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DOI: 10.4230/LIPIcs.ITCS.2022.114

Uniform Bounds for Scheduling with Job Size Estimates

Authors: Ziv Scully, Isaac Grosof, and Michael Mitzenmacher

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

We consider the problem of scheduling to minimize mean response time in M/G/1 queues where only estimated job sizes (processing times) are known to the scheduler, where a job of true size s has estimated size in the interval [β s, α s] for some α ≥ β > 0. We evaluate each scheduling policy by its approximation ratio, which we define to be the ratio between its mean response time and that of Shortest Remaining Processing Time (SRPT), the optimal policy when true sizes are known. Our question: is there a scheduling policy that (a) has approximation ratio near 1 when α and β are near 1, (b) has approximation ratio bounded by some function of α and β even when they are far from 1, and (c) can be implemented without knowledge of α and β? We first show that naively running SRPT using estimated sizes in place of true sizes is not such a policy: its approximation ratio can be arbitrarily large for any fixed β < 1. We then provide a simple variant of SRPT for estimated sizes that satisfies criteria (a), (b), and (c). In particular, we prove its approximation ratio approaches 1 uniformly as α and β approach 1. This is the first result showing this type of convergence for M/G/1 scheduling. We also study the Preemptive Shortest Job First (PSJF) policy, a cousin of SRPT. We show that, unlike SRPT, naively running PSJF using estimated sizes in place of true sizes satisfies criteria (b) and (c), as well as a weaker version of (a).

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Ziv Scully, Isaac Grosof, and Michael Mitzenmacher. Uniform Bounds for Scheduling with Job Size Estimates. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 114:1-114:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{scully_et_al:LIPIcs.ITCS.2022.114,
  author =	{Scully, Ziv and Grosof, Isaac and Mitzenmacher, Michael},
  title =	{{Uniform Bounds for Scheduling with Job Size Estimates}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{114:1--114:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.114},
  URN =		{urn:nbn:de:0030-drops-157108},
  doi =		{10.4230/LIPIcs.ITCS.2022.114},
  annote =	{Keywords: Scheduling, queueing systems, algorithms with predictions, shortest remaining processing time (SRPT), preemptive shortest job first (PSJF), M/G/1 queue}
}

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DOI: 10.4230/LIPIcs.FUN.2018.18

Computational Complexity of Motion Planning of a Robot through Simple Gadgets

Authors: Erik D. Demaine, Isaac Grosof, Jayson Lynch, and Mikhail Rudoy

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract

We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change the state. This type of setup is common to many robot motion planning hardness proofs. We characterize the complexity for a natural simple case: each gadget connects up to four locations in a perfect matching (but each direction can be traversable or not in the current state), has one or two states, every gadget traversal is immediately undoable, and that gadget locations are connected by an always-traversable forest, possibly restricted to avoid crossings in the plane. Specifically, we show that any single nontrivial four-location two-state gadget type is enough for motion planning to become PSPACE-complete, while any set of simpler gadgets (effectively two-location or one-state) has a polynomial-time motion planning algorithm. As a sample application, our results show that motion planning games with "spinners" are PSPACE-complete, establishing a new hard aspect of Zelda: Oracle of Seasons.

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Erik D. Demaine, Isaac Grosof, Jayson Lynch, and Mikhail Rudoy. Computational Complexity of Motion Planning of a Robot through Simple Gadgets. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demaine_et_al:LIPIcs.FUN.2018.18,
  author =	{Demaine, Erik D. and Grosof, Isaac and Lynch, Jayson and Rudoy, Mikhail},
  title =	{{Computational Complexity of Motion Planning of a Robot through Simple Gadgets}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.18},
  URN =		{urn:nbn:de:0030-drops-88098},
  doi =		{10.4230/LIPIcs.FUN.2018.18},
  annote =	{Keywords: PSPACE, hardness, motion planning, puzzles}
}

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Documents authored by Grosof, Isaac

Uniform Bounds for Scheduling with Job Size Estimates

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Computational Complexity of Motion Planning of a Robot through Simple Gadgets

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