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
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
Universal sequences for complete graphs
Discrete Applied Mathematics - Computational combinatiorics
Lower bounds on universal traversal sequences for cycles and other low degree graphs
SIAM Journal on Computing
Universal traversal sequences for expander graphs
Information Processing Letters
Lower bounds on the length of universal traversal sequences
Journal of Computer and System Sciences
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
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Derandomizing Random Walks in Undirected Graphs Using Locally Fair Exploration Strategies
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
How to meet when you forget: log-space rendezvous in arbitrary graphs
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
How much memory is needed for leader election
DISC'10 Proceedings of the 24th international conference on Distributed computing
Tree exploration with logarithmic memory
ACM Transactions on Algorithms (TALG)
Constructing a map of an anonymous graph: applications of universal sequences
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Deterministic network exploration by a single agent with Byzantine tokens
Information Processing Letters
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In this paper we introduce a new notion of traversal sequences that we call exploration sequences. Exploration sequences share many properties with the traversal sequences defined in Aleliunas et al. (Proceedings on the 20th Annual Symposium of Foundations of Computer Science, 1979, pp. 218-223), but they also exhibit some new properties. In particular, they have an ability to backtrack, and their random properties are robust under choice of the probability distribution on labels.Further, we present simple constructions of polynomial-length universal exploration sequences for some previously studied classes of graphs (e.g., 2-regular graphs, cliques, expanders), and we also present universal exploration sequences for trees. These constructions do not obey previously known lower bounds on the length of universal traversal sequences; thus, they highlight another difference between exploration and traversal sequences.