arXiv subjects

Debajyoti Mondal

Publications and source records attributed to Debajyoti Mondal.

At least 19 recordsLinked to original sources

arXiv2026

Faraday Complexity and Depolarisation in a High-Rotation-Measure Radio Galaxy from the Spectra and Polarisation In Cutouts of Extragalactic Sources (SPICE-RACS) DR2

We present a broadband spectro-polarimetric analysis of the extragalactic radio source \texttt{RACS\_0900-28\_7036} using SPICE-RACS DR2 observations with the Australian Square Kilometre Array Pathfinder (ASKAP). The source was selected for its large rotation measure (${\rm RM}=345.7\pm0.2~{\rm rad~m^{-2}}$), substantial excess relative to the local foreground ($Δ{\rm RM}\approx171~{\rm rad~m^{-2}}$), and strong evidence of Faraday complexity ($σ_{\rm add}/δσ_{\rm add}\approx8.6$). Observations span 803--1083~MHz in 36 spectral channels, enabling detailed characterization of Faraday rotation and wavelength-dependent depolarization. One-dimensional QU-fitting and Bayesian model selection identify a multi-component model comprising one Burn-slab component and two external Faraday dispersion components (1 Slab + 2 EFD) as the preferred description. The dominant astrophysical component exhibits ${\rm RM}\approx345.5~{\rm rad~m^{-2}}$ with modest Faraday dispersion ($σ_{\rm RM}\approx3~{\rm rad~m^{-2}}$), consistent with the Galactic foreground rotation measure at the source position (${\rm RM}_{\rm Gal}=331.9\pm33.1~{\rm rad~m^{-2}}$). A secondary broader component at ${\rm RM}\approx131.5~{\rm rad~m^{-2}}$ shows strong depolarization ($σ_{\rm RM}\approx19.5~{\rm rad~m^{-2}}$), indicating an additional turbulent Faraday-active medium along the line of sight. The fractional polarization spectrum and $q$--$u$ plane evolution further confirm multiple Faraday-active regions along the line of sight. These results demonstrate that ASKAP broadband spectropolarimetry can resolve complex Faraday structures and probe turbulent magnetized environments, providing a framework for systematic depolarization studies across the full SPICE-RACS catalog and enabling statistical investigations of Faraday complexity in diverse extragalactic radio sources.

astro-ph.CO↗

arXiv2025

Finding Cliques in Geometric Intersection Graphs with Grounded or Stabbed Constraints

A geometric intersection graph is constructed over a set of geometric objects, where each vertex represents a distinct object and an edge connects two vertices if and only if the corresponding objects intersect. We examine the problem of finding a maximum clique in the intersection graphs of segments and disks under grounded and stabbed constraints. In the grounded setting, all objects lie above a common horizontal line and touch that line. In the stabbed setting, all objects can be stabbed with a common line. - We prove that finding a maximum clique is NP-hard for the intersection graphs of upward rays. This strengthens the previously known NP-hardness for ray graphs and settles the open question for the grounded segment graphs. The hardness result holds in the stabbed setting. - We show that the problem is polynomial-time solvable for intersection graphs of grounded unit-length segments, but NP-hard for stabbed unit-length segments. - We give a polynomial-time algorithm for the case of grounded disks. If the grounded constraint is relaxed, then we give an $O(n^3 f(n))$-time $3/2$-approximation for disk intersection graphs with radii in the interval $[1,3]$, where $n$ is the number of disks and $f(n)$ is the time to compute a maximum clique in an $n$-vertex cobipartite graph. This is faster than previously known randomized EPTAS, QPTAS, or 2-approximation algorithms for arbitrary disks. We obtain our result by proving that pairwise intersecting disks with radii in $[1,3]$ are 3-pierceable, which extends the 3-pierceable property from the long known unit disk case to a broader class.

cs.CG↗

arXiv2025

Computing Conforming Partitions with Low Stabbing Number for Rectilinear Polygons

