10 Search Results for "Xu, Chenyang"

Document
DOI: 10.4230/LIPIcs.ESA.2024.47
Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem

Authors: Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a bicriterial (α,μ)-approximation is possible, i.e., a solution that with budget B+α for all B ∈ ℝ_{≥ 0} is a multiplicative μ-approximation compared to the optimum solution with budget B. For the case that the underlying graph is a tree, we present a polynomial-time density-greedy algorithm that computes a (χ,1)-approximation, where χ denotes the eccentricity of the root vertex in the underlying graph, and show that this is best possible. An adaptation of the density-greedy algorithm for general graphs is (γ,2)-competitive where γ is the maximal length of a vertex-disjoint path starting in the root. While this algorithm does not run in polynomial time, it can be adapted to a (γ,3)-competitive algorithm that runs in polynomial time. We further devise a capacity-scaling algorithm that guarantees a (3χ,8)-approximation and, more generally, a ((4𝓁 - 1)χ, (2^{𝓁 + 2})/(2^𝓁 -1))-approximation for every fixed 𝓁 ∈ ℕ.
Cite as

Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz. Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{disser_et_al:LIPIcs.ESA.2024.47,
  author =	{Disser, Yann and Griesbach, Svenja M. and Klimm, Max and Lutz, Annette},
  title =	{{Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.47},
  URN =		{urn:nbn:de:0030-drops-211188},
  doi =		{10.4230/LIPIcs.ESA.2024.47},
  annote =	{Keywords: incremental optimization, competitive analysis, prize-collecting Steiner-tree}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.2
Online Time-Windows TSP with Predictions

Authors: Shuchi Chawla and Dimitris Christou

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
In the Time-Windows TSP (TW-TSP) we are given requests at different locations on a network; each request is endowed with a reward and an interval of time; the goal is to find a tour that visits as much reward as possible during the corresponding time window. For the online version of this problem, where each request is revealed at the start of its time window, no finite competitive ratio can be obtained. We consider a version of the problem where the algorithm is presented with predictions of where and when the online requests will appear, without any knowledge of the quality of this side information. Vehicle routing problems such as the TW-TSP can be very sensitive to errors or changes in the input due to the hard time-window constraints, and it is unclear whether imperfect predictions can be used to obtain a finite competitive ratio. We show that good performance can be achieved by explicitly building slack into the solution. Our main result is an online algorithm that achieves a competitive ratio logarithmic in the diameter of the underlying network, matching the performance of the best offline algorithm to within factors that depend on the quality of the provided predictions. The competitive ratio degrades smoothly as a function of the quality and we show that this dependence is tight within constant factors.
Cite as

Shuchi Chawla and Dimitris Christou. Online Time-Windows TSP with Predictions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chawla_et_al:LIPIcs.APPROX/RANDOM.2024.2,
  author =	{Chawla, Shuchi and Christou, Dimitris},
  title =	{{Online Time-Windows TSP with Predictions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  URN =		{urn:nbn:de:0030-drops-209954},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  annote =	{Keywords: Travelling Salesman Problem, Predictions, Learning-Augmented Algorithms, Approximation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.3
Degrees and Network Design: New Problems and Approximations

Authors: Michael Dinitz, Guy Kortsarz, and Shi Li

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum Degree Spanning Tree problem), or as constraints that might be violated to give bicriteria approximations (e.g., the Minimum Cost Degree Bounded Spanning Tree problem). We extend the study of degrees in network design in two ways. First, we introduce and study a new variant of the Survivable Network Design Problem where in addition to the traditional objective of minimizing the cost of the chosen edges, we add a constraint that the 𝓁_p-norm of the node degree vector is bounded by an input parameter. This interpolates between the classical settings of maximum degree (the 𝓁_∞-norm) and the number of edges (the 𝓁₁-degree), and has natural applications in distributed systems and VLSI design. We give a constant bicriteria approximation in both measures using convex programming. Second, we provide a polylogarithmic bicriteria approximation for the Degree Bounded Group Steiner problem on bounded treewidth graphs, solving an open problem from [Guy Kortsarz and Zeev Nutov, 2022] and [X. Guo et al., 2022].
Cite as

Michael Dinitz, Guy Kortsarz, and Shi Li. Degrees and Network Design: New Problems and Approximations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dinitz_et_al:LIPIcs.APPROX/RANDOM.2024.3,
  author =	{Dinitz, Michael and Kortsarz, Guy and Li, Shi},
  title =	{{Degrees and Network Design: New Problems and Approximations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.3},
  URN =		{urn:nbn:de:0030-drops-209969},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.3},
  annote =	{Keywords: Network Design, Degrees}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.24
Learning-Augmented Maximum Independent Set

