8 Search Results for "Li, Shi"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.86
Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems

Authors: Shi Li

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives such as makespan and weighted completion time. For many problems, we develop nearly-linear time approximation algorithms with approximation ratios matching the current best ones achieved in polynomial time. Our main technique is linear programming relaxation. For the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. For the makespan objective, we develop a rounding algorithm with (2+ε)-approximation ratio. For the weighted completion time objective, we prove the LP is as strong as the rectangle LP used by Im and Li, leading to a nearly-linear time (1.45 + ε)-approximation for the problem. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the nearly-linear running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope.
Cite as

Shi Li. Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 86:1-86:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{li:LIPIcs.ICALP.2023.86,
  author =	{Li, Shi},
  title =	{{Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{86:1--86:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.86},
  URN =		{urn:nbn:de:0030-drops-181386},
  doi =		{10.4230/LIPIcs.ICALP.2023.86},
  annote =	{Keywords: Nearly-Linear Time, Sheduling, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.33
Minimizing the Maximum Flow Time in the Online Food Delivery Problem

Authors: Xiangyu Guo, Kelin Luo, Shi Li, and Yuhao Zhang

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where k vehicles of capacity c are serving a set of requests ordering food from one restaurant. After a request arrives, it can be served by a vehicle moving from the restaurant to its delivery location. We are interested in serving all requests while minimizing the maximum flow-time, i.e., the maximum time length a customer waits to receive his/her food after submitting the order. We show that the problem is hard in both offline and online settings even when k = 1 and c = ∞: There is a hardness of approximation of Ω(n) for the offline problem, and a lower bound of Ω(n) on the competitive ratio of any online algorithm, where n is number of points in the metric. We circumvent the strong negative results in two directions. Our main result is an O(1)-competitive online algorithm for the uncapacitated (i.e, c = ∞) food delivery problem on tree metrics; we also have negative result showing that the condition c = ∞ is needed. Then we explore the speed-augmentation model where our online algorithm is allowed to use vehicles with faster speed. We show that a moderate speeding factor leads to a constant competitive ratio, and we prove a tight trade-off between the speeding factor and the competitive ratio.
Cite as

Xiangyu Guo, Kelin Luo, Shi Li, and Yuhao Zhang. Minimizing the Maximum Flow Time in the Online Food Delivery Problem. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{guo_et_al:LIPIcs.ISAAC.2022.33,
  author =	{Guo, Xiangyu and Luo, Kelin and Li, Shi and Zhang, Yuhao},
  title =	{{Minimizing the Maximum Flow Time in the Online Food Delivery Problem}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.33},
  URN =		{urn:nbn:de:0030-drops-173181},
  doi =		{10.4230/LIPIcs.ISAAC.2022.33},
  annote =	{Keywords: Online algorithm, Capacitated Vehicle Routing, Flow Time Optimization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.36
Nested Active-Time Scheduling

Authors: Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to g jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. In this way, the active time models parallel scheduling when there is a fixed cost for turning the machine on at each discrete step. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This result improves on the previous best 2-approximation for the general case.
Cite as

Nairen Cao, Jeremy T. Fineman, Shi Li, Julián Mestre, Katina Russell, and Seeun William Umboh. Nested Active-Time Scheduling. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2022.36,
  author =	{Cao, Nairen and Fineman, Jeremy T. and Li, Shi and Mestre, Juli\'{a}n and Russell, Katina and Umboh, Seeun William},
  title =	{{Nested Active-Time Scheduling}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.36},
  URN =		{urn:nbn:de:0030-drops-173214},
  doi =		{10.4230/LIPIcs.ISAAC.2022.36},
  annote =	{Keywords: Scheduling algorithms, Active time, Approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.35
Algorithms and Hardness for Multidimensional Range Updates and Queries

Authors: Joshua Lau and Angus Ritossa

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class of data structure problems over arbitrarily large integer arrays in one or more dimensions. These problems allow range updates (such as filling all points in a range with a constant) and queries (such as finding the sum or maximum of values in a range). In this work, we consider these operations along with updates that replace each point in a range with the minimum, maximum, or sum of its existing value, and a constant. In one dimension, it is known that segment trees can be leveraged to facilitate any n of these operations in Õ(n) time overall. Other than a few specific cases, until now, higher dimensional variants have been largely unexplored. Despite their tightly-knit complexity in one dimension, we show that variants induced by subsets of these operations exhibit polynomial separation in two dimensions. In particular, no truly subquadratic time algorithm can support certain pairs of these updates simultaneously without falsifying several popular conjectures. On the positive side, we show that truly subquadratic algorithms can be obtained for variants induced by other subsets. We provide two general approaches to designing such algorithms that can be generalised to online and higher dimensional settings. First, we give almost-tight Õ(n^{3/2}) time algorithms for single-update variants where the update and query operations meet a set of natural conditions. Second, for other variants, we provide a general framework for reducing to instances with a special geometry. Using this, we show that O(m^{3/2-ε}) time algorithms for counting paths and walks of length 2 and 3 between vertex pairs in sparse graphs imply truly subquadratic data structures for certain variants; to this end, we give an Õ(m^{(4ω-1)/(2ω+1)}) = O(m^1.478) time algorithm for counting simple 3-paths between vertex pairs.
Cite as

