On r-Gatherings on the Line

Akagi, Toshihiro; Nakano, Shin-ichi

doi:10.1007/978-3-319-19647-3_3

Cited by 16 publications

(14 citation statements)

References 7 publications

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“…Armon [3] describes a simple 3-approximation algorithm for this problem. Akagi and Nakano [1] provide an O((|C| + |F |) log |C| + |F |) time algorithm to solve the r-gathering problem when all customers in C and facilities in F are on the real line.…”

Section: Related Workmentioning

confidence: 99%

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Online facility assignment

Ahmed

Rahman

Kobourov

2020

Theoretical Computer Science

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We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer ci to facility fj before the next customer ci+1 arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most |F |l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F | and another one with competitive ratio |F |. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.

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Section: Related Workmentioning

confidence: 99%

“…Algorithm σ-Randomized-Greedy chooses either f 1 or f 2 with equal probability 1 2 . Similarly for every customer c k , Algorithm σ-Randomized-Greedy chooses either f k+1 or f k with equal probability 1 2 . Then E[Cost σ-Randomized-Greedy(…”

Section: Algorithm σ-Randomized-greedymentioning

confidence: 99%

Online facility assignment

Ahmed

Rahman

Kobourov

2020

Theoretical Computer Science

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“…In this section we give a linear time algorithm to solve a decision version of the r-gathering problem [3].…”

Section: (K R)-gathering On the Linementioning

confidence: 99%

“…The minimum cost k * of a solution of a new branch problem is co(c, f ) with some c ∈ C and some f ∈ F. By using the sorted matrix searching method in Sect. 3 we can find such k * in at most O(log(n + m)) rounds, and each round needs O(n + m) time to solve the decision version of the problem.…”

Section: New Branch Locationmentioning

confidence: 99%

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On <i>r</i>-Gatherings on the Line

Akagi

Nakano

2017

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper we study a recently proposed variant of the facility location problem, called the r-gathering problem. Given an integer r, a set C of customers, a set F of facilities, and a connecting cost co(c, f ) for each pair of c ∈ C and f ∈ F, an r-gathering of customers C to facilities F is an assignment A of C to open facilities F ⊆ F such that at least r customers are assigned to each open facility. We give an algorithm to find an r-gathering with the minimum cost, where the cost is max c∈C {co(c, A(c))}, when all C and F are on the real line.

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