Authors: Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of n^(1-δ) for any δ > 0. We show that we can break this barrier in the presence of an oracle obtained through predictions from a machine learning model that answers vertex membership queries for a fixed MIS with probability 1/2+ε. In the first setting we consider, the oracle can be queried once per vertex to know if a vertex belongs to a fixed MIS, and the oracle returns the correct answer with probability 1/2 + ε. Under this setting, we show an algorithm that obtains an Õ((√Δ)/ε)-approximation in O(m) time where Δ is the maximum degree of the graph. In the second setting, we allow multiple queries to the oracle for a vertex, each of which is correct with probability 1/2 + ε. For this setting, we show an O(1)-approximation algorithm using O(n/ε²) total queries and Õ(m) runtime.
Cite as

Vladimir Braverman, Prathamesh Dharangutte, Vihan Shah, and Chen Wang. Learning-Augmented Maximum Independent Set. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{braverman_et_al:LIPIcs.APPROX/RANDOM.2024.24,
  author =	{Braverman, Vladimir and Dharangutte, Prathamesh and Shah, Vihan and Wang, Chen},
  title =	{{Learning-Augmented Maximum Independent Set}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.24},
  URN =		{urn:nbn:de:0030-drops-210179},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.24},
  annote =	{Keywords: Learning-augmented algorithms, maximum independent set, graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.18
A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction

Authors: Dongjie He, Jingbo Lu, and Jingling Xue

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
In object-oriented languages, the traditional CFL-reachability formulation for k-callsite-sensitive pointer analysis (kCFA) focuses on modeling field accesses and calling contexts, but it relies on a separate algorithm for call graph construction. This division can result in a loss of precision in kCFA, a problem that persists even when using the most precise call graphs, whether pre-constructed or generated on the fly. Moreover, pre-analyses based on this framework aiming to improve the efficiency of kCFA may inadvertently reduce its precision, due to the framework’s lack of native call graph construction, essential for precise analysis. Addressing this gap, this paper introduces a novel CFL-reachability formulation of kCFA for Java, uniquely integrating on-the-fly call graph construction. This advancement not only addresses the precision loss inherent in the traditional CFL-reachability-based approach but also enhances its overall applicability. In a significant secondary contribution, we present the first precision-preserving pre-analysis to accelerate kCFA. This pre-analysis leverages selective context sensitivity to improve the efficiency of kCFA without sacrificing its precision. Collectively, these contributions represent a substantial step forward in pointer analysis, offering both theoretical and practical advancements that could benefit future developments in the field.
Cite as

Dongjie He, Jingbo Lu, and Jingling Xue. A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{he_et_al:LIPIcs.ECOOP.2024.18,
  author =	{He, Dongjie and Lu, Jingbo and Xue, Jingling},
  title =	{{A CFL-Reachability Formulation of Callsite-Sensitive Pointer Analysis with Built-In On-The-Fly Call Graph Construction}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.18},
  URN =		{urn:nbn:de:0030-drops-208674},
  doi =		{10.4230/LIPIcs.ECOOP.2024.18},
  annote =	{Keywords: Pointer Analysis, CFL Reachability, Call Graph Construction}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.2
SlackCheck: A Linux Kernel Module to Verify Temporal Properties of a Task Schedule

Authors: Michele Castrovilli and Enrico Bini

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
The Linux Kernel offers several scheduling classes. From SCHED_DEADLINE down to SCHED_FIFO, SCHED_RR and SCHED_OTHER, the scheduling classes can provide different responsiveness to very diverse user workloads. Still, Linux does not offer any mechanism to take some action upon the violation of temporal constraints at runtime. The lack of such a feature is also due to the difficulty of extending the established notion of deadline to workloads which are not releasing periodic/sporadic jobs. Exploiting the notion of supply functions for any resource schedule, we implemented SlackCheck, a kernel module which is capable to verify at runtime if a given task is assigned a desired amount of resource or not. SlackCheck adds a constant-time check at every scheduling decision and leverages the recent availability of a Runtime Verification engine in the kernel.
Cite as

Michele Castrovilli and Enrico Bini. SlackCheck: A Linux Kernel Module to Verify Temporal Properties of a Task Schedule. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{castrovilli_et_al:LIPIcs.ECRTS.2024.2,
  author =	{Castrovilli, Michele and Bini, Enrico},
  title =	{{SlackCheck: A Linux Kernel Module to Verify Temporal Properties of a Task Schedule}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.2},
  URN =		{urn:nbn:de:0030-drops-203054},
  doi =		{10.4230/LIPIcs.ECRTS.2024.2},
  annote =	{Keywords: Linux scheduler, Runtime verification, bounded-delay resource partition, supply function, service curve, real-time calculus, network calculus}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.106
Polylogarithmic Approximations for Robust s-t Path

