Tradeoffs between cost and information for rendezvous and treasure hunt

Rendezvous and treasure hunt are two basic tasks performed by mobile agents in networks. In rendezvous, two agents, initially located at distinct nodes of the network, traverse edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target (treasure) situated at an unknown node. The network is modeled as an undirected connected graph whose nodes have distinct identities. The cost of a rendezvous algorithm is the worst-case total number of edge traversals performed by both agents until meeting. The cost of a treasure hunt algorithm is the worst-case number of edge traversals performed by the agent until the treasure is found. If the agents have no information about the network, the cost of both rendezvous and treasure hunt can be as large as Θ(e) for networks with e edges.

[1]  Andrzej Pelc,et al.  Exploring unknown undirected graphs , 1999, SODA '98.

[2]  Andrzej Pelc,et al.  Tree exploration with advice , 2008, Inf. Comput..

[3]  Andrzej Pelc,et al.  Asynchronous Deterministic Rendezvous in Graphs , 2005, MFCS.

[4]  Pat Morin,et al.  Randomized Rendez-Vous with Limited Memory , 2008, LATIN.

[5]  David Peleg,et al.  Labeling schemes for flow and connectivity , 2002, SODA '02.

[6]  Andrzej Pelc,et al.  Deterministic Rendezvous in Graphs , 2003 .

[7]  Xiaotie Deng,et al.  Exploring an unknown graph , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[8]  Andrzej Pelc,et al.  Fast radio broadcasting with advice , 2008, Theor. Comput. Sci..

[9]  Prosenjit Bose,et al.  Revisiting the Problem of Searching on a Line , 2013, ESA.

[10]  Shmuel Gal,et al.  The theory of search games and rendezvous , 2002, International series in operations research and management science.

[11]  Andrzej Pelc,et al.  Trade-offs Between the Size of Advice and Broadcasting Time in Trees , 2008, SPAA '08.

[12]  Andrzej Pelc,et al.  Time versus cost tradeoffs for deterministic rendezvous in networks , 2014, Distributed Computing.

[13]  Haim Kaplan,et al.  Compact labeling schemes for ancestor queries , 2001, SODA '01.

[14]  Andrzej Pelc,et al.  Drawing maps with advice , 2010, J. Parallel Distributed Comput..

[15]  Jurek Czyzowicz,et al.  Almost Optimal Asynchronous Rendezvous in Infinite Multidimensional Grids , 2010, DISC.

[16]  Ricardo A. Baeza-Yates,et al.  Searching in the Plane , 1993, Inf. Comput..

[17]  S. Gal,et al.  Rendezvous on the Line when the Players' Initial Distance is Given by an Unknown Probability Distribution , 1998 .

[18]  Pierre Fraigniaud,et al.  Local MST computation with short advice , 2007, SPAA.

[19]  S. Alpern.  The Rendezvous Search Problem , 1995 .

[20]  Nicola Santoro,et al.  Gathering of asynchronous robots with limited visibility , 2005, Theor. Comput. Sci..

[21]  Andrzej Pelc,et al.  Deterministic rendezvous in networks: A comprehensive survey , 2012, Networks.

[22]  Reuven Cohen,et al.  Label-guided graph exploration by a finite automaton , 2005, TALG.

[23]  Andrzej Pelc,et al.  How to meet asynchronously at polynomial cost , 2013, PODC '13.

[24]  Mikkel Thorup,et al.  Approximate distance oracles , 2001, JACM.

[25]  Rolf Klein,et al.  How to Find a Point on a Line Within a Fixed Distance , 1999, Discret. Appl. Math..

[26]  S. Gal,et al.  Rendezvous search when marks are left at the starting points , 2001 .

[27]  Andrzej Pelc,et al.  Fast rendezvous with advice , 2015, Theor. Comput. Sci..

[28]  Richard Weber,et al.  The rendezvous problem on discrete locations , 1990, Journal of Applied Probability.

[29]  Qin Xin,et al.  Faster Treasure Hunt and Better Strongly Universal Exploration Sequences , 2007, ISAAC.

[30]  Uri Zwick,et al.  Deterministic rendezvous, treasure hunts and strongly universal exploration sequences , 2007, SODA '07.

[31]  Andrzej Pelc,et al.  How to meet when you forget: log-space rendezvous in arbitrary graphs , 2010, Distributed Computing.

[32]  Sándor P. Fekete,et al.  Two Dimensional Rendezvous Search , 2001, Oper. Res..

[33]  Susanne Albers,et al.  Exploring unknown environments , 1997, STOC '97.

[34]  Pierre Fraigniaud,et al.  Online computation with advice , 2009, Theor. Comput. Sci..

[35]  Dariusz R. Kowalski,et al.  How to meet in anonymous network , 2006, Theor. Comput. Sci..

[36]  Ran Raz,et al.  Distance labeling in graphs , 2001, SODA '01.

[37]  Saverio Caminiti,et al.  Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors , 2008, ESA.

[38]  Steve Alpern.  Rendezvous search on labeled networks , 2002 .

[39]  Omer Reingold,et al.  Undirected connectivity in log-space , 2008, JACM.

[40]  Nicola Santoro,et al.  Distributed Computing by Mobile Robots: Gathering , 2012, SIAM J. Comput..

[41]  Andrzej Pelc,et al.  How to Meet Asynchronously (Almost) Everywhere , 2010, SODA.

[42]  Andrzej Pelc,et al.  Communication algorithms with advice , 2010, J. Comput. Syst. Sci..

[43]  Andrzej Pelc,et al.  Distributed computing with advice: information sensitivity of graph coloring , 2007, Distributed Computing.

[44]  Sándor P. Fekete,et al.  Asymmetric rendezvous on the plane , 1998, SCG '98.

[45]  Nicolas Nisse,et al.  Graph searching with advice , 2007, Theor. Comput. Sci..

[46]  Steve Alpern.  Rendezvous Search on Labelled Networks , 2000 .

[47]  V. S. Anil Kumar,et al.  Optimal constrained graph exploration , 2001, SODA '01.

[48]  Alejandro López-Ortiz,et al.  The ultimate strategy to search on m rays? , 2001, Theor. Comput. Sci..

[49]  Richard S. Ellis.  Volume of an N-Simplex by multiple Integration. , 1976 .

[50]  Andrzej Pelc,et al.  Use Knowledge to Learn Faster: Topology Recognition with Advice , 2013, DISC.

[51]  Shay Kutten,et al.  Proof labeling schemes , 2005, PODC '05.