Abstract
We revisit an old topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and ball-covering (metric entropy) measures. For some familiar models of random graphs, this connection allows the order of magnitude of the cover time to be deduced from first passage percolation estimates. Establishing sharper results seems a challenging problem.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Reference23 articles.
1. Weak Concentration for First Passage Percolation
Times on Graphs and General Increasing Set-valued
Processes
2. The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence
3. Aspects of first passage percolation
4. A replica analysis of the travelling salesman problem
5. 13. Johnson, D.S. & Papadimitriou, C.H. (1985). Performance guarantees for heuristics. In E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, & D. B. Shmoys (eds), The traveling salesman problem. Wiley-Interscience Series in Discrete Mathematics. Chichester: Wiley, pp. 145–180.
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