Horn clauses and the fixpoint query hierarchy
Ashok K. Chandra, David Harel
SIGMOD/PODS 1982
View an n-vertex, m-edge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the effective resistance Rst between s and t: commute time = 2mRst. As a corollary, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR ≤ cover time ≤ O(mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, we improve known bounds on cover times for high-degree graphs and expanders, and give new proofs of known results for multidimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.
Ashok K. Chandra, David Harel
SIGMOD/PODS 1982
Paul Beame, Allan Borodin, et al.
Information and Computation
Ashok K. Chandra, David Harel
STOC 1979
Paul Beame, Allan Borodin, et al.
SIAM Journal on Computing