Facility location problems in the plane based on reverse nearest neighbor queries

Cabello, Sergio; Díaz-Báñez, José Miguel; Langerman, Stefan; Seara, Carlos; Ventura, Inmaculada

doi:10.1016/j.ejor.2009.04.021

Cited by 41 publications

(26 citation statements)

References 36 publications

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“…In [10], the same authors introduce and solve the k-influence region problem for weighted facilities, which returns a region of suitable sub-optimal locations as to open a new facility so that a minimum weighted area of its k-influence region can be guaranteed. On the other hand, a ''discrete'' version of the problem of optimizing the area of an influence region, based on reverse nearest neighbor queries, has been widely studied [2,20,21]. Fort and Sellarès in [8], solve the problem of finding influential location regions based on reverse k-nearest/farthest neighbor queries.…”

Section: Common Influence Location Problemsmentioning

confidence: 99%

Common influence region problems

Fort

Sellarès

2015

Information Sciences

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Section: Common Influence Location Problemsmentioning

confidence: 99%

Common influence region problems

Fort

Sellarès

2015

Information Sciences

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“…Although MaxOverlap is shown to be much more efficient than the algorithms presented in [4], [5], scalability remains an issue. This is because the computation of intersection points of NLCs is very expensive and these intersection points increase rapidly with the number of objects.…”

Section: Related Workmentioning

confidence: 99%

“…The MaxBRNN problem was first introduced by Cabello et al [4], [5]. They called it the MAXCOV problem and present a solution for Euclidean space.…”

Section: Related Workmentioning

confidence: 99%

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MaxFirst for MaxBRkNN

Zhou

et al. 2011

2011 IEEE 27th International Conference on Data Engineering

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The MaxBRNN problem finds a region such that setting up a new service site within this region would guarantee the maximum number of customers by proximity. This problem assumes that each customer only uses the service provided by his/her nearest service site. However, in reality, a customer tends to go to his/her k nearest service sites. To handle this, MaxBRNN can be extended to the MaxBRkNN problem which finds an optimal region such that setting up a service site in this region guarantees the maximum number of customers who would consider the site as one of their k nearest service locations. We further generalize the MaxBRkNN problem to reflect the real world scenario where customers may have different preferences for different service sites, and at the same time, service sites may have preferred targeted customers. In this paper, we present an efficient solution called MaxFirst to solve this generalized MaxBRkNN problem. The algorithm works by partitioning the space into quadrants and searches only in those quadrants that potentially contain an optimal region. During the space partitioning, we compute the upper and lower bounds of the size of a quadrant's BRkNN, and use these bounds to prune the unpromising quadrants. Experiment results show that MaxFirst can be two to three orders of magnitude faster than the stateof-the-art algorithm. I. INTRODUCTIONReverse Nearest Neighbor (RNN) and Bichromatic RNN (BRNN) queries (and their variants RkNN and BRkNN) have attracted much research attention [10], [11], [12], [1], [3], [15], [8], [14]. The optimal location problem [6] and the MaxBRNN problem [5], [13] are defined using BRNN queries.Given a set of objects O and a set of objects P in space S, a BRNN query [9] issued by an object p ∈ P finds the set of objects in O for which p is their nearest neighbor in P. The optimal location problem [6] aims to find a location point that maximizes the number of objects returned by BRNN. The MaxBRNN problem [5], [13], which is also called the optimal region problem, is to find the region Q such that any point in Q is an optimal location point.The MaxBRNN problem has many interesting applications. For example, given a set of customers and a set of service sites (e.g. base stations), MaxBRNN finds a region such that setting up a new service site within this region would guarantee the maximal number of customers by proximity.The state-of-the-art algorithm MaxOverlap [13] uses a technique called region-to-point transformation to solve the MaxBRNN problem. Each service site has a sphere of influence denoted by the nearest location circle (NLC). The MaxOverlap algorithm assumes that each NLC intersects with

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“…Cabello et al [5] study the case when only one new facility by P 2 is introduced. This problem is referred to as the MaxCov problem.…”

Section: Introductionmentioning

confidence: 99%

The Discrete Voronoi Game in a Simple Polygon

Banik

Das

Maheshwari

et al. 2013

Lecture Notes in Computer Science

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Abstract. Let P be a simple polygon with m vertices and let U be a set of n points in P . We consider the points of U to be "users". We consider a game with two players P1 and P2. In this game, P1 places a point facility inside P , after which P2 places another point facility inside P . We say that a user u ∈ U is served by its nearest facility, where distances are measured by the geodesic distance in P . The objective of each player is to maximize the number of users they serve. We show that for any given placement of a facility by P1, an optimal placement for P2 can be computed in O(m + n(log n + log m)) time. We also provide a polynomial-time algorithm for computing an optimal placement for P1.

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Facility location problems in the plane based on reverse nearest neighbor queries

Cited by 41 publications

References 36 publications

Common influence region problems

Common influence region problems

MaxFirst for MaxBRkNN

The Discrete Voronoi Game in a Simple Polygon

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