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
Multiparty protocols and logspace-hard pseudorandom sequences
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Universal sequences for complete graphs
Discrete Applied Mathematics - Computational combinatiorics
Universal traversal sequences for expander graphs
Information Processing Letters
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Lower bounds on universal traversal sequences based on chains of length five
Information and Computation
Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Better Bounds for Online Scheduling
SIAM Journal on Computing
Exploring unknown undirected graphs
Journal of Algorithms
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
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
Journal of Graph Theory
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Label-guided graph exploration by a finite automaton
ACM Transactions on Algorithms (TALG)
Undirected connectivity in log-space
Journal of the ACM (JACM)
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
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Deterministic network exploration by a single agent with Byzantine tokens
Information Processing Letters
Collaborative search on the plane without communication
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Linear time and space gathering of anonymous mobile agents in asynchronous trees
Theoretical Computer Science
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We consider the task of network exploration by a mobile agent (robot) with small memory. The agent has to traverse all nodes and edges of a network (represented as an undirected connected graph), and return to the starting node. Nodes of the network are unlabeled and edge ports are locally labeled at each node. The agent has no a priori knowledge of the topology of the network or of its size, and cannot mark nodes in any way. Under such weak assumptions, cycles in the network may prevent feasibility of exploration, hence we restrict attention to trees. We present an algorithm to accomplish tree exploration (with return) using O(log n)-bit memory for all n-node trees. This strengthens the result from Diks et al. [2004], where O(log 2 n)-bit memory was used for tree exploration, and matches the lower bound on memory size proved there. We also extend our O(log n)-bit memory traversal mechanism to a weaker model in which ports at each node are ordered in circular manner, however, the explicit values of port numbers are not available.