, tool use, and multi-stage dependencies. We introduce a benchmark of 35 tasks, 14K filtered trajectories, and scalable tools for generating diverse scenarios. Experiments reveal a consistent gap: vision language models show partial physical reasoning ability but fail to produce executable plans, while state-of-the-art vision-language-action models struggle to satisfy task constraints and generalize across scenarios. These results identify intuitive manipulation as a missing axis in current foundation models and generalist robot policies, and position IMBENCH as a step toward evaluating and enabling more integrated, adaptive physical intelligence.

cs.RO

Online Algorithms for Geometric Independent Set

In the classical online model, the maximum independent set problem admits an $Ω(n)$ lower bound on the competitive ratio even for interval graphs, motivating the study of the problem under additional assumptions. We first study the problem on graphs with a bounded independent kissing number $ζ$, defined as the size of the largest induced star in the graph minus one. We show that a simple greedy algorithm, requiring no geometric representation, achieves a competitive ratio of $ζ$. Moreover, this bound is optimal for deterministic online algorithms and asymptotically optimal for randomized ones. This extends previous results from specific geometric graph families to more general graph classes. Since this bound rules out further improvements through randomization alone, we investigate the power of randomization with access to geometric representation. When the geometric representation of the objects is known, we present randomized online algorithms with improved guarantees. For unit ball graphs in $\mathbb{R}^3$, we present an algorithm whose expected competitive ratio is strictly smaller than the deterministic lower bound implied by the independent kissing number. For $α$-fat objects and for axis-aligned hyper-rectangles in $\mathbb{R}^d$ with bounded diameters, we obtain algorithms with expected competitive ratios that depend polylogarithmically on the ratio between the maximum and minimum object diameters. In both cases, the randomized lower bound implied by the independent kissing number grows polynomially with the ratio between the maximum and minimum object diameters, implying substantial performance guarantees for our algorithms.

cs.CG

Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs

A \emph{disk graph} is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time $O(n^{7/3+ o(1)})$, where $n$ denotes the number of disks~\cite{EspenantKM23, keil_et_al:LIPIcs.SoCG.2025.63}. Moreover, for the case of disk graphs with $t$ distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time $O^*(n^{2t})$~\cite{keil_et_al:LIPIcs.SoCG.2025.63}. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: - for unit disk graphs, we give an algorithm that, with constant success probability, computes a $(1-\varepsilon)$-approximate maximum clique in expected time $\tilde{O}(n/\varepsilon^2)$; and - for disk graphs with $t$ distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a $(1-\varepsilon)$-approximate maximum clique in expected time $\tilde{O}(f(t)\cdot (1/\varepsilon)^{O(t)} \cdot n)$, for some (exponential) function $f(t)$.

cs.CG

Gap-ETH-Tight Algorithms for Hyperbolic TSP and Steiner Tree

We give an approximation scheme for the TSP in $d$-dimensional hyperbolic space that has optimal dependence on $\varepsilon$ under Gap-ETH. For any fixed dimension $d\geq 2$ and for any $\varepsilon>0$ our randomized algorithm gives a $(1+\varepsilon)$-approximation in time $2^{O(1/\varepsilon^{d-1})}n^{1+o(1)}$. We also provide an algorithm for the hyperbolic Steiner tree problem with the same running time. Our algorithm is an Arora-style dynamic program based on a randomly shifted hierarchical decomposition. However, we introduce a new hierarchical decomposition called the hybrid hyperbolic quadtree to achieve the desired large-scale structure, which deviates significantly from the recently proposed hyperbolic quadtree of Kisfaludi-Bak and Van Wordragen (JoCG'25). Moreover, we have a new non-uniform portal placement, and our structure theorem employs a new weighted crossing analysis. We believe that these techniques could form the basis for further developments in geometric optimization in curved spaces.

cs.CG

KELP: Robust Online Log Parsing Through Evolutionary Grouping Trees

Real-time log analysis is the cornerstone of observability for modern infrastructure. However, existing online parsers are architecturally unsuited for the dynamism of production environments. Built on fundamentally static template models, they are dangerously brittle: minor schema drifts silently break parsing pipelines, leading to lost alerts and operational toil. We propose \textbf{KELP} (\textbf{K}elp \textbf{E}volutionary \textbf{L}og \textbf{P}arser), a high-throughput parser built on a novel data structure: the Evolutionary Grouping Tree. Unlike heuristic approaches that rely on fixed rules, KELP treats template discovery as a continuous online clustering process. As logs arrive, the tree structure evolves, nodes split, merge, and re-evaluate roots based on changing frequency distributions. Validating this adaptability requires a dataset that models realistic production complexity, yet we identify that standard benchmarks rely on static, regex-based ground truths that fail to reflect this. To enable rigorous evaluation, we introduce a new benchmark designed to reflect the structural ambiguity of modern production systems. Our evaluation demonstrates that KELP maintains high accuracy on this rigorous dataset where traditional heuristic methods fail, without compromising throughput. Our code and dataset can be found at codeberg.org/stonebucklabs/kelp

cs.DB

Online Hitting of Unit Balls and Hypercubes in $\mathbb{R}^d$ using Points from $\mathbb{Z}^d$

