Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
SIAM Journal on Control and Optimization
Asymmetric rendezvous on the plane
Proceedings of the fourteenth annual symposium on Computational geometry
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Agent Rendezvous: A Dynamic Symmetry-Breaking Problem
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Operations Research
Two Dimensional Rendezvous Search
Operations Research
Mobile Agent Rendezvous in a Ring
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Deterministic Rendezvous in Graphs
Algorithmica
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
How to meet in anonymous network
Theoretical Computer Science
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Asynchronous Deterministic Rendezvous on the Line
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring
Theoretical Computer Science
How to meet asynchronously (almost) everywhere
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Two mobile agents (robots) have to meet in an a priori unknown bounded terrain modeled as a polygon, possibly with polygonal obstacles. Robots are modeled as points, and each of them is equipped with a compass. Compasses of robots may be incoherent. Robots construct their routes, but the actual walk of each robot is decided by the adversary that may, e.g., speed up or slow down the robot. We consider several scenarios, depending on three factors: (1) obstacles in the terrain are present, or not, (2) compasses of both robots agree, or not, (3) robots have or do not have a map of the terrain with their positions marked. The cost of a rendezvous algorithm is the worst-case sum of lengths of the robots' trajectories until they meet. For each scenario, we design a deterministic rendezvous algorithm and analyze its cost. We also prove lower bounds on the cost of any deterministic rendezvous algorithm in each case. For all scenarios these bounds are tight.