Parameterized Complexity of Safe Set

Belmonte, Rémy; Hanaka, Tesshu; Katsikarelis, Ioannis; Lampis, Michael; Ono, Hiroyuki; Otachi, Yota

doi:10.1007/978-3-030-17402-6_4

Cited by 6 publications

(5 citation statements)

References 19 publications

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“…Furthermore, some authors in [17] studied the SS and computed the SN and CSN of a cartesian product of two complete graphs. Belmonte et al [5] studied the parameterized complexity of safe set problems. Different classes of graphs and their CSN have been studied and computed as shown in TABLE 1.…”

Section: Introductionmentioning

confidence: 99%

Robustness in Mesh Networks Using Connected Safe Set and Applications

Iqbal,

Kashif,

Alharbi

et al. 2024

IEEE Access

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The robustness of the networks is their capacity to remain operational in the presence of faults and disruptions, and thereby it is an important tool to provide data transmission in telecommunications networks, enterprise networks, and cloud computing networks. The connected collection of nodes in a network, excluding which results in the decomposition of a network into components such that the cardinality of each component is at most equal to the cardinality of the collection, is referred to as a connected safe set (CSS). The least size of CSS is known as connected safe number (CSN). The identification of the connected collection of nodes in the networks, capable of enduring dual load in case of faults and disruption, can be realized as CSS. Mesh networks (MNs) have become an integral part of a variety of domains, such as smart cities, disaster recovery, and military defense, due to their decentralized nature and ability to reconfigure as conditions change dynamically. In this paper, the CSS and CSN for various types of MNs, such as triangular, triangular circular, double triangular circular, and quadrangular necklace mesh are computed. Finally, an application of CSS in the context of optimal router installation on certain MNs is included.INDEX TERMS Connected safe number, connected safe set, mesh networks, robustness.

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Section: Introductionmentioning

confidence: 99%

Robustness in Mesh Networks Using Connected Safe Set and Applications

Iqbal,

Kashif,

Alharbi

et al. 2024

IEEE Access

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“…In recent years, for the CSN of a weighted tree, Ehard and Rautenbach [6] presented a polynomial-time approximation scheme. Belmonte et al [3] studied the parameterized complexity of SS problems. Fujita et.…”

Section: Introductionmentioning

confidence: 99%

Computation of Connected Safe Set of Cycle-Related Networks and Applications

Iqbal,

Zafar,

Kashif

et al. 2024

Preprint

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A connected collection of nodes in a network excluding which results in the decomposition of a network into components such that the cardinality of each component is at most equal to the cardinality of the collection is referred to as a connected safe set (CSS). A CSS of the least size is called connected safe basis and its cardinality is referred to as a connected safe number (CSN). In this article, we computed CSS and CSN of certain cycle-related networks, namely tadpole network, helm network, and prism network. In addition, we presented an application of the CSS for ensuring an optimal water distribution network in a smart city.

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“…Furthermore, the study on safe set and weighted safe set was conducted by several authors. e parameterized complexity of safe set problems was investigated by Belmonte et al [10]. Macambiraa et al [11] presented a mixed integer linear programming formulation and an algorithm for both the weighted safe set and the safe set problems.…”

Section: Introductionmentioning

confidence: 99%

On the Connected Safe Number of Some Classes of Graphs

Iqbal

Sardar

Alrowaili

et al. 2021

Journal of Mathematics

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For a connected simple graph G , a nonempty subset S of V G is a connected safe set if the induced subgraph G S is connected and the inequality S ≥ D satisfies for each connected component D of G∖S whenever an edge of G exists between S and D . A connected safe set of a connected graph G with minimum cardinality is called the minimum connected safe set and that minimum cardinality is called the connected safe numbers. We study connected safe sets with minimal cardinality of the ladder, sunlet, and wheel graphs.

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Parameterized Complexity of Safe Set

Cited by 6 publications

References 19 publications

Robustness in Mesh Networks Using Connected Safe Set and Applications

Robustness in Mesh Networks Using Connected Safe Set and Applications

Computation of Connected Safe Set of Cycle-Related Networks and Applications

On the Connected Safe Number of Some Classes of Graphs

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