We consider the online hitting set problem for the range space $Σ=(\cal X,\cal R)$, where the point set $\cal X$ is known beforehand, but the set $\cal R$ of geometric objects is not known in advance. Here, objects from $\cal R$ arrive one by one. The objective of the problem is to maintain a hitting set of the minimum cardinality by taking irrevocable decisions. In this paper, we consider the problem when objects are unit balls or unit hypercubes in $\mathbb{R}^d$, and the points from $\mathbb{Z}^d$ are used for hitting them. First, we address the case when objects are unit intervals in $\mathbb{R}$ and present an optimal deterministic algorithm with a competitive ratio of~$2$. Then, we consider the case when objects are unit balls. For hitting unit balls in $\mathbb{R}^2$ and $\mathbb{R}^3$, we present $4$ and $14$-competitive deterministic algorithms, respectively. On the other hand, for hitting unit balls in $\mathbb{R}^d$, we propose an $O(d^4)$-competitive deterministic algorithm, and we demonstrate that}, for $d<4$, the competitive ratio of any deterministic algorithm is at least $d+1$. In the end, we explore the case where objects are unit hypercubes. For hitting unit hypercubes in $\mathbb{R}^2$ and $\mathbb{R}^3$, we obtain $4$ and $8$-competitive deterministic algorithms, respectively. For hitting unit hypercubes in $\mathbb{R}^d$ ($d\geq 3$), we present an $O(d^2)$-competitive randomized algorithm. Furthermore, we prove that the competitive ratio of any deterministic algorithm for the problem is at least $d+1$ for any $d\in\mathbb{N}$.

cs.CG

Online Hitting Sets for Disks of Bounded Radii

We present algorithms for the online minimum hitting set problem in geometric range spaces: given a set $P$ of $n$ points in the plane and a sequence of geometric objects that arrive one-by-one, we need to maintain a hitting set at all times by making irrevocable decisions. For disks of radii in the interval $[1,M]$, we present an $O(\log M \log n)$-competitive algorithm. This result generalizes from disks to positive homothets of any convex body in the plane with scaling factors in the interval $[1,M]$. As a main technical tool, we reduce the problem to the online hitting set problem for a finite subset of integer points and geometric objects with the lowest point property, introduced in this paper, which behave similarly to bottomless rectangles. Specifically, for a given $N>1$, we present an $O(\log N)$-competitive algorithm for the variant where $P$ is a subset of an $N\times N$ section of the integer lattice, and the geometric objects have the lowest point property.

cs.CG

Online Hitting Set for Axis-Aligned Squares

We are given a set $P$ of $n$ points in the plane, and a sequence of axis-aligned squares that arrive in an online fashion. The online hitting set problem consists of maintaining, by adding new points if necessary, a set $H\subseteq P$ that contains at least one point in each input square. We present an $O(\log n)$-competitive deterministic algorithm for this problem. The competitive ratio is the best possible, apart from constant factors. In fact, this is the first $O(\log n)$-competitive algorithm for the online hitting set problem that works for geometric objects of arbitrary sizes (i.e., arbitrary scaling factors) in the plane. We further generalize this result to positive homothets of a polygon with $k\geq 3$ vertices in the plane and provide an $O(k^2\log n)$-competitive algorithm.

