Skip to main content

Advertisement

SpringerLink
Go to cart
  1. Home
  2. Journal of Scheduling
  3. Article
Scheduling search procedures: The wheel of fortune
Download PDF
Your article has downloaded

Similar articles being viewed by others

Slider with three articles shown per slide. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide.

Scheduling in the Random-Order Model

09 June 2021

Susanne Albers & Maximilian Janke

Online machine minimization with lookahead

09 August 2020

Cong Chen, Huili Zhang & Yinfeng Xu

Non-clairvoyantly Scheduling to Minimize Convex Functions

14 June 2019

Kyle Fox, Sungjin Im, … Benjamin Moseley

Progressive stopping heuristics that excel in individual and competitive sequential search

10 March 2022

Amnon Rapoport, Darryl A. Seale & Leonidas Spiliopoulos

Competitive two-agent scheduling with release dates and preemption on a single machine

27 March 2023

Shi-Sheng Li & Ren-Xia Chen

Algorithms for single machine scheduling problem with release dates and submodular penalties

30 April 2023

Xiaofei Liu, Man Xiao, … Lei Ma

Primal–Dual and Dual-Fitting Analysis of Online Scheduling Algorithms for Generalized Flow-Time Problems

11 May 2019

Spyros Angelopoulos, Giorgio Lucarelli & Nguyen Kim Thang

Online Minimization of the Maximum Starting Time: Migration Helps

26 January 2023

Asaf Levin

An optimal online algorithm for scheduling with general machine cost functions

09 December 2019

Islam Akaria & Leah Epstein

Download PDF
  • Papers
  • Open Access
  • Published: December 2006

Scheduling search procedures: The wheel of fortune

  • Peter Damaschke1 

Journal of Scheduling volume 9, pages 545–557 (2006)Cite this article

  • 395 Accesses

  • 1 Citations

  • Metrics details

Abstract

Suppose that a player can make progress on n jobs, and her goal is to complete a target job among them, as soon as possible. Unfortunately she does not know what the target job is, perhaps not even if the target exists. This is a typical situation in searching and testing. Depending on the player’s prior knowledge and optimization goals, this gives rise to various optimization problems in the framework of game theory and, sometimes, competitive analysis. Continuing earlier work on this topic, we study another two versions. In the first game, the player knows only the job lengths and wants to minimize the completion time. A simple strategy that we call wheel-of-fortune (WOF) is optimal for this objective. A slight and natural modification, however makes this game considerably more difficult: If the player can be sure that the target is present, WOF fails. However, we can still construct in polynomial time an optimal strategy based on WOF. We also prove that the tight absolute bounds on the expected search time. In the final part, we study two competitive-ratio minimization problems where either the job lengths or the target probabilities are known. We show their equivalence, describe the structure of optimal strategies, and give a heuristic solution.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  • Baeza-Yates, R. A., J. C. Culberson, and G. J. E. Rawlins, “Searching in the plane,” Information and Computation, 106, 234–252 (1993).

    Article  Google Scholar 

  • Bansal, N., K. Dhamdhere, J. Könemann, and A. Sinha, “Non-clairvoyant scheduling for minimizing mean slowdown,” 20th Symposium on Theoretical Aspects of Computer Science, STACS’2003, LNCS 2607, pp. 260–270.

  • Benkoski, S., M. G. Monticino, and J. R. Weisinger, “A survey of the search theory literature,” Naval Research Logistics, 38, 469–494 (1991).

    Google Scholar 

  • Borodin, A. and R. El-Yaniv, Online Computation and Competitive Analysis. Cambridge University Press (1998).

  • Charnes A. and W.W. Cooper, “The theory of search: Optimal distribution of search effort,” Management Science 5, 44–50 (1958).

    Article  Google Scholar 

  • Chrobak, M., L. Epstein, J. Noga, J. Sgall, R. van Stee, T. Tichy, and N. Vakhania, “Preemptive scheduling in overloaded systems,” 29th Int. Colloquium on Automata, Languages and Programming, ICALP’2002, LNCS 2380, pp. 800–811.

  • Cooper, D.C., J.R. Frost, and R. Quincy Robe, “Compatibility of Land SAR procedures with search theory,” prepared for U.S. Dept. of Homeland Security, 2003, available on http://www.uscg.mil/hq/G-O/G-OPR/nsarc/nsarc.htm

  • Damaschke, P., “Scheduling search procedures,” Journal of Scheduling, 7, 349–364 (2004).

    Article  Google Scholar 

  • Frost. J. R., “Principles of search theory,” part I–IV, in: Response, 17 (1999).

  • Gal, S., “On the optimality of a simple strategy for searching graphs,” Int. Journal of Game Theory, 29, 533–542 (2001).

    Article  Google Scholar 

  • Kao, M. Y. and M. L. Littman, “Algorithms for informed cows,” AAAI-97 Workshop on On-Line Search, 1997.

  • Kao, M. Y., J. H. Reif, and S. R. Tate, “Searching an unknown environment: an optimal randomized algorithm for the cow-path problem,” Information and Computation, 131, 63–79 (1996).

    Article  Google Scholar 

  • Kao, M. Y., Y. Ma, M. Sipser, and Y. Yin, “Optimal constructions of hybrid algorithms,” 5th ACM-SIAM Symposium on Discrete Algorithms, SODA 1994, pp. 372–381.

  • Koopman, B. O., “Search and screening,” OEG Report 56, Columbia Univ. Division of War Research, 1946.

  • Koutsoupias, E. and C. Papadimitriou, “Beyond competitive analysis,” SIAM Journal on Computing, 30, 300–317 2000.

    Article  Google Scholar 

  • Lopez-Ortiz, A. and S. Schuierer, “The ultimate strategy to search on m rays?,” 4th Conf. on Computing and Combinatorics COCOON 1998, LNCS 1449, pp. 75–84.

  • Lopez-Ortiz, A. and S. Schuierer, “Online parallel heuristics and robot searching under the competitive framework,” 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002, LNCS 2368, pp. 260–269.

  • Mastrolilli, M., “Scheduling to minimize max flow time: Offline and online algorithms,” 14th Symposium on Fundamentals of Computation Theory, FCT 2003, LNCS 2751, pp. 49–60.

  • Motwani, R., S. Phillips, and E. Torng, “Nonclairvoyant scheduling,” Theoretical Computer Science, 130, 17–47 1994.

    Article  Google Scholar 

  • Myerson, R. B., Game Theory: Analysis of Conflict. Harvard University Press, 1991.

  • Stengel, B. V. and R. Werchner, “Complexity of searching an immobile hider in a graph,” Discrete Applied Mathematics, 78, 235–249 (1997).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, Chalmers University, 41296, Göteborg, Sweden

    Peter Damaschke

Authors
  1. Peter Damaschke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Damaschke.

Additional information

This work has been supported by a grant from the Swedish Research Council (Vetenskapsrådet), file no. 621-2002-4574.

Rights and permissions

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Cite this article

Damaschke, P. Scheduling search procedures: The wheel of fortune. J Sched 9, 545–557 (2006). https://doi.org/10.1007/s10951-006-8788-y

Download citation

  • Issue Date: December 2006

  • DOI: https://doi.org/10.1007/s10951-006-8788-y

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Searching
  • Game theory
  • Nonclairvoyant scheduling
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • Your US state privacy rights
  • How we use cookies
  • Your privacy choices/Manage cookies
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.