Joshua Lau and Angus Ritossa. Algorithms and Hardness for Multidimensional Range Updates and Queries. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lau_et_al:LIPIcs.ITCS.2021.35,
  author =	{Lau, Joshua and Ritossa, Angus},
  title =	{{Algorithms and Hardness for Multidimensional Range Updates and Queries}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.35},
  URN =		{urn:nbn:de:0030-drops-135742},
  doi =		{10.4230/LIPIcs.ITCS.2021.35},
  annote =	{Keywords: Orthogonal range, Range updates, Online and Dynamic Data Structures, Fine-grained complexity, Cycle counting}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.39
On Approximating Degree-Bounded Network Design Problems

Authors: Xiangyu Guo, Guy Kortsarz, Bundit Laekhanukit, Shi Li, Daniel Vaz, and Jiayi Xian

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph G = (V, E) with edge costs c ∈ ℝ_{≥ 0}^E, a root r ∈ V and k terminals K ⊆ V, we need to output a minimum-cost arborescence in G that contains an rrightarrow t path for every t ∈ K. Recently, Grandoni, Laekhanukit and Li, and independently Ghuge and Nagarajan, gave quasi-polynomial time O(log²k/log log k)-approximation algorithms for the problem, which are tight under popular complexity assumptions. In this paper, we consider the more general Degree-Bounded Directed Steiner Tree (DB-DST) problem, where we are additionally given a degree bound d_v on each vertex v ∈ V, and we require that every vertex v in the output tree has at most d_v children. We give a quasi-polynomial time (O(log n log k), O(log² n))-bicriteria approximation: The algorithm produces a solution with cost at most O(log nlog k) times the cost of the optimum solution that violates the degree constraints by at most a factor of O(log²n). This is the first non-trivial result for the problem. While our cost-guarantee is nearly optimal, the degree violation factor of O(log²n) is an O(log n)-factor away from the approximation lower bound of Ω(log n) from the Set Cover hardness. The hardness result holds even on the special case of the Degree-Bounded Group Steiner Tree problem on trees (DB-GST-T). With the hope of closing the gap, we study the question of whether the degree violation factor can be made tight for this special case. We answer the question in the affirmative by giving an (O(log nlog k), O(log n))-bicriteria approximation algorithm for DB-GST-T.
Cite as

Xiangyu Guo, Guy Kortsarz, Bundit Laekhanukit, Shi Li, Daniel Vaz, and Jiayi Xian. On Approximating Degree-Bounded Network Design Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 39:1-39:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guo_et_al:LIPIcs.APPROX/RANDOM.2020.39,
  author =	{Guo, Xiangyu and Kortsarz, Guy and Laekhanukit, Bundit and Li, Shi and Vaz, Daniel and Xian, Jiayi},
  title =	{{On Approximating Degree-Bounded Network Design Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{39:1--39:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.39},
  URN =		{urn:nbn:de:0030-drops-126420},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.39},
  annote =	{Keywords: Directed Steiner Tree, Group Steiner Tree, degree-bounded}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.42
On the Facility Location Problem in Online and Dynamic Models

