arXiv subjects

Souvik Saha

Publications and source records attributed to Souvik Saha.

4 recordsLinked to original sources

arXiv2026

Fixed Budget vs. Covering Target: The Partial Set Cover Boundary for Bounded VC-Dimension

Maximum Coverage and Partial Set Cover are fundamental parameterized covering problems. The former fixes a budget $k$ and maximizes coverage; the latter meets a target with as few sets as possible. Badanidiyuru, Kleinberg, and Lee (SoCG 2012) give an EPAS for the former on bounded-VC set systems, while Jain et al. (SODA 2023) show that on $K_{d,d}$-free incidence graphs, $k+1$ sets suffice whenever $k$ sets meet the target. We ask whether this guarantee extends to all bounded-VC set systems. Our first result is negative. Unless FPT = W[1], Partial Set Cover admits no parameterized $(2-\delta)$-approximation even at VC-dimension seven. Under ETH, it has no parameterized approximation scheme there and no $2^{o(d)}$-approximation at VC-dimension $d$. On the positive side, bounded semi-ladder index restores this guarantee. It is stronger than bounded VC-dimension but strictly generalizes the $K_{d,d}$-free setting. For Weighted Partial Set Cover, if $k$ sets cover weight $W$, we find $k+1$ sets covering weight $W$ in $2^{O(\Gamma k\log k)}N$ time, where $\Gamma$ is the downward intersection complexity and $N$ is the input size. The framework supports per-class targets and matroid independence, with applications to partial dominating set and geometric and bounded-size covering. Finally, we give a deterministic FPT reduction from Weighted CC-MaxSAT to a bounded family of Weighted Maximum Coverage instances, preserving incidence structure and approximation schemes with constant-factor accuracy loss. This gives an EPAS at bounded semi-ladder index. We improve the deterministic BKL bounded-VC implementation; combined with our reduction, it yields a $2^{\widetilde{O}(kd/\varepsilon)}N^{O(1)}$-time EPAS for bounded-VC Weighted CC-MaxSAT.

cs.DS↗

arXiv2026

Evaluating Hardware Abstraction Layer Concepts for Software Defined Vehicles: Insights into Applicability and Effectiveness

The emergence of Software-Defined Vehicles represents a fundamental shift in automotive design, prioritizing software-centric architectures over traditional hardware-driven models. SDVs require modularity, interoperability, real-time processing, and over-the-air update capabilities throughout the vehicle lifecycle. However, current vehicle systems, characterized by tightly coupled software and hardware, struggle to meet these demands due to their complexity and heterogeneity. A critical first step toward enabling SDVs is the decoupling of software from hardware, which can be facilitated through a robust Hardware Abstraction Layer. While existing HALs offer hardware independence and standardized interfaces, their applicability and effectiveness in SDV contexts remain uncertain. This paper systematically evaluates current automotive HALs and explores HAL mechanisms from non-automotive domains, including smartphones, networking, and industrial automation, to extract cross-domain insights relevant to SDV development. A criteria-driven evaluation framework is developed to assess HALs against SDV-specific needs. Findings reveal that while middleware-based HALs offer portability and modularity, hypervisor-based approaches better support safety, OTA readiness, and hardware efficiency. Limitations in both approaches are identified, prompting recommendations for a hybrid HAL design that integrates hypervisor isolation with middleware standardization. This paper contributes to the ongoing developments in automotive software architecture by offering insights into the applicability and effectiveness of current HAL strategies. It provides actionable guidance for designing flexible, scalable, and future-ready HALs to support SDVs across their lifecycle.

cs.SE↗

arXiv2025

Line Cover and Related Problems

We study extensions of the classic \emph{Line Cover} problem, which asks whether a set of $n$ points in the plane can be covered using $k$ lines. Line Cover is known to be NP-hard, and we focus on two natural generalizations. The first is \textbf{Line Clustering}, where the goal is to find $k$ lines minimizing the sum of squared distances from the input points to their nearest line. The second is \textbf{Hyperplane Cover}, which asks whether $n$ points in $\mathbb{R}^d$ can be covered by $k$ hyperplanes. We also study the more general \textbf{Projective Clustering} problem, which unifies both settings and has applications in machine learning, data analysis, and computational geometry. In this problem, one seeks $k$ affine subspaces of dimension $r$ that minimize the sum of squared distances from the given points in $\mathbb{R}^d$ to the nearest subspace. Our results reveal notable differences in the parameterized complexity of these problems. While Line Cover is fixed-parameter tractable when parameterized by $k$, we show that Line Clustering is W[1]-hard with respect to $k$ and does not admit an algorithm with running time $n^{o(k)}$ unless the Exponential Time Hypothesis fails. Hyperplane Cover has been known to be NP-hard since the 1980s, following work of Megiddo and Tamir, even for $d=2$, we show that it remains NP-hard even when $k=2$. Finally, we present an algorithm for Projective Clustering running in $n^{O(dk(r+1))}$ time. This bound matches our lower bound for Line Clustering and generalizes the classic algorithm for $k$-Means Clustering ($r=0$) by Inaba, Katoh, and Imai [SoCG 1994].

cs.CG↗

arXiv2025

More Efforts Towards Fixed-Parameter Approximability of Multiwinner Rules

Multiwinner Elections have emerged as a prominent area of research with numerous practical applications. We contribute to this area by designing parameterized approximation algorithms and also resolving an open question by Yang and Wang [AAMAS'18]. More formally, given a set of candidates, \mathcal{C}, a set of voters,\mathcal{V}, approving a subset of candidates (called approval set of a voter), and an integer $k$, we consider the problem of selecting a ``good'' committee using Thiele rules. This problem is computationally challenging for most Thiele rules with monotone submodular satisfaction functions, as there is no (1-\frac{1}{e}-\epsilon)\footnote{Here, $e$ denotes the base of the natural logarithm.}-approximation algorithm in f(k)(|\mathcal{C}| + |\mathcal{V}|)^{o(k)} time for any fixed $\epsilon > 0$ and any computable function $f$, and no {\sf PTAS} even when the length of approval set is two. Skowron [WINE'16] designed an approximation scheme running in FPT time parameterized by the combined parameter, size of the approval set and $k$. In this paper, we consider a parameter $d+k$ (no $d$ voters approve the same set of $d$ candidates), where $d$ is upper bounded by the size of the approval set (thus, can be much smaller). With respect to this parameter, we design parameterized approximation schemes, a lossy polynomial-time preprocessing method, and show that an extra committee member suffices to achieve the desired score (i.e., $1$-additive approximation). Additionally, we resolve an open question by Yang and Wang~[AAMAS'18] regarding the fixed-parameter tractability of the problem under the PAV rule with the total score as the parameter, demonstrating that it admits an FPT algorithm.

cs.GT↗