A conforming partition of a rectilinear n-gon P (possibly with holes) is a partition of P into rectangles without using Steiner points (i.e., all corners of all rectangles must lie on the boundary of P). The stabbing number of such a partition is the maximum number of rectangles intersected by an axis-aligned segment lying in the interior of P. In this paper, we examine the problem of computing conforming partitions with low stabbing number. We show that computing a conforming partition with stabbing number at most 4 is NP-hard, which strengthens a previously known hardness result [Durocher \& Mehrabi, Theor. Comput. Sci. 689: 157-168 (2017)] and eliminates the possibility for fixed-parameter-tractable algorithms parameterized by the stabbing number unless P = NP. In contrast, we give (i) an O(n log n)-time algorithm to decide whether a conforming partition with stabbing number 2 exists, (ii) a fixed-parameter-tractable algorithm parameterized by both the stabbing number and treewidth of the pixel graph of the polygon, and (iii) a fixed-parameter-tractable algorithm parameterized by the stabbing number for polygons without holes in general position.

cs.CG↗

arXiv2025

A Space-Efficient Algorithm for Longest Common Almost Increasing Subsequence of Two Sequences

Let $A$ and $B$ be two number sequences of length $n$ and $m$, respectively, where $m\le n$. Given a positive number $δ$, a common almost increasing sequence $s_1\ldots s_k$ is a common subsequence for both $A$ and $B$ such that for all $2\le i\le k$, $s_i+δ> \max_{1\le j < i} s_j$. The LCaIS problem seeks to find the longest common almost increasing subsequence (LCaIS) of $A$ and $B$. An LCaIS can be computed in $O(nm\ell)$ time and $O(nm)$ space [Ta, Shieh, Lu (TCS 2021)], where $\ell$ is the length of the LCaIS of $A$ and $B$. In this paper we first give an $O(nm\ell)$-time and $O(n+m\ell)$-space algorithm to find LCaIS, which improves the space complexity. We then design an $O((n+m)\log n +\mathcal{M}\log \mathcal{M} + \mathcal{C}\ell)$-time and $O(\mathcal{M}(\ell+\log \mathcal{M}))$-space algorithm, which is faster when the number of matching pairs $\mathcal{M}$ and the number of compatible matching pairs $\mathcal{C}$ are in $o(nm/\log m)$.

cs.DS↗

arXiv2025

Subsetwise and Multi-Level Additive Spanners with Lightness Guarantees

An \emph{additive +$βW$ spanner} of an edge weighted graph $G=(V,E)$ is a subgraph $H$ of $G$ such that for every pair of vertices $u$ and $v$, $d_{H}(u,v) \le d_G(u,v) + βW$, where $d_G(u,v)$ is the shortest path length from $u$ to $v$ in $G$. While additive spanners are very well studied in the literature, spanners that are both additive and lightweight have been introduced more recently [Ahmed et al., WG 2021]. Here the \emph{lightness} is the ratio of the spanner weight to the weight of a minimum spanning tree of $G$. In this paper, we examine the widely known subsetwise setting when the distance conditions need to hold only among the pairs of a given subset $S$. We generalize the concept of lightness to subset-lightness using a Steiner tree and provide polynomial-time algorithms to compute subsetwise additive $+εW$ spanner and $+(4+ε) W$ spanner with $O_ε(|S|)$ and $O_ε(|V_H|^{1/3} |S|^{1/3})$ subset-lightness, respectively, where $ε$ is an arbitrary positive constant. We next examine a multi-level version of spanners that often arises in network visualization and modeling the quality of service requirements in communication networks. The goal here is to compute a nested sequence of spanners with the minimum total edge weight. We provide an $e$-approximation algorithm to compute multi-level spanners assuming that an oracle is given to compute single-level spanners, improving a previously known 4-approximation [Ahmed et al., IWOCA 2023].

