ISSN 0032-9460, Problems of Information Transmission, 2017, Vol. 53, No. 2, pp. 183–201.
Pleiades Publishing, Inc., 2017.
Original Russian Text
M.N. Vyalyi, I.M. Khuziev, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 2, pp. 91–111.
COMMUNICATION NETWORK THEORY
Fast Protocols for Leader Election and Spanning Tree
Construction in a Distributed Network
M. N. Vyalyi
a, b, c,1,∗
and I. M. Khuziev
Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, Russia
National Research University—Higher School of Economics, Moscow, Russia
Moscow Institute of Physics and Technology (State University), Moscow, Russia
Received May 3, 2016; in ﬁnal form, January 27, 2017
Abstract—We consider leader election and spanning tree construction problems in a syn-
chronous network. Protocols are designed under the assumption that nodes in the network
have identiﬁers but the size of an identiﬁer is unlimited. We present fast protocols with run-
time O(D log L+L), where L is the size of the minimal identiﬁer and D is the network diameter.
We study deterministic distributed protocols for leader election and spanning tree construction
in a synchronous network. These problems play an important role in distributed computation
theory (see, e.g., the books [1,2]).
It is well known that for anonymous networks (processors are indistinguishable) there are no
deterministic protocols solving these problems. Thus, we assume that processors (nodes)ina
network have unique names (identiﬁers). Under this assumption, a natural way for leader election
is to solve the minimal identiﬁer broadcast problem: if all nodes in the network know the value of
the minimal identiﬁer, then the node having this identiﬁer is elected.
Most papers on these problems were based on the assumptions that identiﬁers are rather short
(say nodes are numbered in the range from 1 to V ,whereV is the network size) and messages are
rather long (the message size is O(log V )). In these settings, near-optimal protocols are known for
these problems and for the more general problem of minimum spanning tree construction [2,3].
We use another network model, the unbounded identiﬁer model. It sits in between the anonymous
case and the well-numbered case. In this model we assume that nodes have identiﬁers, but there is
no a priori upper bound on the size of the identiﬁers. Also, we restrict the communication speed
by O(1) bit per message. Here we consider deterministic protocols only and do not analyze possible
errors in the process of information transmission.
In this model, bounds for the bit complexity (the total number of transmitted bits) of protocols
are known. For asynchronous ring and chain networks, rather close upper and lower bounds on the
bit complexity were obtained in . In , for the spanning tree construction problem in general
synchronous networks, protocols with near-optimal bit complexity bounds were presented. More
precisely, for each monotone unbounded function g(·) there is a protocol that constructs a spanning
tree and sends O(Eg(V )) bits, where E is the number of links in the network and V is the number
The research was made under the 5-100 Russian Academic Excellence Project.
Supported in part by the Russian Foundation for Basic Research, project no. 14-01-00641.