 
Summary: On the complexity of global computation in the
presence of link failures: The general case
Y. Afek D. Hendler
Computer Science Department Computer Science Department
TelAviv University TelAviv University
Israel 69978 Israel 69978
Abstract
This paper
presents\Omega\Gamma m log n)
and\Omega\Gamma mn) messages lower bounds on the problem of
computing a global sensitive function in bidirectional networks with link failures (i.e.,
dynamically changing topology), where n and m are the total number of nodes and
links in the network.
The\Omega\Gamma m log n) lower bound is under the assumption that n
is apriori known to the nodes, while the second bound is for the case in which such
knowledge is not available.
A global sensitive function of n variables is a function that may not be computed
without the knowledge of the values of all the n variables (e.g. maximum, sum, etc).
Thus, computing such a function at one node of a distributed network requires this
node to communicate with every other node in the network.
