, Volume 63, Issue 1, pp 158-190

First online:

A Distributed Algorithm for Computing the Node Search Number in Trees

  • David CoudertAffiliated withMASCOTTE, INRIA, I3S, CNRS, Univ. Nice Sophia
  • , Florian HucAffiliated withEPFL, Laboratory of Distributed Programming
  • , Dorian MazauricAffiliated withMASCOTTE, INRIA, I3S, CNRS, Univ. Nice Sophia Email author 

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We present a distributed algorithm to compute the node search number in trees. This algorithm extends the centralized algorithm proposed by Ellis et al. (Inf. Comput. 113(1):50–79, 1994). It can be executed in an asynchronous environment, requires an overall computation time of O(nlog n), and n messages of log 3 n+4 bits each.

The main contribution of this work lies in the data structure proposed to design our algorithm, called hierarchical decomposition. This simple and flexible data structure is used for four operations: updating the node search number after addition or deletion of any tree-edges in a distributed fashion; computing it in a tree whose edges are added sequentially and in any order; computing other graph invariants such as the process number and the edge search number, by changing only initialization rules; extending our algorithms for trees and forests of unknown size (using messages of up to 2log 3 n+5 bits).


Distributed algorithm Edge search number Graph searching Node search number Pathwidth Process number