Skip to main content

2013 | OriginalPaper | Buchkapitel

14. Ten Open Problems in Rendezvous Search

verfasst von : Steve Alpern

Erschienen in: Search Theory

Verlag: Springer New York

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The rendezvous search problem asks how two (or more) agents who are lost in a common region can optimize the process by which they meet. Usually they have restricted speed (unit speed in the continuous time context; moves allowed to adjacent nodes in discrete time). In all cases the agents are not aware of each other’s location. This chapter is concerned with the ‘operations research’ version of the problem – where optimization of the search process is interpreted as minimizing the expected time to meet, or possibly maximizing the probability of meeting within a given time. The deterministic approaches taken by the theoretical computer science community will not be considered here.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Alpern, S. Hide an seek games. Seminar, Institut fur Hohere Studien, Vienna, 26 July 1976. Alpern, S. Hide an seek games. Seminar, Institut fur Hohere Studien, Vienna, 26 July 1976.
2.
Zurück zum Zitat Alpern, S. The rendezvous search problem. LSE CDAM Research Report 1993 53, London School of Economics. Alpern, S. The rendezvous search problem. LSE CDAM Research Report 1993 53, London School of Economics.
7.
Zurück zum Zitat Alpern, S. Rendezvous search with revealed information: applications to the line. Journal of Applied Probability 2007; 44 (1):1–15.MathSciNetMATHCrossRef Alpern, S. Rendezvous search with revealed information: applications to the line. Journal of Applied Probability 2007; 44 (1):1–15.MathSciNetMATHCrossRef
9.
Zurück zum Zitat Alpern, S. Rendezvous Search Games, Wiley Encyclopedia of Operations Research and Management Science 2012, John Wiley & Sons, Inc. Alpern, S. Rendezvous Search Games, Wiley Encyclopedia of Operations Research and Management Science 2012, John Wiley & Sons, Inc.
10.
Zurück zum Zitat Alpern, S, and Beck, A. Asymmetric rendezvous on the line is a double linear search problem. Mathematics of Operations Research 1999; 24 (3): 604–618.MathSciNetMATHCrossRef Alpern, S, and Beck, A. Asymmetric rendezvous on the line is a double linear search problem. Mathematics of Operations Research 1999; 24 (3): 604–618.MathSciNetMATHCrossRef
11.
Zurück zum Zitat Alpern, S and Gal, S. Rendezvous search on the line with distinguishable players. SIAM J. Control & Optimization 1995; 33:1270–1276.MathSciNetMATHCrossRef Alpern, S and Gal, S. Rendezvous search on the line with distinguishable players. SIAM J. Control & Optimization 1995; 33:1270–1276.MathSciNetMATHCrossRef
12.
Zurück zum Zitat Alpern, S and Gal, S. Search Games and Rendezvous Theory, Springer, 2003. Alpern, S and Gal, S. Search Games and Rendezvous Theory, Springer, 2003.
14.
Zurück zum Zitat Alpern, S and Lim, WS. Rendezvous of three agents on the line. Naval Research Logistics 2002; 49:244–255. (6):2233–2252. Alpern, S and Lim, WS. Rendezvous of three agents on the line. Naval Research Logistics 2002; 49:244–255. (6):2233–2252.
15.
Zurück zum Zitat Anderson, EJ and Essegaier, S. Rendezvous search on the line with indistinguishable players, SIAM Journal of Control and Optimization 1995; 33:1637–1642.MathSciNetMATHCrossRef Anderson, EJ and Essegaier, S. Rendezvous search on the line with indistinguishable players, SIAM Journal of Control and Optimization 1995; 33:1637–1642.MathSciNetMATHCrossRef
16.
18.
Zurück zum Zitat Benkoski, S, Monticino, M and Weisinger, J. . A survey of the search theory literature. Naval Research Logistics 1991; 38:469–494.MATHCrossRef Benkoski, S, Monticino, M and Weisinger, J. . A survey of the search theory literature. Naval Research Logistics 1991; 38:469–494.MATHCrossRef
19.
Zurück zum Zitat Chester, EJ and Tutuncu, RH. Rendezvous search on the labelled line Operations Research 2004; 52(2):330–334. Operations Research 1999; 47 (6):849–861.CrossRef Chester, EJ and Tutuncu, RH. Rendezvous search on the labelled line Operations Research 2004; 52(2):330–334. Operations Research 1999; 47 (6):849–861.CrossRef
