Universal traversal sequences for paths and cycles
Journal of Algorithms
Universal traversal sequences of length nO(log n) for cliques
Information Processing Letters
Polynomial universal traversing sequences for cycles are constructible
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
SIAM Journal on Computing
The electrical resistance of a graph captures its commute and cover times
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The cover time of a regular expander is O(n log n)
Information Processing Letters
Universal sequences for complete graphs
Discrete Applied Mathematics - Computational combinatiorics
A technique for lower bounding the cover time
SIAM Journal on Discrete Mathematics
Universal traversal sequences for expander graphs
Information Processing Letters
Trading Space for Time in Undirected $s-t$ Connectivity
SIAM Journal on Computing
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Lower bounds on universal traversal sequences based on chains of length five
Information and Computation
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
Random Structures & Algorithms
Navigating in Unfamiliar Geometric Terrain
SIAM Journal on Computing
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
On the impact of sense of direction on message complexity
Information Processing Letters
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
Piecemeal graph exploration by a mobile robot
Information and Computation
Exploring Unknown Environments
SIAM Journal on Computing
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Interval routing schemes allow broadcasting with linear message-complexity
Distributed Computing
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
Log-Space constructible universal traversal sequences for cycles of length O(n4.03)
Theoretical Computer Science - Computing and combinatorics
Tree exploration with little memory
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The Cover Time of Random Regular Graphs
SIAM Journal on Discrete Mathematics
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
Simulating a Random Walk with Constant Error
Combinatorics, Probability and Computing
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic random walks on the integers
European Journal of Combinatorics
Deterministic random walks on regular trees
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Journal of Graph Theory
On the power of the compass (or, why mazes are easier to search than graphs)
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of 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
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Impact of local topological information on random walks on finite graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Setting port numbers for fast graph exploration
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Deterministic random walks on the two-dimensional grid
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Robustness of the Rotor-router Mechanism
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Online graph exploration: new results on old and new algorithms
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Online graph exploration: New results on old and new algorithms
Theoretical Computer Science
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Efficient exploration of unknown or unmapped environments has become one of the fundamental problem domains in algorithm design. Its applications range from robot navigation in hazardous environments to rigorous searching, indexing and analysing digital data available on the Internet. A large number of exploration algorithms has been proposed under various assumptions about the capability of mobile (exploring) entities and various characteristics of the environment which are to be explored. This paper considers the graph model , where the environment is represented by a graph of connections in which discrete moves are permitted only along its edges. Designing efficient exploration algorithms in this model has been extensively studied under a diverse set of assumptions, e.g., directed vs undirected graphs, anonymous nodes vs nodes with distinct identities, deterministic vs probabilistic solutions, single vs multiple agent exploration, as well as in the context of different complexity measures including the time complexity, the memory consumption, and the use of other computational resources such as tokens and messages. In this work the emphasis is on memory efficient exploration of anonymous graphs. We discuss in more detail three approaches: random walk , Propp machine and basic walk , reviewing major relevant results, presenting recent developments, and commenting on directions for further research.