cs.CG

Online Geometric Hitting Set and Set Cover Beyond Unit Balls in $\mathbb{R}^2$

We investigate the geometric hitting set problem in the online setup for the range space $Σ=({\cal P},{\cal S})$, where the set $¶\subset\mathbb{R}^2$ is a collection of $n$ points and the set $\cal S$ is a family of geometric objects in $\mathbb{R}^2$. In the online setting, the geometric objects arrive one by one. Upon the arrival of an object, an online algorithm must maintain a valid hitting set by making an irreversible decision, i.e., once a point is added to the hitting set by the algorithm, it can not be deleted in the future. The objective of the geometric hitting set problem is to find a hitting set of the minimum cardinality. Even and Smorodinsky (Discret. Appl. Math., 2014) considered an online model (Model-I) in which the range space $Σ$ is known in advance, but the order of arrival of the input objects in $\cal S$ is unknown. They proposed online algorithms having optimal competitive ratios of $Θ(\log n)$ for intervals, half-planes and unit disks in $\mathbb{R}^2$. Whether such an algorithm exists for unit squares remained open for a long time. This paper considers an online model (Model-II) in which the entire range space $Σ$ is not known in advance. We only know the set $\cal P$ but not the set $\cal S$ in advance. Note that any algorithm for Model-II will also work for Model-I, but not vice-versa. In Model-II, we obtain an optimal competitive ratio of $Θ(\log(n))$ for unit disks and regular $k$-gon with $k\geq 4$ in $\mathbb{R}^2$. All the above-mentioned results also hold for the equivalent geometric set cover problem in Model-II.

cs.CG

Online Epsilon Net and Piercing Set for Geometric Concepts

VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry, asserts that if the VC-dimension of a set system is bounded, then a small sample exists that intersects all sufficiently large sets. In online learning scenarios where data arrives sequentially, the VC-dimension helps to bound the complexity of the set system, and $\varepsilon$-nets ensure the selection of a small representative set. This sampling framework is crucial in various domains, including spatial data analysis, motion planning in dynamic environments, optimization of sensor networks, and feature extraction in computer vision, among others. Motivated by these applications, we study the online $\varepsilon$-net problem for geometric concepts with bounded VC-dimension. While the offline version of this problem has been extensively studied, surprisingly, there are no known theoretical results for the online version to date. We present the first deterministic online algorithm with an optimal competitive ratio for intervals in $\mathbb{R}$. Next, we give a randomized online algorithm with a near-optimal competitive ratio for axis-aligned boxes in $\mathbb{R}^d$, for $d\le 3$. Furthermore, we introduce a novel technique to analyze similar-sized objects of constant description complexity in $\mathbb{R}^d$, which may be of independent interest. Next, we focus on the continuous version of this problem, where ranges of the set system are geometric concepts in $\mathbb{R}^d$ arriving in an online manner, but the universe is the entire space, and the objective is to choose a small sample that intersects all the ranges.

cs.LG

New Lower Bound and Algorithms for Online Geometric Hitting Set Problem

The hitting set problem is one of the fundamental problems in combinatorial optimization and is well-studied in offline setup. We consider the online hitting set problem, where only the set of points is known in advance, and objects are introduced one by one. Our objective is to maintain a minimum-sized hitting set by making irrevocable decisions. Here, we present the study of two variants of the online hitting set problem depending on the point set. In the first variant, we consider the point set to be the entire $\mathbb{Z}^d$, while in the second variant, we consider the point set to be a finite subset of $\mathbb{R}^2$. If you use points in $\mathbb{Z}^d$ to hit homothetic hypercubes in $\mathbb{R}^d$ with side lengths in $[1,M]$, we show that the competitive ratio of any algorithm is $Ω(d\log M)$, whether it is deterministic or random. This improves the recently known deterministic lower bound of $Ω(\log M)$ by a factor of $d$. Then, we present an almost tight randomized algorithm with a competitive ratio $O(d^2\log M)$ that significantly improves the best-known competitive ratio of $25^d\log M$. Next, we propose a simple deterministic ${\lfloor\frac{2}α+2\rfloor^d}(\lfloor\log_{2}M\rfloor+1)$ competitive algorithm to hit similarly sized {$α$-fat objects} in $\mathbb{R}^d$ having diameters in the range $[1, M]$ using points in $\mathbb{Z}^d$. This improves the current best-known upper bound by a factor of at least $5^d$. Finally, we consider the hitting set problem when the point set consists of $n$ points in $\mathbb{R}^2$, and the objects are homothetic regular $k$-gons having diameter in the range $[1, M]$. We present an $O(\log n\log M)$ competitive randomized algorithm for that. Whereas no result was known even for squares. In particular, our results answer some of the open questions raised by Khan et al. (SoCG'23) and Alefkhani et al. (WAOA'23).