cs.DS↗

arXiv2024

On the Use of Deep Learning Models for Semantic Clone Detection

Detecting and tracking code clones can ease various software development and maintenance tasks when changes in a code fragment should be propagated over all its copies. Several deep learning-based clone detection models have appeared in the literature for detecting syntactic and semantic clones, widely evaluated with the BigCloneBench dataset. However, class imbalance and the small number of semantic clones make BigCloneBench less ideal for interpreting model performance. Researchers also use other datasets such as GoogleCodeJam, OJClone, and SemanticCloneBench to understand model generalizability. To overcome the limitations of existing datasets, the GPT-assisted semantic and cross-language clone dataset GPTCloneBench has been released. However, how these models compare across datasets remains unclear. In this paper, we propose a multi-step evaluation approach for five state-of-the-art clone detection models leveraging existing benchmark datasets, including GPTCloneBench, and using mutation operators to study model ability. Specifically, we examine three highly-performing single-language models (ASTNN, GMN, CodeBERT) on BigCloneBench, SemanticCloneBench, and GPTCloneBench, testing their robustness with mutation operations. Additionally, we compare them against cross-language models (C4, CLCDSA) known for detecting semantic clones. While single-language models show high F1 scores for BigCloneBench, their performance on SemanticCloneBench varies (up to 20%). Interestingly, the cross-language model (C4) shows superior performance (around 7%) on SemanticCloneBench over other models and performs similarly on BigCloneBench and GPTCloneBench. On mutation-based datasets, C4 has more robust performance (less than 1% difference) compared to single-language models, which show high variability.

cs.SE↗

arXiv2024

Representing Hypergraphs by Point-Line Incidences

We consider hypergraph visualizations that represent vertices as points in the plane and hyperedges as curves passing through the points of their incident vertices. Specifically, we consider several different variants of this problem by (a) restricting the curves to be lines or line segments, (b) allowing two curves to cross if they do not share an element, or not; and (c) allowing two curves to overlap or not. We show $\exists\mathbb{R}$-hardness for six of the eight resulting decision problem variants and describe polynomial-time algorithms in some restricted settings. Lastly, we briefly touch on what happens if we allow the lines of the represented hyperedges to have bends - to this we generalize a counterexample to a long-standing result that was sometimes assumed to be correct.

cs.CG↗

arXiv2024

The Maximum Clique Problem in a Disk Graph Made Easy

A disk graph is an intersection graph of disks in $\mathbb{R}^2$. Determining the computational complexity of finding a maximum clique in a disk graph is a long-standing open problem. In 1990, Clark, Colbourn, and Johnson gave a polynomial-time algorithm for computing a maximum clique in a unit disk graph. However, finding a maximum clique when disks are of arbitrary size is widely believed to be a challenging open problem. The problem is open even if we restrict the disks to have at most two different sizes of radii, or restrict the radii to be within $[1,1+\varepsilon]$ for some $ε>0$. In this paper, we provide a new perspective to examine adjacencies in a disk graph that helps obtain the following results. - We design an $O(2^k n^{2k} poly(n))$-time algorithm to find a maximum clique in a $n$-vertex disk graph with $k$ different sizes of radii. This is polynomial for every fixed $k$, and thus settles the open question for the case when $k=2$. - Given a set of $n$ unit disks, we show how to compute a maximum clique inside each possible axis-aligned rectangle determined by the disk centers in $O(n^5\log n)$-time. This is at least a factor of $n^{4/3}$ faster than applying the fastest known algorithm for finding a maximum clique in a unit disk graph for each rectangle independently. - We give an $O(2^kn^{2rk} poly(n,r))$-time algorithm to find a maximum clique in a $n$-vertex ball graph with $k$ different sizes of radii where the ball centers lie on $r$ parallel planes. This is polynomial for every fixed $k$ and $r$, and thus contrasts the previously known NP-hardness result for finding a maximum clique in an arbitrary ball graph.

