Filters








259,238 Hits in 7.6 sec

On the Online Unit Clustering Problem [chapter]

Leah Epstein, Rob van Stee
2008 Lecture Notes in Computer Science  
We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh (Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p.121-131. Springer, 2006.  ...  We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2.  ...  [2] considered a problem which is called the online unit covering problem.  ... 
doi:10.1007/978-3-540-77918-6_16 fatcat:x5hcri2dwjh7nmcdqwljnpag4a

On the online unit clustering problem

Leah Epstein, Rob Van Stee
2010 ACM Transactions on Algorithms  
We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh (Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p.121-131. Springer, 2006.  ...  We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2.  ...  [2] considered a problem which is called the online unit covering problem.  ... 
doi:10.1145/1868237.1868245 fatcat:pfcmmi5tvfes5pyapkjb7xsfn4

An improved lower bound for one-dimensional online unit clustering [article]

Jun Kawahara, Koji M. Kobayashi
2015 arXiv   pre-print
studied including some variants of the unit clustering problem.  ...  The online unit clustering problem was proposed by Chan and Zarrabi-Zadeh (WAOA2007 and Theory of Computing Systems 45(3), 2009), which is defined as follows: "Points" are given online in the d-dimensional  ...  The goal of the problem is to minimize the number of created balls. Chan and Zarrabi-Zadeh have introduced the online unit clustering problem [2] . In this problem, an input is a sequence of points.  ... 
arXiv:1502.02422v1 fatcat:lr5ip65yqzb35fjwh6o3ywl5s4

A Randomized Algorithm for Online Unit Clustering [chapter]

Timothy M. Chan, Hamid Zarrabi-Zadeh
2007 Lecture Notes in Computer Science  
Recently, many researchers have considered clustering problems in more practical settings, for example, in the online and data stream models [4, 5, 12] , where the input is given as a sequence of points  ...  In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used.  ...  We focus on the online setting in this paper. The online version of the unit covering problem is one of the problems addressed in the paper by Charikar et al. [4] .  ... 
doi:10.1007/11970125_10 fatcat:l7myjvfuafbnfip57zofnzebcy

A Randomized Algorithm for Online Unit Clustering

Timothy M. Chan, Hamid Zarrabi-Zadeh
2007 Theory of Computing Systems  
Recently, many researchers have considered clustering problems in more practical settings, for example, in the online and data stream models [4, 5, 12] , where the input is given as a sequence of points  ...  In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used.  ...  We focus on the online setting in this paper. The online version of the unit covering problem is one of the problems addressed in the paper by Charikar et al. [4] .  ... 
doi:10.1007/s00224-007-9085-7 fatcat:zw4zwi4i4vd5bk4wxck75by6vu

Online Clustering on the Line with Square Cost Variable Sized Clusters

Gabriella Divéki
2013 Acta Cybernetica  
In the online clustering problems, the classification of points into sets (called clusters) is done in an online fashion.  ...  In this paper we investigate the problem on the line.  ...  Other variants of the one-dimensional online unit clustering problem were studied in [9] .  ... 
doi:10.14232/actacyb.21.1.2013.6 fatcat:nqv223syxzh55i4jogdjlochgy

Online Unit Clustering in Higher Dimensions [chapter]

Adrian Dumitrescu, Csaba D. Tóth
2018 Lecture Notes in Computer Science  
We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in R d , that arrive one by one, partition the points into clusters (subsets) of diameter at most one, so as  ...  We complement these results with some additional lower bounds for related problems in higher dimensions. Problem 3. Unit Clustering.  ...  Chan and Zarrabi-Zadeh [7] introduced the online Unit Clustering problem at WAOA 2006.  ... 
doi:10.1007/978-3-319-89441-6_18 fatcat:bsw2tmso2bdtzojthumahiaxse

WAOA 2005 Special Issue of TOCS

Thomas Erlebach, Giuseppe Persiano
2007 Theory of Computing Systems  
In Online k-Server Routing Problems, Bonifaci and Stougie study the problem of minimizing the makespan or the sum of completion times in the setting where k T. Erlebach ( )  ...  In Covering Many or Few Points with Unit Disks, de Berg, Cabello and Har-Peled consider, for a given set of weighted points in the plane, the problem of placing m unit disks so as to cover points of maximum  ...  for Online Unit Clustering.  ... 
doi:10.1007/s00224-007-9041-6 fatcat:r2loksvkkrafjijyizmkkvkqxm