cs.CG

Online Geometric Covering and Piercing

We consider the online version of the piercing set problem, where geometric objects arrive one by one, and the online algorithm must maintain a valid piercing set for the already arrived objects by making irrevocable decisions. It is easy to observe that any deterministic algorithm solving this problem for intervals in $\mathbb{R}$ has a competitive ratio of at least $Ω(n)$. This paper considers the piercing set problem for similarly sized objects. We propose a deterministic online algorithm for similarly sized fat objects in $\mathbb{R}^d$. For homothetic hypercubes in $\mathbb{R}^d$ with side length in the range $[1,k]$, we propose a deterministic algorithm having a competitive ratio of at most~$3^d\lceil\log_2 k\rceil+2^d$. In the end, we show deterministic lower bounds of the competitive ratio for similarly sized $α$-fat objects in $\mathbb{R}^2$ and homothetic hypercubes in $\mathbb{R}^d$. Note that piercing translated copies of a convex object is equivalent to the unit covering problem, which is well-studied in the online setup. Surprisingly, no upper bound of the competitive ratio was known for the unit covering problem when the corresponding object is anything other than a ball or a hypercube. Our result yields an upper bound of the competitive ratio for the unit covering problem when the corresponding object is any convex object in $\mathbb{R}^d$.

cs.CG

Power-Efficient Image Storage: Leveraging Super Resolution Generative Adversarial Network for Sustainable Compression and Reduced Carbon Footprint

In recent years, large-scale adoption of cloud storage solutions has revolutionized the way we think about digital data storage. However, the exponential increase in data volume, especially images, has raised environmental concerns regarding power and resource consumption, as well as the rising digital carbon footprint emissions. The aim of this research is to propose a methodology for cloud-based image storage by integrating image compression technology with SuperResolution Generative Adversarial Networks (SRGAN). Rather than storing images in their original format directly on the cloud, our approach involves initially reducing the image size through compression and downsizing techniques before storage. Upon request, these compressed images will be retrieved and processed by SRGAN to generate images. The efficacy of the proposed method is evaluated in terms of PSNR and SSIM metrics. Additionally, a mathematical analysis is given to calculate power consumption and carbon footprint assesment. The proposed data compression technique provides a significant solution to achieve a reasonable trade off between environmental sustainability and industrial efficiency.

eess.IV

Online Dominating Set and Coloring for Geometric Intersection Graphs

We present online deterministic algorithms for minimum coloring and minimum dominating set problems in the context of geometric intersection graphs. We consider a graph parameter: the independent kissing number $ζ$, which is a number equal to `the size of the largest induced star in the graph $-1$'. For a graph with an independent kissing number at most $ζ$, we show that the famous greedy algorithm achieves an optimal competitive ratio of $ζ$ for the minimum dominating set and the minimum independent dominating set problems. However, for the minimum connected dominating set problem, we obtain a competitive ratio of at most $2ζ$. To complement this, we prove that for the minimum connected dominating set problem, any deterministic online algorithm has a competitive ratio of at least $2(ζ-1)$ for the geometric intersection graph of translates of a convex object in $\mathbb{R}^2$. Next, for the minimum coloring problem, we obtain algorithms having a competitive ratio of $O\left({ζ'}{\log m}\right)$ for geometric intersection graphs of bounded scaled $α$-fat objects in $\mathbb{R}^d$ having widths in the interval $[1,m]$, where $ζ'$ is the independent kissing number of the geometric intersection graph of bounded scaled $α$-fat objects having widths in the interval $[1,2]$. Finally, we investigate the value of $ζ$ for geometric intersection graphs of various families of geometric objects.

cs.CG

Online Dominating Set and Independent Set

Finding minimum dominating set and maximum independent set for graphs in the classical online setup are notorious due to their disastrous $Ω(n)$ lower bound of the competitive ratio that even holds for interval graphs, where $n$ is the number of vertices. In this paper, inspired by Newton number, first, we introduce the independent kissing number $ζ$ of a graph. We prove that the well known online greedy algorithm for dominating set achieves optimal competitive ratio $ζ$ for any graph. We show that the same greedy algorithm achieves optimal competitive ratio $ζ$ for online maximum independent set of a class of graphs with independent kissing number $ζ$. For minimum connected dominating set problem, we prove that online greedy algorithm achieves an asymptotic competitive ratio of $2(ζ-1)$, whereas for a family of translated convex objects the lower bound is $\frac{2ζ-1}{3}$. Finally, we study the value of $ζ$ for some specific families of geometric objects: fixed and arbitrary oriented unit hyper-cubes in $I\!\!R^d$, congruent balls in $I\!\!R^3$, fixed oriented unit triangles, fixed and arbitrary oriented regular polygons in $I\!\!R^2$. For each of these families, we also present lower bounds of the minimum connected dominating set problem.

cs.CG