20.
21.
Zurück zum Zitat Dobrev,S, Flocchini,P, Prencipe,G and Santoro, N. Multiple agents rendezvous in a ring in spite of a black hole. Lecture Notes in Computer Science 2004: Volume 3144/2004, 34–46 Dobrev,S, Flocchini,P, Prencipe,G and Santoro, N. Multiple agents rendezvous in a ring in spite of a black hole. Lecture Notes in Computer Science 2004: Volume 3144/2004, 34–46
23.
Zurück zum Zitat Kikuta, K and Ruckle, W. Rendezvous search on a star graph with examination costs. European Journal of Operational Research 2007; 181 (1):298–304.MathSciNetMATHCrossRef Kikuta, K and Ruckle, W. Rendezvous search on a star graph with examination costs. European Journal of Operational Research 2007; 181 (1):298–304.MathSciNetMATHCrossRef
24.
25.
Zurück zum Zitat Kranakis, E, Krizanc, D and Rajsbaum, S. Mobile agent rendezvous: a survey. Lecture Notes in Computer Science 2006, Volume 4056/2006, Springer Berlin / Heidelberg. Kranakis, E, Krizanc, D and Rajsbaum, S. Mobile agent rendezvous: a survey. Lecture Notes in Computer Science 2006, Volume 4056/2006, Springer Berlin / Heidelberg.
27.
Zurück zum Zitat Lim, WS, Alpern, S and Beck, A. Rendezvous search on the line with more than two players. Operations Research 1997; 45 (3):357–364.MathSciNetMATHCrossRef Lim, WS, Alpern, S and Beck, A. Rendezvous search on the line with more than two players. Operations Research 1997; 45 (3):357–364.MathSciNetMATHCrossRef
28.
Zurück zum Zitat Lin, J Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 1: The synchronous Case. SIAM J. Control Optim 2007; 46(6):2096–2119.MathSciNetCrossRef Lin, J Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 1: The synchronous Case. SIAM J. Control Optim 2007; 46(6):2096–2119.MathSciNetCrossRef
29.
Zurück zum Zitat Lin, J, Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 2: The asynchronous Case. SIAM J. Control Optim 2007; 46(6):2120–2147.MathSciNetMATHCrossRef Lin, J, Morse, AS and Anderson, BDO. The Multi-Agent Rendezvous Problem. Part 2: The asynchronous Case. SIAM J. Control Optim 2007; 46(6):2120–2147.MathSciNetMATHCrossRef
30.
Zurück zum Zitat Marco,G, Gargano, Kranakis,E, Krizanc,D and Pelc, A. Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 2006; 355:315–326.MathSciNetCrossRef Marco,G, Gargano, Kranakis,E, Krizanc,D and Pelc, A. Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 2006; 355:315–326.MathSciNetCrossRef
31.
Zurück zum Zitat Qiaoming H, Du, D, Vera,J and Zuluaga, LF. Improved Bounds for the Symmetric Rendezvous Value on the Line Operations Research 2008; 56 (3):772–782.MATH Qiaoming H, Du, D, Vera,J and Zuluaga, LF. Improved Bounds for the Symmetric Rendezvous Value on the Line Operations Research 2008; 56 (3):772–782.MATH
32.
Zurück zum Zitat Schelling, T. The Strategy of Conflict. Harvard University Press, Cambridge, 1960. Schelling, T. The Strategy of Conflict. Harvard University Press, Cambridge, 1960.
33.
Zurück zum Zitat Stone, LD. Theory of Optimal Search, 2nd edition. Operations Research Society of America, Arlington, VA, 1989. Stone, LD. Theory of Optimal Search, 2nd edition. Operations Research Society of America, Arlington, VA, 1989.
34.
Zurück zum Zitat Uthaisombut, P. Symmetric rendezvous search on the line using moving patterns with different lengths. Department of Computer Science, University of Pittsburgh, 2006. Uthaisombut, P. Symmetric rendezvous search on the line using moving patterns with different lengths. Department of Computer Science, University of Pittsburgh, 2006.
35.
Zurück zum Zitat Weber, R. Optimal Symmetric Rendezvous Search on Three Locations. Mathematics of Operations Research 2012; 37 (1): 111–122.MathSciNetMATHCrossRef Weber, R. Optimal Symmetric Rendezvous Search on Three Locations. Mathematics of Operations Research 2012; 37 (1): 111–122.MathSciNetMATHCrossRef
Metadaten
Titel
Ten Open Problems in Rendezvous Search
verfasst von
Steve Alpern
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-6825-7_14