p-Center Problems

Çalık, Hatice; Labbé, Martine; Yaman, Hande

doi:10.1007/978-3-319-13111-5_4

Cited by 32 publications

(15 citation statements)

References 45 publications

(63 reference statements)

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“…Another family of problems related to location analysis is the p-center problem (PCP). It comes in several variations, but the general idea is to minimize the maximum distance between a demand point and a closest point belonging to a set of p supply points [4].…”

Section: Location Analysis and Districting Problemsmentioning

confidence: 99%

Wildfire burn scar encapsulation

2021

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Wildfires burn annually across the United States (US), which threaten those in close proximity to them. Due to drastic alterations of soil properties and to the land surfaces by these fires, risks of flash floods, debris flows, and severe erosion increases for these areas, which can have catastrophic consequences for biota, people and property. Computational tools, such as the WildfireRain algorithm, have been designed and implemented to assess the potential occurrence of debris flows over burn scars. However, in order to efficiently operate these tools, they require independent, non-overlapping buffers around burned areas to be defined, which is not a trivial task. In this paper we consider the problem of efficiently subsetting the conterminous US (CONUS) domain into optimal subdomains around burn scars, aiming to enable domain-wide WildfireRain product outputs to be used for operations by the National Weather Service (NWS). To achieve this, we define the Object Encapsulation Problem, where burn scars are represented by single-cell objects in a gridded domain, and circular buffers must be constructed around them. We propose a Linear Programming (LP) model that solves this problem efficiently. Optimal results produced using this model are presented for both a simplified synthetic data set, as well as for a subset of burn scars produced by severe wildfires in 2012 over the CONUS.

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Section: Location Analysis and Districting Problemsmentioning

confidence: 99%

Wildfire burn scar encapsulation

2021

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“…The task of this problem is to find a k-center of a graph [15]. The problem and many variants of it including some approximations are known to be NP-hard [3,12]. It is shown in [18] that choosing the nodes of a k-center for amnesiac flooding does not lead to a minimal termination time.…”

Section: State Of the Artmentioning

confidence: 99%

Stateless Information Dissemination Algorithms

Turau

2020

Structural Information and Communication Complexity

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Stateless protocols are advantageous in high volume applications, increasing performance by removing the load caused by retention of session information and by providing crash tolerance. In this paper we present an optimal stateless information dissemination algorithm for synchronous distributed systems. The termination time is considerable lower than that of a recently proposed stateless dissemination protocol. Apart from a special case the new algorithm achieves the minimum possible termination time. The problem of selecting k dissemination nodes with minimal termination time is NP-hard. We prove that unless NP = P there is no approximation algorithm for this problem with approximation ratio 3/2 − . We also prove for asynchronous systems that deterministic stateless information dissemination is only possible if a large enough part of the message can be updated by each node.

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“…Some of the simplest and most studied problems in Discrete Location are the Simple Plant Location Problem (SPLP) (Cho et al 1983;Cornuéjols et al 1977;Cornuéjols and Thizy 1982;Fernández and Landete 2015;Guignard 1980), where the aim is to minimize the sum of the distances from installed facilities to customers; the p-median problem (pM), where the number of facilities to be installed is known beforehand (García et al 2011;Marín and Pelegrín 2019;ReVelle and Swain 1970); and the p-center problem (pCP), where the objective is to minimize the maximum of these distances (Calik et al 2015;Elloumi et al 2004;Hakimi 1964). The simplicity of these models has given rise to many variants.…”

Section: Introductionmentioning

confidence: 99%

Discrete ordered median problem with induced order

Domínguez

Marı́n

2020

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Ordered median functions have been developed to model flexible discrete location problems. To do this, a weight is associated to the distance from a customer to its closest facility, depending on the position of that distance relative to the distances of all the customers. In this paper this idea is extended in the following way. The position of each customer in the ordering with respect to the closest facility is used to choose a second weight that will be multiplied times a second measure of the customer. In our case, this second measure is the distance from the customer to the closest facility of a different type. For the solution of this model several integer programming formulations are built and computationally compared.

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p-Center Problems

Cited by 32 publications

References 45 publications

Wildfire burn scar encapsulation

Wildfire burn scar encapsulation

Stateless Information Dissemination Algorithms

Discrete ordered median problem with induced order

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