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Track A: Algorithms, Complexity and Games

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

Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis - including potential functions and primal-dual techniques - give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [Ibrahimpur et al., 2022] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.

Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Efficient Caching with Reserves via Marking. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 80:1-80:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ibrahimpur_et_al:LIPIcs.ICALP.2023.80, author = {Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.}, title = {{Efficient Caching with Reserves via Marking}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {80:1--80:20}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.80}, URN = {urn:nbn:de:0030-drops-181328}, doi = {10.4230/LIPIcs.ICALP.2023.80}, annote = {Keywords: Approximation Algorithms, Online Algorithms, Caching} }

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APPROX

**Published in:** LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Caching is among the most well-studied topics in algorithm design, in part because it is such a fundamental component of many computer systems. Much of traditional caching research studies cache management for a single-user or single-processor environment. In this paper, we propose two related generalizations of the classical caching problem that capture issues that arise in a multi-user or multi-processor environment. In the caching with reserves problem, a caching algorithm is required to maintain at least k_i pages belonging to user i in the cache at any time, for some given reserve capacities k_i. In the public-private caching problem, the cache of total size k is partitioned into subcaches, a private cache of size k_i for each user i and a shared public cache usable by any user. In both of these models, as in the classical caching framework, the objective of the algorithm is to dynamically maintain the cache so as to minimize the total number of cache misses.
We show that caching with reserves and public-private caching models are equivalent up to constant factors, and thus focus on the former. Unlike classical caching, both of these models turn out to be NP-hard even in the offline setting, where the page sequence is known in advance. For the offline setting, we design a 2-approximation algorithm, whose analysis carefully keeps track of a potential function to bound the cost. In the online setting, we first design an O(ln k)-competitive fractional algorithm using the primal-dual framework, and then show how to convert it online to a randomized integral algorithm with the same guarantee.

Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Caching with Reserves. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 52:1-52:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ibrahimpur_et_al:LIPIcs.APPROX/RANDOM.2022.52, author = {Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.}, title = {{Caching with Reserves}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {52:1--52:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-249-5}, ISSN = {1868-8969}, year = {2022}, volume = {245}, editor = {Chakrabarti, Amit and Swamy, Chaitanya}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.52}, URN = {urn:nbn:de:0030-drops-171741}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.52}, annote = {Keywords: Approximation Algorithms, Online Algorithms, Caching} }

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**Published in:** LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

We consider the problem of efficiently scheduling jobs with precedence constraints on a set of identical machines in the presence of a uniform communication delay. Such precedence-constrained jobs can be modeled as a directed acyclic graph, G = (V, E). In this setting, if two precedence-constrained jobs u and v, with v dependent on u (u ≺ v), are scheduled on different machines, then v must start at least ρ time units after u completes. The scheduling objective is to minimize makespan, i.e. the total time from when the first job starts to when the last job finishes. The focus of this paper is to provide an efficient approximation algorithm with near-linear running time. We build on the algorithm of Lepere and Rapine [STACS 2002] for this problem to give an O((ln ρ)/(ln ln ρ))-approximation algorithm that runs in Õ(|V|+|E|) time.

Quanquan C. Liu, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Scheduling with Communication Delay in Near-Linear Time. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 47:1-47:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.STACS.2022.47, author = {Liu, Quanquan C. and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.}, title = {{Scheduling with Communication Delay in Near-Linear Time}}, booktitle = {39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)}, pages = {47:1--47:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-222-8}, ISSN = {1868-8969}, year = {2022}, volume = {219}, editor = {Berenbrink, Petra and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.47}, URN = {urn:nbn:de:0030-drops-158570}, doi = {10.4230/LIPIcs.STACS.2022.47}, annote = {Keywords: near-linear time scheduling, scheduling with duplication, precedence-constrained jobs, graph algorithms} }

Document

**Published in:** LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

In this paper we introduce the semi-online model that generalizes the classical online computational model. The semi-online model postulates that the unknown future has a predictable part and an adversarial part; these parts can be arbitrarily interleaved. An algorithm in this model operates as in the standard online model, i.e., makes an irrevocable decision at each step.
We consider bipartite matching in the semi-online model. Our main contributions are competitive algorithms for this problem and a near-matching hardness bound. The competitive ratio of the algorithms nicely interpolates between the truly offline setting (i.e., no adversarial part) and the truly online setting (i.e., no predictable part).

Ravi Kumar, Manish Purohit, Aaron Schild, Zoya Svitkina, and Erik Vee. Semi-Online Bipartite Matching. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 50:1-50:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kumar_et_al:LIPIcs.ITCS.2019.50, author = {Kumar, Ravi and Purohit, Manish and Schild, Aaron and Svitkina, Zoya and Vee, Erik}, title = {{Semi-Online Bipartite Matching}}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, pages = {50:1--50:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-095-8}, ISSN = {1868-8969}, year = {2019}, volume = {124}, editor = {Blum, Avrim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.50}, URN = {urn:nbn:de:0030-drops-101436}, doi = {10.4230/LIPIcs.ITCS.2019.50}, annote = {Keywords: Semi-Online Algorithms, Bipartite Matching} }

Document

**Published in:** LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

We introduce and study the {\em donation center location} problem, which
has an additional application in network
testing and may also be of independent interest as a general graph-theoreticproblem.Given a set of agents and a set of centers, where agents have preferences over centers and centers have capacities,
the goal is to open a subset of centers and to assign a maximum-sized subset of agents to their most-preferred
open centers, while respecting the capacity constraints.
We prove that in general, the problem
is hard to approximate within $n^{1/2-\epsilon}$ for any $\epsilon>0$.
In view of this, we investigate two special cases.
In one, every agent has a bounded number of centers on her preference list,
and in the other, all preferences are induced by a line-metric.
We present constant-factor approximation algorithms
for the former and exact polynomial-time algorithms for the latter.
Of particular interest among our techniques are an analysis of the greedy
algorithm for a variant of the maximum coverage problem called\emph{frugal coverage}, the use of maximum matching subroutine with subsequent
modification, analyzed using a counting argument, and a reduction to the independent set problem
on \emph{terminal intersection graphs}, which we show to be
a subclass of trapezoid graphs.

Chien-Chung Huang and Zoya Svitkina. Donation Center Location Problem. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 227-238, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)

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@InProceedings{huang_et_al:LIPIcs.FSTTCS.2009.2321, author = {Huang, Chien-Chung and Svitkina, Zoya}, title = {{Donation Center Location Problem}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {227--238}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-13-2}, ISSN = {1868-8969}, year = {2009}, volume = {4}, editor = {Kannan, Ravi and Narayan Kumar, K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2321}, URN = {urn:nbn:de:0030-drops-23212}, doi = {10.4230/LIPIcs.FSTTCS.2009.2321}, annote = {Keywords: Approximation Algorithms, Facility Location, Matching with Preferences} }

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