cs.CG↗

arXiv2024

Improved Outerplanarity Bounds for Planar Graphs

In this paper, we study the outerplanarity of planar graphs, i.e., the number of times that we must (in a planar embedding that we can initially freely choose) remove the outerface vertices until the graph is empty. It is well-known that there are $n$-vertex graphs with outerplanarity $\tfrac{n}{6}+Θ(1)$, and not difficult to show that the outerplanarity can never be bigger. We give here improved bounds of the form $\tfrac{n}{2g}+2g+O(1)$, where $g$ is the fence-girth, i.e., the length of the shortest cycle with vertices on both sides. This parameter $g$ is at least the connectivity of the graph, and often bigger; for example, our results imply that planar bipartite graphs have outerplanarity $\tfrac{n}{8}+O(1)$. We also show that the outerplanarity of a planar graph $G$ is at most $\tfrac{1}{2}$diam$(G)+O(\sqrt{n})$, where diam$(G)$ is the diameter of the graph. All our bounds are tight up to smaller-order terms, and a planar embedding that achieves the outerplanarity bound can be found in linear time.

cs.DS↗

arXiv2024

Quantum Speedup for Some Geometric 3SUM-Hard Problems and Beyond

The classical 3SUM conjecture states that the class of 3SUM-hard problems does not admit a truly subquadratic $O(n^{2-δ})$-time algorithm, where $δ>0$, in classical computing. The geometric 3SUM-hard problems have widely been studied in computational geometry and recently, these problems have been examined under the quantum computing model. For example, Ambainis and Larka [TQC'20] designed a quantum algorithm that can solve many geometric 3SUM-hard problems in $O(n^{1+o(1)})$-time, whereas Buhrman [ITCS'22] investigated lower bounds under quantum 3SUM conjecture that claims there does not exist any sublinear $O(n^{1-δ})$-time quantum algorithm for the 3SUM problem. The main idea of Ambainis and Larka is to formulate a 3SUM-hard problem as a search problem, where one needs to find a point with a certain property over a set of regions determined by a line arrangement in the plane. The quantum speed-up then comes from the application of the well-known quantum search technique called Grover search over all regions. This paper further generalizes the technique of Ambainis and Larka for some 3SUM-hard problems when a solution may not necessarily correspond to a single point or the search regions do not immediately correspond to the subdivision determined by a line arrangement. Given a set of $n$ points and a positive number $q$, we design $O(n^{1+o(1)})$-time quantum algorithms to determine whether there exists a triangle among these points with an area at most $q$ or a unit disk that contains at least $q$ points. We also give an $O(n^{1+o(1)})$-time quantum algorithm to determine whether a given set of intervals can be translated so that it becomes contained in another set of given intervals and discuss further generalizations.

cs.CG↗

arXiv2023

Investigating Technology Usage Span by Analyzing Users' Q&A Traces in Stack Overflow

Choosing an appropriate software development technology (e.g., programming language) is challenging due to the proliferation of diverse options. The selection of inappropriate technologies for development may have a far-reaching effect on software developers' career growth. Switching to a different technology after working with one may lead to a complex learning curve and, thus, be more challenging. Therefore, it is crucial for software developers to find technologies that have a high usage span. Intuitively, the usage span of a technology can be determined by the time span developers have used that technology. Existing literature focuses on the technology landscape to explore the complex and implicit dependencies among technologies but lacks formal studies to draw insights about their usage span. This paper investigates the technology usage span by analyzing the question and answering (Q&A) traces of Stack Overflow (SO), the largest technical Q&A website available to date. In particular, we analyze 6.7 million Q&A traces posted by about 97K active SO users and see what technologies have appeared in their questions or answers over 15 years. According to our analysis, C# and Java programming languages have a high usage span, followed by JavaScript. Besides, developers used the .NET framework, iOS & Windows Operating Systems (OS), and SQL query language for a long time (on average). Our study also exposes the emerging (i.e., newly growing) technologies. For example, usages of technologies such as SwiftUI, .NET-6.0, Visual Studio 2022, and Blazor WebAssembly framework are increasing. The findings from our study can assist novice developers, startup software industries, and software users in determining appropriate technologies. This also establishes an initial benchmark for future investigation on the use span of software technologies.

