arXiv subjects

Rahnuma Islam Nishat

Publications and source records attributed to Rahnuma Islam Nishat.

4 recordsLinked to original sources

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

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

A Review of AI and Machine Learning Contribution in Predictive Business Process Management (Process Enhancement and Process Improvement Approaches)

Purpose- The significance of business processes has fostered a close collaboration between academia and industry. Moreover, the business landscape has witnessed continuous transformation, closely intertwined with technological advancements. Our main goal is to offer researchers and process analysts insights into the latest developments concerning Artificial Intelligence (AI) and Machine Learning (ML) to optimize their processes in an organization and identify research gaps and future directions in the field. Design/methodology/approach- In this study, we perform a systematic review of academic literature to investigate the integration of AI/ML in business process management (BPM). We categorize the literature according to the BPM life-cycle and employ bibliometric and objective-oriented methodology, to analyze related papers. Findings- In business process management and process map, AI/ML has made significant improvements using operational data on process metrics. These developments involve two distinct stages: (1) process enhancement, which emphasizes analyzing process information and adding descriptions to process models, and (2) process improvement, which focuses on redesigning processes based on insights derived from analysis. Research limitations/implications- While this review paper serves to provide an overview of different approaches for addressing process-related challenges, it does not delve deeply into the intricacies of fine-grained technical details of each method. This work focuses on recent papers conducted between 2010 and 2024. Originality/value- This paper adopts a pioneering approach by conducting an extensive examination of the integration of AI/ML techniques across the entire process management lifecycle. Additionally, it presents groundbreaking research and introduces AI/ML-enabled integrated tools, further enhancing the insights for future research.

cs.AI↗

arXiv2022

The Hamiltonian Path Graph is Connected for Simple $s,t$ Paths in Rectangular Grid Graphs

A \emph{simple} $s,t$ path $P$ in a rectangular grid graph $\mathbb{G}$ is a Hamiltonian path from the top-left corner $s$ to the bottom-right corner $t$ such that each \emph{internal} subpath of $P$ with both endpoints $a$ and $b$ on the boundary of $\mathbb{G}$ has the minimum number of bends needed to travel from $a$ to $b$ (i.e., $0$, $1$, or $2$ bends, depending on whether $a$ and $b$ are on opposite, adjacent, or the same side of the bounding rectangle). Here, we show that $P$ can be reconfigured to any other simple $s,t$ path of $\mathbb{G}$ by \emph{switching $2\times 2$ squares}, where at most ${5}|\mathbb{G}|/{4}$ such operations are required. Furthermore, each \emph{square-switch} is done in $O(1)$ time and keeps the resulting path in the same family of simple $s,t$ paths. Our reconfiguration result proves that the \emph{Hamiltonian path graph} $\cal{G}$ for simple $s,t$ paths is connected and has diameter at most ${5}|\mathbb{G}|/{4}$ which is asymptotically tight.

cs.DM↗