Authors: Xiangyu Guo, Janardhan Kulkarni, Shi Li, and Jiayi Xian

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
In this paper we study the facility location problem in the online with recourse and dynamic algorithm models. In the online with recourse model, clients arrive one by one and our algorithm needs to maintain good solutions at all time steps with only a few changes to the previously made decisions (called recourse). We show that the classic local search technique can lead to a (1+√2+ε)-competitive online algorithm for facility location with only O(log n/ε log 1/ε) amortized facility and client recourse, where n is the total number of clients arrived during the process. We then turn to the dynamic algorithm model for the problem, where the main goal is to design fast algorithms that maintain good solutions at all time steps. We show that the result for online facility location, combined with the randomized local search technique of Charikar and Guha [Charikar and Guha, 2005], leads to a (1+√2+ε)-approximation dynamic algorithm with total update time of Õ(n²) in the incremental setting against adaptive adversaries. The approximation factor of our algorithm matches the best offline analysis of the classic local search algorithm. Finally, we study the fully dynamic model for facility location, where clients can both arrive and depart. Our main result is an O(1)-approximation algorithm in this model with O(|F|) preprocessing time and O(nlog³ D) total update time for the HST metric spaces, where |F| is the number of potential facility locations. Using the seminal results of Bartal [Bartal, 1996] and Fakcharoenphol, Rao and Talwar [Fakcharoenphol et al., 2003], which show that any arbitrary N-point metric space can be embedded into a distribution over HSTs such that the expected distortion is at most O(log N), we obtain an O(log |F|) approximation with preprocessing time of O(|F|²log |F|) and O(nlog³ D) total update time. The approximation guarantee holds in expectation for every time step of the algorithm, and the result holds in the oblivious adversary model.
Cite as

Xiangyu Guo, Janardhan Kulkarni, Shi Li, and Jiayi Xian. On the Facility Location Problem in Online and Dynamic Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guo_et_al:LIPIcs.APPROX/RANDOM.2020.42,
  author =	{Guo, Xiangyu and Kulkarni, Janardhan and Li, Shi and Xian, Jiayi},
  title =	{{On the Facility Location Problem in Online and Dynamic Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{42:1--42:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.42},
  URN =		{urn:nbn:de:0030-drops-126452},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.42},
  annote =	{Keywords: Facility location, online algorithm, recourse}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.16
Flow-time Optimization for Concurrent Open-Shop and Precedence Constrained Scheduling Models

Authors: Janardhan Kulkarni and Shi Li

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
Scheduling a set of jobs over a collection of machines is a fundamental problem that needs to be solved millions of times a day in various computing platforms: in operating systems, in large data clusters, and in data centers. Along with makespan, flow-time, which measures the length of time a job spends in a system before it completes, is arguably the most important metric to measure the performance of a scheduling algorithm. In recent years, there has been a remarkable progress in understanding flow-time based objective functions in diverse settings such as unrelated machines scheduling, broadcast scheduling, multi-dimensional scheduling, to name a few. Yet, our understanding of the flow-time objective is limited mostly to the scenarios where jobs have no dependencies. On the other hand, in almost all real world applications, think of MapReduce settings for example, jobs have dependencies that need to be respected while making scheduling decisions. In this paper, we take first steps towards understanding this complex problem. In particular, we consider two classical scheduling problems that capture dependencies across jobs: 1) concurrent open-shop scheduling (COSSP) and 2) precedence constrained scheduling. Our main motivation to study these problems specifically comes from their relevance to two scheduling problems that have gained importance in the context of data centers: co-flow scheduling and DAG scheduling. We design almost optimal approximation algorithms for COSSP and PCSP, and show hardness results.
Cite as

Janardhan Kulkarni and Shi Li. Flow-time Optimization for Concurrent Open-Shop and Precedence Constrained Scheduling Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kulkarni_et_al:LIPIcs.APPROX-RANDOM.2018.16,
  author =	{Kulkarni, Janardhan and Li, Shi},
  title =	{{Flow-time Optimization for Concurrent Open-Shop and Precedence Constrained Scheduling Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.16},
  URN =		{urn:nbn:de:0030-drops-94205},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.16},
  annote =	{Keywords: Approximation, Weighted Flow Time, Concurrent Open Shop, Precedence Constraints}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.73
Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation

Authors: Gökalp Demirci and Shi Li

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural LP relaxation for the problem, one can only hope to get the violation factor down to 2. Li [SODA'16] introduced a novel LP to go beyond the limit of 2 and gave a constant-factor approximation algorithm that opens (1 + epsilon)*k facilities. We use the configuration LP of Li [SODA'16] to give a constant-factor approximation for the Capacitated k-Median problem in a seemingly harder configuration: we violate only the capacities by 1 + epsilon. This result settles the problem as far as pseudo-approximation algorithms are concerned.
Cite as

Gökalp Demirci and Shi Li. Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{demirci_et_al:LIPIcs.ICALP.2016.73,
  author =	{Demirci, G\"{o}kalp and Li, Shi},
  title =	{{Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{73:1--73:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.73},
  URN =		{urn:nbn:de:0030-drops-62112},
  doi =		{10.4230/LIPIcs.ICALP.2016.73},
  annote =	{Keywords: Approximation Algorithms, Capacitated k-Median, Pseudo Approximation, Capacity Violation}
}
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