cs.SE↗

arXiv2023

Finding a Maximum Clique in a Disk Graph

A disk graph is an intersection graph of disks in the Euclidean plane, where the disks correspond to the vertices of the graph and a pair of vertices are adjacent if and only if their corresponding disks intersect. The problem of determining the time complexity of computing a maximum clique in a disk graph is a long-standing open question. The problem is known to be open even when the radii of all the disks are in the interval $[1,(1+\varepsilon)]$, where $\varepsilon>0$. However, the maximum clique problem is known to be APX-hard for the intersection graphs of many other convex objects such as intersection graphs of ellipses, triangles, and a combination of unit disks and axis-parallel rectangles. Furthermore, there exists an $O(n^3\log n)$-time algorithm to compute a maximum clique for unit disks. Here we obtain the following results. - We give an algorithm to compute a maximum clique in a unit disk graph in $O(n^{2.5}\log n)$-time, which improves the previously best known running time of $O(n^3\log n)$ [Eppstein '09]. - We extend a widely used `co-2-subdivision approach' to prove that computing a maximum clique in a combination of unit disks and axis-parallel rectangles is NP-hard to approximate within $4448/4449 \approx 0.9997 $. The use of a `co-2-subdivision approach' was previously thought to be unlikely in this setting [Bonnet et al. '20]. Our result improves the previously known inapproximability factor of $7633010347/7633010348\approx 0.9999$. - We show that the parameter minimum lens width of the disk arrangement may be used to make progress in the case when disk radii are in $[1,(1+\varepsilon)]$. For example, if the minimum lens width is at least $0.265$ and $ \varepsilon\le 0.0001$, which still allows for non-Helly triples in the arrangement, then one can find a maximum clique in polynomial time.

cs.CG↗

arXiv2023

Pathways to Leverage Transcompiler based Data Augmentation for Cross-Language Clone Detection

Software clones are often introduced when developers reuse code fragments to implement similar functionalities in the same or different software systems. Many high-performing clone detection tools today are based on deep learning techniques and are mostly used for detecting clones written in the same programming language, whereas clone detection tools for detecting cross-language clones are also emerging rapidly. The popularity of deep learning-based clone detection tools creates an opportunity to investigate how known strategies that boost the performances of deep learning models could be further leveraged to improve clone detection tools. In this paper, we investigate such a strategy, data augmentation, which has not yet been explored for cross-language clone detection as opposed to single-language clone detection. We show how the existing knowledge on transcompilers (source-to-source translators) can be used for data augmentation to boost the performance of cross-language clone detection models, as well as to adapt single-language clone detection models to create cross-language clone detection pipelines. To demonstrate the performance boost for cross-language clone detection through data augmentation, we exploit Transcoder, which is a pre-trained source-to-source translator. To show how to extend single-language models for cross-language clone detection, we extend a popular single-language model, Graph Matching Network (GMN) in a combination with the transcompilers. We evaluated our models on popular benchmark datasets. Our experimental results showed improvements in F1 scores (sometimes up to 3%) for the cutting-edge cross-language clone detection models. Even when extending GMN for cross-language clone detection, the models built leveraging data augmentation outperformed the baseline with scores of 0.90, 0.92, and 0.91 for precision, recall, and F1 score, respectively.

cs.SE↗

arXiv2023

Token Swapping on Trees

The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge. We present some results about token swapping on a tree, also known as "sorting with a transposition tree": 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a "happy leaf"), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves -- as all known approximation algorithms for the problem do -- has approximation factor at least $4/3$. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem -- weighted coloured token swapping -- is NP-complete on trees, even when they are restricted to be subdivided stars, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.