Authors: Shi Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
The paper revisits the Robust s-t Path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with n vertices and k distinct cost functions (scenarios) defined over edges, and aim to choose an s-t path such that the total cost of the path is always provable no matter which scenario is realized. Viewing each cost function as an agent, our goal is to find a fair s-t path, which minimizes the maximum cost among all agents. The problem is NP-hard to approximate within a factor of o(log k) unless NP ⊆ DTIME(n^{polylog n}), and the best-known approximation ratio is Õ(√n), which is based on the natural flow linear program. A longstanding open question is whether we can achieve a polylogarithmic approximation for the problem; it remains open even if a quasi-polynomial running time is allowed. Our main result is a O(log n log k) approximation for the Robust s-t Path problem in quasi-polynomial time, solving the open question in the quasi-polynomial time regime. The algorithm is built on a novel linear program formulation for a decision-tree-type structure, which enables us to overcome the Ω(√n) integrality gap for the natural flow LP. Furthermore, we show that for graphs with bounded treewidth, the quasi-polynomial running time can be improved to a polynomial. We hope our techniques can offer new insights into this problem and other related problems in robust optimization.
Cite as

Shi Li, Chenyang Xu, and Ruilong Zhang. Polylogarithmic Approximations for Robust s-t Path. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 106:1-106:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ICALP.2024.106,
  author =	{Li, Shi and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Polylogarithmic Approximations for Robust s-t Path}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{106:1--106:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.106},
  URN =		{urn:nbn:de:0030-drops-202497},
  doi =		{10.4230/LIPIcs.ICALP.2024.106},
  annote =	{Keywords: Approximation Algorithm, Randomized LP Rounding, Robust s-t Path}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.111
Approximation Algorithms for 𝓁_p-Shortest Path and 𝓁_p-Group Steiner Tree

Authors: Yury Makarychev, Max Ovsiankin, and Erasmo Tani

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We present polylogarithmic approximation algorithms for variants of the Shortest Path, Group Steiner Tree, and Group ATSP problems with vector costs. In these problems, each edge e has a vector cost c_e ∈ ℝ_{≥0}^𝓁. For a feasible solution - a path, subtree, or tour (respectively) - we find the total vector cost of all the edges in the solution and then compute the 𝓁_p-norm of the obtained cost vector (we assume that p ≥ 1 is an integer). Our algorithms for series-parallel graphs run in polynomial time and those for arbitrary graphs run in quasi-polynomial time. To obtain our results, we introduce and use new flow-based Sum-of-Squares relaxations. We also obtain a number of hardness results.
Cite as

Yury Makarychev, Max Ovsiankin, and Erasmo Tani. Approximation Algorithms for 𝓁_p-Shortest Path and 𝓁_p-Group Steiner Tree. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 111:1-111:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{makarychev_et_al:LIPIcs.ICALP.2024.111,
  author =	{Makarychev, Yury and Ovsiankin, Max and Tani, Erasmo},
  title =	{{Approximation Algorithms for 𝓁\underlinep-Shortest Path and 𝓁\underlinep-Group Steiner Tree}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{111:1--111:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.111},
  URN =		{urn:nbn:de:0030-drops-202542},
  doi =		{10.4230/LIPIcs.ICALP.2024.111},
  annote =	{Keywords: Shortest Path, Asymmetric Group Steiner Tree, Sum-of-Squares}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.38
Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings

Authors: Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, [Christoph Dürr et al., 2020] has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a (4+ε)-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a (2+ε)-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time 𝒪(poly(n/ε)). Lastly, we show that our results are essentially optimal by providing matching lower bounds.
Cite as

Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang. Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{damerius_et_al:LIPIcs.ESA.2023.38,
  author =	{Damerius, Christoph and Kling, Peter and Li, Minming and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.38},
  URN =		{urn:nbn:de:0030-drops-186915},
  doi =		{10.4230/LIPIcs.ESA.2023.38},
  annote =	{Keywords: scheduling, total completion time, makespan, LP rounding, competitive analysis, approximation algorithm, NP hardness, PTAS}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.59
Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing

Authors: Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data. Instance robustness ensures that the prediction is robust to modest changes in the problem input, where the measure of the change may be problem specific. Instance robustness insists on a smooth degradation in performance as a function of the change. Ideally, the performance is never worse than worst-case bounds. This also allows predictions to be objectively compared. We design online algorithms with predictions for a network flow allocation problem and restricted assignment makespan minimization. For both problems, two key properties are established: high quality predictions can be learned from a small sample of prior instances and these predictions are robust to errors that smoothly degrade as the underlying problem instance changes.
Cite as

Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu. Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{lavastida_et_al:LIPIcs.ESA.2021.59,
  author =	{Lavastida, Thomas and Moseley, Benjamin and Ravi, R. and Xu, Chenyang},
  title =	{{Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{59:1--59:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.59},
  URN =		{urn:nbn:de:0030-drops-146405},
  doi =		{10.4230/LIPIcs.ESA.2021.59},
  annote =	{Keywords: Learning-augmented algorithms, Online algorithms, Flow allocation}
}
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