SIAM Journal on Computing
Lower bounds on the length of universal traversal 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
Lower bounds on universal traversal sequences for cycles and other low degree graphs
SIAM Journal on Computing
Lower bounds on universal traversal sequences based on chains of length five
Information and Computation
Improved Length Lower Bounds for Reflecting Sequences
COCOON '96 Proceedings of the Second Annual International Conference on Computing and Combinatorics
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Time-space tradeoffs for undirected graph traversal
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
| Hi-index | 0.00 |
We refine and optimize a computationally intensive enumeration method, based on the traversal of a quadtree, for finding lower bounds on the lengths of reflecting sequences for labeled chains. The improvement results from the introduction of a redundancy relation defined on vertex-pairs of the underlying quadtree, which enables the pruning of redundant branches near the root of the quadtree, as well as locally at deeper depths. The test run of the implementation showed a length lower bound of 19t-214 for t-reflecting sequences for labeled 7-chains with significant speedup, which yields the current length lower bound Ω(n1.51) for universal traversal sequences for 2-regular graphs of n vertices, and Ω(d2-1.51n2.51) for universal traversal sequences for d-regular graphs of n vertices, where 3 ≤ d ≤ n/17+1.