cs.CC↗

arXiv2022

Emanation Graph: A Plane Geometric Spanner with Steiner Points

An emanation graph of grade $k$ on a set of points is a plane spanner made by shooting $2^{k+1}$ equally spaced rays from each point, where the shorter rays stop the longer ones upon collision. The collision points are the Steiner points of the spanner. Emanation graphs of grade one were studied by Mondal and Nachmanson in the context of network visualization. They proved that the spanning ratio of such a graph is bounded by $(2+\sqrt{2})\approx 3.414$. We improve this upper bound to $\sqrt{10} \approx 3.162$ and show this to be tight, i.e., there exist emanation graphs with spanning ratio $\sqrt{10}$. We show that for every fixed $k$, the emanation graphs of grade $k$ are constant spanners, where the constant factor depends on $k$. An emanation graph of grade two may have twice the number of edges compared to grade one graphs. Hence we introduce a heuristic method for simplifying them. In particular, we compare simplified emanation graphs against Shewchuk's constrained Delaunay triangulations on both synthetic and real-life datasets. Our experimental results reveal that the simplified emanation graphs outperform constrained Delaunay triangulations in common quality measures (e.g., edge count, angular resolution, average degree, total edge length) while maintaining a comparable spanning ratio and Steiner point count.

cs.CG↗

arXiv2022

Burning Number for the Points in the Plane

The burning process on a graph $G$ starts with a single burnt vertex, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as one other unburnt vertex. The burning number of $G$ is the smallest number of steps required to burn all the vertices of the graph. In this paper, we examine the problem of computing the burning number in a geometric setting. The input is a set of points $P$ in the Euclidean plane. The burning process starts with a single burnt point, and at each subsequent step, burns all the points that are within a distance of one unit from the currently burnt points and one other unburnt point. The burning number of $P$ is the smallest number of steps required to burn all the points of $P$. We call this variant \emph{point burning}. We consider another variant called \emph{anywhere burning}, where we are allowed to burn any point of the plane. We show that point burning and anywhere burning problems are both NP-complete, but $(2+\varepsilon)$ approximable for every $\varepsilon>0$. Moreover, if we put a restriction on the number of burning sources that can be used, then the anywhere burning problem becomes NP-hard to approximate within a factor of $\frac{2}{\sqrt{3}}-\varepsilon$.

cs.CG↗

arXiv2022

Improved and Generalized Algorithms for Burning a Planar Point Set

Given a set $P$ of points in the plane, a point burning process is a discrete time process to burn all the points of $P$ where fires must be initiated at the given points. Specifically, the point burning process starts with a single burnt point from $P$, and at each subsequent step, burns all the points in the plane that are within one unit distance from the currently burnt points, as well as one other unburnt point of $P$ (if exists). The point burning number of $P$ is the smallest number of steps required to burn all the points of $P$. If we allow the fire to be initiated anywhere, then the burning process is called an anywhere burning process, and the corresponding burning number is called anywhere burning number. Computing the point and anywhere burning number is known to be NP-hard. In this paper we show that both these problems admit PTAS in one dimension. We then show that in two dimensions, point burning and anywhere burning are $(1.96296+\varepsilon)$ and $(1.92188+\varepsilon)$ approximable, respectively, for every $\varepsilon>0$, which improves the previously known $(2+\varepsilon)$ factor for these problems. We also observe that a known result on set cover problem can be leveraged to obtain a 2-approximation for burning the maximum number of points in a given number of steps. We show how the results generalize if we allow the points to have different fire spreading rates. Finally, we prove that even if the burning sources are given as input, finding a point burning sequence itself is NP-hard.

cs.CG↗

arXiv2022

Minimum Ply Covering of Points with Unit Squares

Given a set $P$ of points and a set $U$ of axis-parallel unit squares in the Euclidean plane, a minimum ply cover of $P$ with $U$ is a subset of $U$ that covers $P$ and minimizes the number of squares that share a common intersection, called the minimum ply cover number of $P$ with $U$. Biedl et al. [Comput. Geom., 94:101712, 2020] showed that determining the minimum ply cover number for a set of points by a set of axis-parallel unit squares is NP-hard, and gave a polynomial-time 2-approximation algorithm for instances in which the minimum ply cover number is constant. The question of whether there exists a polynomial-time approximation algorithm remained open when the minimum ply cover number is $ω(1)$. We settle this open question and present a polynomial-time $(8+\varepsilon)$-approximation algorithm for the general problem, for every fixed $\varepsilon>0$.

cs.CG↗