Online Bottleneck Semi-matching

Xiao, Man; Zhao, Siwen; Li, Weidong; Yang, Jing

doi:10.1007/978-3-030-92681-6_35

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…The cost of assigning j r to i s is ij d [1]. The classical Online Minimum Matching (OMM) [8] is to find a matching such that the total cost of matching all requests is minimized. This kind of problems can be applied to many real scenarios, such as facility assignment, taxi server, network location and donated food transportation.…”

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confidence: 99%

“…In 2021, Itoh et al [7] analyzed the competition ratio of the online metric matching problem when the number of servers is different, and proved that the greedy algorithm can achieve a competition ratio of 3 under the condition of limiting the location of servers. In 2021, Xiao et al [8] introduced the online bottleneck semi-matching (OBSM) problem and proposed a lower bound 1 m + and an online algorithm with competition ratio ( )…”

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confidence: 99%

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An optimal algorithm for an online facility assignment problem with constraint capacities and costs

Wang

Chen²

2023

Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022)

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Given a set of facilities, or servers S = { s1, s2, . . ., sm} and a set of requests R = { r1, r2, . . ., rn} with each server si having the serving capacity of ci and the assignment cost dij occurred if the request rj has been assigned to server si , the online facility problem under our consideration is to find an assignment for a new coming request rj to a server before the next one arrived, such that in the end each si serves exactly ci requests and such that the total occurring cost ∑ nj=1 {dij|rj is assigned to si} is minimized. This paper considers a constrained version of online facility problem (COFP, for short) in which ci = 2 for all i = {1, 2, . . ., m} and dij = 2 |j-i| for all i , j. First, we obtain the optimal assignment for the offline version of COFP by exploiting a nice property of powers of two and the so-called the natural order assignment. Second, we design an online algorithm for COFP is based on the optimal assignment for the offline version of COFP. We show that our online algorithm runs in linear time and always achieves the optimal assignment for the COFP.

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Section: { }mentioning

confidence: 99%

Section: { }mentioning

confidence: 99%

An optimal algorithm for an online facility assignment problem with constraint capacities and costs

Wang

Chen²

2023

Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022)

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“…The online bottleneck matching problem with two heterogeneous sensors (OBM(2)) is to find a matching σ such that the maximum cost max{ max j:r j =σ −1 (1) d(r j , s 1 ), max j:r j =σ −1 (2) d(r j , s 2 )/w} is minimized. Clearly, if w = 1, this problem is exactly the problem considered in [18] and has an optimal online algorithm with competitive ratio 3.…”

Section: Preliminariesmentioning

confidence: 99%

Online Bottleneck Matching Problem with Two Heterogeneous Sensors in a Metric Space

Xiao

Yang

2022

Computation

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In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of r is the distance d(r,s1). Otherwise, r is assigned to sensor s2, and the service cost of r is d(r,s2)w, where w≥1 is the weight of sensor s2. The goal is to minimize the maximum matching cost, we design an optimal online algorithm with a competitive ratio of 1+w+1w for 1≤w≤1.839, and an optimal online algorithm with a competitive ratio of w+1+w2+6w+12 for w>1.839.

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The Bound Coverage Problem by Aligned Disks in $$L_1$$ Metric

Liu

2022

Lecture Notes in Computer Science

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Online Bottleneck Semi-matching

Cited by 6 publications

References 12 publications

An optimal algorithm for an online facility assignment problem with constraint capacities and costs

An optimal algorithm for an online facility assignment problem with constraint capacities and costs

Online Bottleneck Matching Problem with Two Heterogeneous Sensors in a Metric Space

The Bound Coverage Problem by Aligned Disks in $$L_1$$ Metric

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