Decontaminating a Network from a Black Virus

We consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph that is guaranteed to be free of the fugitive is connected and whenever some node gains a property that it cannot be occupied by the fugitive, the strategy must operate in such a way to keep this property till its end. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids: nodes are placed on the plane at integer coordinates and only nodes at distance one can be adjacent. Agents do not have any knowledge about the graph a priori, but they recognize the direction of the incident edge (up, down, left or right). We give an on-line algorithm for the searchers that allows them to compute a connected and monotone strategy that guarantees searching any unknown partial grid with the use of $O(\sqrt {n})$ O ( n ) searchers, where n is the number of nodes in the grid. As for a lower bound, there exist partial grids that require ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers. Moreover, we prove that for each on-line searching algorithm there is a partial grid that forces the algorithm to use ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers but $O(\log n)$ O ( log n ) searchers are sufficient in the off-line scenario. This gives a lower bound on ${\varOmega }(\sqrt {n}/\log n)$ Ω ( n / log n ) in terms of achievable competitive ratio of any on-line algorithm.

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“…For other distributed searching models and algorithms for specific network topologies see [8,20,26,35].…”

Section: Related Workmentioning

confidence: 99%

On-line Search in Two-Dimensional Environment

Dereniowski

Urbańska

2019

Theory Comput Syst

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“…An interesting variation to the black-hole search problem has been recently introduced in [19], where the network must be decontaminated from black-viruses. A black-virus is a harmful process which destroys any agent arriving at the node where it resides; when that occurs, a black-virus moves, spreading to all the neighboring nodes, thus increasing its presence in the network.…”

Section: Related Workmentioning

confidence: 99%

Explore and repair graphs with black holes using mobile entities

D’Emidio

Frigioni

Navarra

2015

Theoretical Computer Science

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“…where q denotes the dimension of the network, and n and m denote the numbers of nodes and of links, respectively. The results of this chapter appeared in [18,19]. In next chapter, the investigation of the BVD problem is extended to arbitrary graph.…”

Section: Discussionmentioning

confidence: 99%

“…The simulation disclosed many interesting behaviors of the solution protocol. Simulation demonstrates the worst case complexity analysis in [19]. In addition to proving the analytical results, simulation provides deep understanding on influence of graph connectivity density and size on complexities (movement, time, and agent size).…”

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confidence: 82%

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Network Decontamination from Black Viruses

Cai¹

Self Cite

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In this thesis, the problem of decontaminating networks from Black Viruses (BVs) using a team of system mobile agents, i.e., the BVD problem, is investigated. The BV is a dynamic harmful process which, like the extensively studied black hole (BH), destroys any agent arriving at the network site where it resides; when that occurs, unlike a black hole which is static by definition, a BV moves, spreading to all the neighbouring sites, thus increasing its presence in the network. The initial location of Firstly, I would like to express my sincere gratitude to my advisors Professors Nicola Santoro and Paola Flocchini for their enthusiastic motivation, judicious and enlightening advices, and patient guidance throughout this research work! Their passion for distributed computing, dedication to knowledge acquiring and science developing, and an unrelenting attitude to detail all inspire me. On the other hand, their modest academic style creates an excellent research environment. They carefully selected my courses and topics, and at the same time, provided me enough flexibility to suit my work and life. Our meetings and discussions always take away their precious lunch-break time... Without their continuous support of my Ph.D. study and related research, it would not be possible for me to complete this work. Last but not the least, I would like to thank my wife, Yan Gong, and my daughter, Jessica Cai. Working full-time and supporting a family, and at the same time, studying and doing research part-time for my Ph.D. degree are definitely challenge to me. Without my family's understanding, encouragement, support, and sacrifices, I would not achieve this. I also like to thank my parents for their life-time inspiration and encouragement. vTable of Contents Abstract iii Acknowledgements Abbreviations API Application Programming Interface BH Black Hole BHS Black Hole Search BV Black Virus BVC Black Virus Clone BVD Black Virus Decontamination DisJ Distributed Algorithm Simulation Java EA Exploring Agent IC Intruder Capture IZ Impacting Zone LC Locality of Casualty LEA Leader Exploring Agent MBVD Multiple Black Virus Decontamination MF MBV Decontamination -Fertile MS MBV Decontamination -Sterile SA Shadowing Agent SD Standard Deviation xii Chapter 1 networks), settings (synchronous and asynchronous), agent distribution (co-located or dispersed), communicating mechanisms, and etc. More detailed literature review will be provided in Chapter 2. BH is harmful to agents but it is static, that is, it does not propagate in the network and so it is not harmful to other sites. The number of BHs does not increase or decrease during the search. The theoretical work related to harmful agents has focused on the problem called Intruder Capture (IC) (also known as graph decontamination and connected graph search): an extraneous mobile agent, the intruder, moves arbitrarily fast through the network infecting the visited sites; the task is to decontaminate the network using a team of system agents avoiding recontamination. The IC problem has been...

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Decontaminating a Network from a Black Virus

Cited by 15 publications

References 44 publications

On-line Search in Two-Dimensional Environment

On-line Search in Two-Dimensional Environment

Explore and repair graphs with black holes using mobile entities

Network Decontamination from Black Viruses

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