WAOA 2006 Special Issue of TOCS

Thomas Erlebach, Christos Kaklamanis
2009 Theory of Computing Systems  
In Online k-Server Routing Problems, Bonifaci and Stougie study the problem of minimizing the makespan or the sum of completion times in the setting where k T. Erlebach ( )  ...  In Covering Many or Few Points with Unit Disks, de Berg, Cabello and Har-Peled consider, for a given set of weighted points in the plane, the problem of placing m unit disks so as to cover points of maximum  ...  for Online Unit Clustering.  ... 
doi:10.1007/s00224-009-9189-3 fatcat:7h6j73dn6nfkdmqwslmo62bn74

Online unit clustering in higher dimensions [article]

Adrian Dumitrescu, Csaba D. Tóth
2021 arXiv   pre-print
We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of n points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into  ...  In this paper, we work in ℝ^d using the L_∞ norm. We show that the competitive ratio of any online algorithm (deterministic or randomized) for Unit Clustering must depend on the dimension d.  ...  Chan and Zarrabi-Zadeh [10] introduced the online Unit Clustering problem.  ... 
arXiv:1708.02662v3 fatcat:ilyrq4fklve23ew2ejfcjg6axy

Online Unit Covering in Euclidean Space [article]

Adrian Dumitrescu, Anirban Ghosh, Csaba D. Tóth
2018 arXiv   pre-print
We revisit the online Unit Covering problem in higher dimensions: Given a set of n points in R^d, that arrive one by one, cover the points by balls of unit radius, so as to minimize the number of balls  ...  For d=3, the ratio of our online algorithm matches the ratio of the current best offline algorithm for the same problem due to Biniaz et al. (2017), which is remarkable (and rather unusual).  ...  In this paper we focus on the second problem, namely online Unit Covering; we however point out key differences between this problem and online Unit Clustering.  ... 
arXiv:1710.00954v3 fatcat:2cj7f6ybkvcwbdw76xe63a5fou

Online unit clustering: Variations on a theme

Leah Epstein, Asaf Levin, Rob van Stee
2008 Theoretical Computer Science  
Online unit clustering is a clustering problem where classification of points is done in an online fashion, but the exact location of clusters is fixed dynamically.  ...  We study several variants and generalizations of the online unit clustering problem, which are inspired by variants of packing and scheduling problems in the literature.  ...  A study of an online problem of partitioning points into clusters was studied by Charikar et al. [6] . They considered the so called online unit covering problem.  ... 
doi:10.1016/j.tcs.2008.04.046 fatcat:6jppvjtkrvcx5a4eflcnqwddri

Sourcing in the global aerospace supply chain using online reverse auctions

M.L. Emiliani
2004 Industrial Marketing Management  
U.S. economic cluster supporting large tier-one aerospace companies must compete against globally distributed sources of supply favored by their customers due to unit price savings, principally the result  ...  The article also examines if global sourcing practices based on power-based bargaining is an intelligent or effective solution to market pressure demanding lower prices, or whether collaborative problem  ...  Collaborative problem solving and knowledge-sharing networks The online reverse auction purchasing tool is a new technological solution to cost problems.  ... 
doi:10.1016/j.indmarman.2003.08.012 fatcat:zykgjv5vdbetzor24s3nhogubm

Online Sum-Radii Clustering

Dimitris Fotakis, Paraschos Koutris
2014 Theoretical Computer Science  
Exploiting the relation to Parking Permit, we obtain a lower bound of Ω(log log n) on the randomized competitive ratio of Online Sum-Radii Clustering in tree metrics.  ...  We also show that Online Sum-Radii Clustering in HSTs is closely related to the Parking Permit problem introduced by (Meyerson, FOCS 2005) .  ...  In the online setting, where cluster reconfiguration is not allowed, the Unit Covering and the Unit Clustering problems have received considerable attention.  ... 
doi:10.1016/j.tcs.2013.03.010 fatcat:2izq4uqw2ragphlzhhqob4dxmi

Spatio-Temporal Hierarchical Adaptive Dispatching for Ridesharing Systems [article]

Chang Liu, Jiahui Sun, Haiming Jin, Meng Ai, Qun Li, Cheng Zhang, Kehua Sheng, Guobin Wu, Xiaohu Qie, Xinbing Wang
2020 arXiv   pre-print
Nowadays, ridesharing has become one of the most popular services offered by online ride-hailing platforms (e.g., Uber and Didi Chuxing).  ...  Technically, we prove the impossibility of designing constant-competitive-ratio algorithms for the online adaptive interval problem, and propose online algorithms under partial or even zero future order  ...  interval (ADI) problem which makes online decisions of whether to perform an order dispatch operation at the end of each unit time interval for each constructed spatial cluster. en, in the rest of this  ... 
arXiv:2009.02080v1 fatcat:npu6odyuirb3tdpl5jyyqq7vai
« Previous Showing results 1 — 15 out of 259,238 results