Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each node of the graph is visited before its deadline by a reliable robot. The edge weight corresponds to the time needed by a robot to traverse the edge. Given the number of robots which may crash, is it possible to design an algorithm, which will always guarantee the exploration, independently of the choice of the subset of unreliable robots by the adversary? We find the optimal time, during which the graph may be explored. Our approach permits to find the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored.

[1]  Konstantinos Georgiou,et al.  Evacuating Robots from a Disk Using Face-to-Face Communication (Extended Abstract) , 2015, CIAC.

[2]  Jurek Czyzowicz,et al.  Linear Search by a Pair of Distinct-Speed Robots , 2016, Algorithmica.

[3]  Nicola Santoro,et al.  Time-varying graphs and dynamic networks , 2010, Int. J. Parallel Emergent Distributed Syst..

[4]  Dimitrios M. Thilikos,et al.  An annotated bibliography on guaranteed graph searching , 2008, Theor. Comput. Sci..

[5]  Gilbert H. Young,et al.  Single-vehicle scheduling with time window constraints , 1999 .

[6]  Michel Gendreau,et al.  Arc Routing Problems, Part II: The Rural Postman Problem , 1995, Oper. Res..

[7]  David S. Johnson,et al.  Two-Processor Scheduling with Start-Times and Deadlines , 1977, SIAM J. Comput..

[8]  John N. Tsitsiklis,et al.  Special cases of traveling salesman and repairman problems with time windows , 1992, Networks.

[9]  Jurek Czyzowicz,et al.  Search on a Line with Faulty Robots , 2016, PODC.

[10]  Erik D. Demaine,et al.  Online searching with turn cost , 2004, Theor. Comput. Sci..

[11]  Ángel Corberán,et al.  An algorithm for the Rural Postman problem on a directed graph , 1986 .

[12]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

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

[14]  Marek Chrobak,et al.  Group Search on the Line , 2015, SOFSEM.

[15]  Nancy A. Lynch,et al.  Distributed computation in dynamic networks , 2010, STOC '10.

[16]  Ramesh Krishnamurti,et al.  The Multiple Traveling Salesman Problem with Time Windows: Bounds for the Minimum Number of Vehicles , 2002 .

[17]  Á. Corberán,et al.  A polyhedral approach to the rural postman problem , 1994 .

[18]  Louis E. Rosier,et al.  The pinwheel: a real-time scheduling problem , 1989, [1989] Proceedings of the Twenty-Second Annual Hawaii International Conference on System Sciences. Volume II: Software Track.

[19]  David S. Johnson,et al.  The NP-Completeness Column: An Ongoing Guide , 1982, J. Algorithms.

[20]  Konstantinos Georgiou,et al.  Search on a Line by Byzantine Robots , 2016, ISAAC.

[21]  Stefan Bock,et al.  Solving the traveling repairman problem on a line with general processing times and deadlines , 2015, Eur. J. Oper. Res..