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Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.98
Scheduling Under Non-Uniform Job and Machine Delays

Authors: Rajmohan Rajaraman, David Stalfa, and Sheng Yang

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

Abstract
We study the problem of scheduling precedence-constrained jobs on heterogenous machines in the presence of non-uniform job and machine communication delays. We are given a set of n unit size precedence-ordered jobs, and a set of m related machines each with size m_i (machine i can execute at most m_i jobs at any time). Each machine i has an associated in-delay ρ^{in}_i and out-delay ρ^{out}_i. Each job v also has an associated in-delay ρ^{in}_v and out-delay ρ^{out}_v. In a schedule, job v may be executed on machine i at time t if each predecessor u of v is completed on i before time t or on any machine j before time t - (ρ^{in}_i + ρ^{out}_j + ρ^{out}_u + ρ^{in}_v). The objective is to construct a schedule that minimizes makespan, which is the maximum completion time over all jobs. We consider schedules which allow duplication of jobs as well as schedules which do not. When duplication is allowed, we provide an asymptotic polylog(n)-approximation algorithm. This approximation is further improved in the setting with uniform machine speeds and sizes. Our best approximation for non-uniform delays is provided for the setting with uniform speeds, uniform sizes, and no job delays. For schedules with no duplication, we obtain an asymptotic polylog(n)-approximation for the above model, and a true polylog(n)-approximation for symmetric machine and job delays. These results represent the first polylogarithmic approximation algorithms for scheduling with non-uniform communication delays. Finally, we consider a more general model, where the delay can be an arbitrary function of the job and the machine executing it: job v can be executed on machine i at time t if all of v’s predecessors are executed on i by time t-1 or on any machine by time t - ρ_{v,i}. We present an approximation-preserving reduction from the Unique Machines Precedence-constrained Scheduling (umps) problem, first defined in [Sami Davies et al., 2022], to this job-machine delay model. The reduction entails logarithmic hardness for this delay setting, as well as polynomial hardness if the conjectured hardness of umps holds. This set of results is among the first steps toward cataloging the rich landscape of problems in non-uniform delay scheduling.
Cite as

Rajmohan Rajaraman, David Stalfa, and Sheng Yang. Scheduling Under Non-Uniform Job and Machine Delays. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 98:1-98:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rajaraman_et_al:LIPIcs.ICALP.2023.98,
  author =	{Rajaraman, Rajmohan and Stalfa, David and Yang, Sheng},
  title =	{{Scheduling Under Non-Uniform Job and Machine Delays}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{98:1--98:20},
  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.2023.98},
  URN =		{urn:nbn:de:0030-drops-181502},
  doi =		{10.4230/LIPIcs.ICALP.2023.98},
  annote =	{Keywords: Scheduling, Approximation Algorithms, Precedence Constraints, Communication Delay, Non-Uniform Delays}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.91
Correlated Stochastic Knapsack with a Submodular Objective

Authors: Sheng Yang, Samir Khuller, Sunav Choudhary, Subrata Mitra, and Kanak Mahadik

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear constraints from Ma [Mathematics of Operations Research, Volume 43(3), 2018] on correlated stochastic knapsack problem. The relaxation is then solved by the stochastic continuous greedy algorithm, and rounded by a novel method to fit the contention resolution scheme (Feldman et al. [FOCS 2011]). We obtain a pseudo-polynomial time (1 - 1/√e)/2 ≃ 0.1967 approximation algorithm with or without those additional constraints, eliminating the need of a key assumption and improving on the (1 - 1/∜e)/2 ≃ 0.1106 approximation by Fukunaga et al. [AAAI 2019].
Cite as

Sheng Yang, Samir Khuller, Sunav Choudhary, Subrata Mitra, and Kanak Mahadik. Correlated Stochastic Knapsack with a Submodular Objective. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 91:1-91:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{yang_et_al:LIPIcs.ESA.2022.91,
  author =	{Yang, Sheng and Khuller, Samir and Choudhary, Sunav and Mitra, Subrata and Mahadik, Kanak},
  title =	{{Correlated Stochastic Knapsack with a Submodular Objective}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{91:1--91:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.91},
  URN =		{urn:nbn:de:0030-drops-170296},
  doi =		{10.4230/LIPIcs.ESA.2022.91},
  annote =	{Keywords: Stochastic Knapsack, Submodular Optimization, Stochastic Optimization}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.11
Revisiting Connected Dominating Sets: An Optimal Local Algorithm?

Authors: Samir Khuller and Sheng Yang

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
In this paper we consider the classical Connected Dominating Set (CDS) problem. Twenty years ago, Guha and Khuller developed two algorithms for this problem - a centralized greedy approach with an approximation guarantee of H(D) +2, and a local greedy approach with an approximation guarantee of 2(H(D)+1) (where H() is the harmonic function, and D is the maximum degree in the graph). A local greedy algorithm uses significantly less information about the graph, and can be useful in a variety of contexts. However, a fundamental question remained - can we get a local greedy algorithm with the same performance guarantee as the global greedy algorithm without the penalty of the multiplicative factor of "2" in the approximation factor? In this paper, we answer that question in the affirmative.
Cite as

Samir Khuller and Sheng Yang. Revisiting Connected Dominating Sets: An Optimal Local Algorithm?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 11:1-11:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{khuller_et_al:LIPIcs.APPROX-RANDOM.2016.11,
  author =	{Khuller, Samir and Yang, Sheng},
  title =	{{Revisiting Connected Dominating Sets: An Optimal Local Algorithm?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{11:1--11:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.11},
  URN =		{urn:nbn:de:0030-drops-66340},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.11},
  annote =	{Keywords: graph algorithms, approximation algorithms, dominating sets, local information algorithms}
}
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