Explore and repair graphs with black holes using mobile entities

D’Emidio, Mattia; Frigioni, Daniele; Navarra, Alfredo

doi:10.1016/j.tcs.2015.09.002

Cited by 12 publications

(3 citation statements)

References 26 publications

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“…In such systems, the frequency in which virtual machines are tested for undesirable symptoms varies depending on the importance of dedicated cloud operational mechanisms. The BGT problem considered here is also a close relative of several classical algorithmic problems which focus on monitoring including Graph Exploration [5][6][7][8], Art Gallery Problem [9] and its dynamic extension k-Watchmen Problem [10]. In the work on Patrolling [11,12], the studies focus on monitoring a set of points with the same frequency of attendance, whereas in [13], the frequency may vary.…”

Section: Related Workmentioning

confidence: 99%

Bamboo Garden Trimming Problem: Priority Schedulings

2019

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The paper deals with the Bamboo Garden Trimming (BGT) problem introduced in [Gąsieniec et al., SOFSEM’17]. The problem is difficult to solved due to its close relationship to Pinwheel scheduling. The garden with n bamboos is an analogue of a system of n machines that have to be attended (e.g., serviced) with different frequencies. During each day, bamboo b i grows an extra height h i , for i = 1 , ⋯ , n and, on the conclusion of the day, at most one bamboo has its entire height cut.The goal is to design a perpetual schedule of cuts to keep the height of the tallest ever bamboo as low as possible. The contribution in this paper is twofold, and is both theoretical and experimental. In particular, the focus is on understanding what has been called priority schedulings, i.e., cutting strategies where priority is given to bamboos whose current height is above a threshold greater than or equal to H = ∑ i = 1 n h i . Value H represents the total daily growth of the system and it is known that one cannot keep bamboos in the garden below this threshold indefinitely. As the first result, it is proved that, for any distribution of integer growth rates h 1 , ⋯ , h n and any priority scheduling, the system stabilises in a fixed cycle of cuts. Then, the focus is on the so-called ReduceMax strategy, a greedy priority scheduling that each day cuts the tallest bamboo, regardless of the growth rates distribution. ReduceMax is known to provide a O ( log n ) -approximation, with respect to the lower bound H. One of the main results achieved is that, if ReduceMax stabilises in a round-robin type cycle, then it guarantees 2-approximation. Furthermore, preliminary results are provided relating the structure of the input instance, in terms of growth rates, and the behavior of ReduceMax when applied to such inputs. Finally, a conjecture that ReduceMax is 2-approximating for the BGT problem is claimed, hence an extended experimental evaluation was conducted to support the conjecture and to compare ReduceMax with other relevant scheduling algorithms. The obtained results show that ReduceMax : (i) provides 2-approximation in all considered inputs; and (ii) always outperforms other considered strategies, even those for which better worst case approximation guarantees have been proven.

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Section: Related Workmentioning

confidence: 99%

Bamboo Garden Trimming Problem: Priority Schedulings

2019

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“…In this direction, as is well documented in the literature, one of the most effective and widely used strategies, especially in a real-time context, to efficiently collect, store, and process data for decision-support and optimization purposes is to consider a graph model of the data and to employ suitable graph algorithms to solve properly defined computational problems of interest. Successful applications of graph-based modeling and graph algorithms for supporting the provision of services in modern information systems are various and span diverse domains, from navigation systems, where graphs are used to model and represent road networks and shortest-path algorithms are employed to determine the best routes [6,7], to airline management systems, where graphs are used to model flights connecting airports and maximum-flow algorithms are used to schedule departures and arrivals [8], up to distributed systems of entities, where graphs are used to model interactions between entities and coloring algorithms are exploited to achieve various forms of consensus or coordination [9,10]. Thus, on the one hand, research in this context has been extensive from a theoretical perspective in both computer science and engineering, mostly due to the plethora of domains where graph-based modeling and processing find applications [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Route Planning Algorithms for Fleets of Connected Vehicles: State of the Art, Implementation, and Deployment

