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
HARMONIC is a 3–competitive for two servers
Theoretical Computer Science
Random walks on weighted graphs and applications to on-line algorithms
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
The harmonic k-server algorithm is competitive
Journal of the ACM (JACM)
A simple analysis of the harmonic algorithm for two servers
Information Processing Letters
Memory Versus Randomization in On-line Algorithms (Extended Abstract)
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Analysis of the Harmonic Algorithm for Three Servers
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Computer Science Review
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Techniques from electrical network theory have been used to establish various properties of random walks. We explore this connection further, by showing how the classical formulas for the determinant and cofactors of the admittance matrix, due to Maxwell and Kirchoff, yield upper bounds on the edge stretch factor of the harmonic random walk. For any complete, n-vertex graph with distances assigned to its edges, we show the upper bound of (n - 1)2. If the distance function satisfies the triangle inequality, we give the upper bound of ½n(n - 1). Both bounds are tight. As a consequence, we obtain that the harmonic algorithm for the k server problem is ½k(k + 1)-competitive against the lazy adversary.