Theoretical Computer Science
The complexity of searching a graph
Journal of the ACM (JACM)
The vertex separation number of a graph equals its path-width
Information Processing Letters
The vertex separation and search number of a graph
Information and Computation
A survey of graph layout problems
ACM Computing Surveys (CSUR)
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Hi-index | 0.00 |
The process number is the minimum number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the node search number, and thus to the pathwidth, however they are not always equal. In general determining these parameters is NP-complete. We present a distributed algorithm to compute these parameters and the edge search number, in trees. It can be executed in an asynchronous environment, requires n steps, an overall computation time of O (n logn ), and n messages of size log3 n + 2. Then, we propose a distributed algorithm to update these parameters on each component of a forest after addition or deletion of any tree edge. This second algorithm requires O (D ) steps, an overall computation time of O (D logn ), and O (D ) messages of size log3 n + 3, where D is the diameter of the new connected component.