D’Emidio,

Delfaraz,

Di Stefano

et al. 2024

Applied Sciences

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The introduction of 5G technologies has enabled the possibility of designing and building several new classes of networked information systems that were previously impossible to implement due to limitations on data throughput or the reliability of transmission channels. Among them, one of the most interesting and successful examples with a highly positive impact in terms of the quality of urban environments and societal and economical welfare is a system of semi-autonomous connected vehicles, where IoT devices, data centers, and fleets of smart vehicles equipped with communication and computational resources are combined into a heterogeneous and distributed infrastructure, unifying hardware, networks, and software. In order to efficiently provide various services (e.g., patrolling, pickup and delivery, monitoring), these systems typically rely on collecting and broadcasting large amounts of data (e.g., sensor data, GPS traces, or maps), which need to be properly collected and processed in a timely manner. As is well documented in the literature, one of the most effective ways to achieve this purpose, especially in a real-time context, is to adopt a graph model of the data (e.g., to model communication networks, roads, or interactions between vehicles) and to employ suitable graph algorithms to solve properly defined computational problems of interest (e.g., shortest paths or distributed consensus). While research in this context has been extensive from a theoretical perspective, works that have focused on the implementation, deployment, and evaluation of the practical performance of graph algorithms for real-world systems of autonomous vehicles have been much rarer. In this paper, we present a study of this kind. Specifically, we first describe the main features of a real-world information system employing semi-autonomous connected vehicles that is currently being tested in the city of L’Aquila (Italy). Then, we present an overview of the computational challenges arising in the considered application domain and provide a systematic survey of known algorithmic results for one of the most relevant classes of computational problems that have to be addressed in said domain, namely, pickup and delivery problems. Finally, we discuss implementation issues, adopted software tools, and the deployment and testing phases concerning one of the algorithmic components of the mentioned real-world system dedicated to handling a specific problem of the above class, namely, the pickup and delivery multi-vehicle problem with time windows.

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“…The Black Hole Search problem is to determine the location of the black hole; it is solved if, within a finite amount of time, at least one agent survives and knows the location of the black hole. This problem has been extensively investigated, both in synchronous and asynchronous networks (e.g., [13][14][15][16][17][18][19][20][21][22][23][24][25]; see [26] for a recent survey). The case when the network is an asynchronous ring (the setting considered here) has been investigated (e.g., [13,27,28]); however, with the exception of [28], these investigations assume that all agents start from the same node (i.e., they are initially gathered).…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Gathering in a Dangerous Ring

et al. 2023

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Consider a set of k identical asynchronous mobile agents located in an anonymous ring of n nodes. The classical Gather (or Rendezvous) problem requires all agents to meet at the same node, not a priori decided, within a finite amount of time. This problem has been studied assuming that the network is safe for the agents. In this paper, we consider the presence in the ring of a stationary process located at a node that disables any incoming agent without leaving any trace. Such a dangerous node is known in the literature as a black hole, and the determination of its location has been extensively investigated. The presence of the black hole makes it deterministically unfeasible for all agents to gather. So, the research concern is to determine how many agents can gather and under what conditions. In this paper we establish a complete characterization of the conditions under which the problem can be solved. In particular, we determine the maximum number of agents that can be guaranteed to gather in the same location depending on whether k or n is unknown (at least one must be known). These results are tight: in each case, gathering with one more agent is deterministically unfeasible. All our possibility proofs are constructive: we provide mobile agent algorithms that allow the agents to gather within a predefined distance under the specified conditions. The analysis of the time costs of these algorithms show that they are optimal. Our gathering algorithm for the case of unknown k is also a solution for the black hole location problem. Interestingly, its bounded time complexity is Θ(n); this is a significant improvement over the existing O(nlogn) bounded time complexity.

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Explore and repair graphs with black holes using mobile entities

Cited by 12 publications

References 26 publications

Bamboo Garden Trimming Problem: Priority Schedulings

Bamboo Garden Trimming Problem: Priority Schedulings

Route Planning Algorithms for Fleets of Connected Vehicles: State of the Art, Implementation, and Deployment

Asynchronous Gathering in a Dangerous Ring

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